APPARATUS AND METHOD FOR NON-LINEAR OVERFITTING OF NEURAL NETWORK FILTERS AND OVERFITTING DECOMPOSED WEIGHT TENSORS

SUPPORT STATEMENT

[0001] The project leading to this application has received funding from the ECSEL Joint Undertaking (JU) under grant agreement No 876019. The JU receives support from the European Union’s Horizon 2020 research and innovation programme and Germany, Netherlands, Austria, Romania, France, Sweden, Cyprus, Greece, Lithuania, Portugal, Italy, Finland, Turkey.

TECHNICAL FIELD

[0002] The examples and non-limiting embodiments relate generally to multimedia transport and neural networks, and more particularly, to method, apparatus, and computer program product for nonlinear overfitting of neural network filters and/or overfitting decomposed weight tensors.

BACKGROUND

[0003] It is known to provide standardized formats for exchange of neural networks.

SUMMARY

[0004] An example apparatus includes: at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the apparatus at least to: receive an input at the apparatus; and overfit one or more features related to one or more non-linear activation (NLA) functions comprised in one or more neural networks based at least on the input to the apparatus.

[0005] The example apparatus may further include, wherein the one or more features comprise one or more parameters of the one or more NLA functions.

[0006] The example apparatus may further include, wherein the apparatus is further caused to: determine whether the one or more NLA functions comprised in the one or more neural networks are to be used or not; and signal, in or along a bitstream, information based on the determination to a decoder, wherein the information comprises one or more of the following: one or more binary flags for the respective one or more NLA functions; an indication of which subset of NLA functions is to be used out of several subsets of NLA functions; or a list of identifier values, wherein each identifier value identifies an NLA function of the one or more NLA functions.

[0007] The example apparatus may further include, wherein the apparatus is further caused to determine one or more weights that are used for weighting an output of each of the one or more NLA functions.

[0008] The example apparatus may further include, wherein the one or more neural networks are comprised in at least one of a codec or one or more post-processing operations.

[0009] The example apparatus may further include, wherein the one or more NLA functions comprise one or more parametric rectified linear unit (PReLU) functions, and wherein the one or more parameters comprise one or more slopes, and wherein each slope of the one more slopes is associated with a negative side of a PReLU function of the one or more PReLU functions.

[0010] The example apparatus may further include, wherein to overfit the apparatus is further caused to: select at least one PReLU function of the one or more PReLU functions that are comprised within the one or more neural networks; and for each of the selected at least one PReLU function repeat following to obtain one or more updated slopes until a criterion is met: provide an input to a selected PReLU function, wherein the input comprises features extracted by one or more of the neural network layers that precede the selected PReLU function, based at least on an input to the neural network that comprises the selected PReLU function; obtain an output based at least on the provided input; compute a gradient of the output of the selected PReLU function with respect to a slope of the selected PReLU funtion; compute an update to the slope of the selected PReLU function based at least on the computed gradient; and compute an updated slope for the selected PReLU based at least on the computed update.

[0011] The example apparatus may further include, wherein the apparatus is further caused to: update the one or more neural networks based at least on the one or more updated slopes or one or more slopes that are derived from the one or more updated slopes, to obtain one or more overfitted neural networks; and use the one or more overfitted neural networks in an inference.

[0012] The example apparatus may further include, wherein the apparatus is further caused to signal one or more of the following: the overfitted one or more parameters; an indication of the overfitted one or more parameters; or a signal derived from the overfitted one or more parameters to a decoder in or along the bitstream. [0013] The example apparatus may further include, wherein the apparatus is further caused to: compress the one or more overfitted parameters based at least on a lossy and/or a lossless codec; and signal the compressed overfitted one or more parameters to a decoder in or along the bitstream.

[0014] The example apparatus may further include, wherein the apparatus is further caused to: compute an update to the one or more parameters based on the overfitted one or more parameters; compress the update to the one or more parameters based at least on a lossy and/or on a lossless codec; signal the compressed update to the one or more parameters to the decoder, within or along the bitstream.

[0015] The example apparatus may further include, wherein the apparatus is further caused to: determine whether the one or more NLA functions are to be used on an input tensor of one or more input tensors; and apply at least one NLA function of the one or more NLA functions to all elements of the input tensor based on the determination.

[0016] The example apparatus may further include, wherein the apparatus is further caused to: determine whether the one or more NLA functions are to be used on one or more channels of the input tensor; and apply at least one NLA function of the one or more NLA functions to all elements of the one or more channels of the input tensor based on the determination.

[0017] The example apparatus may further include, wherein the apparatus is further caused to: determine whether one or more NLA functions are be used on one or more spatial positions of the input tensor; and apply at least one NLA function of the one or more NLA functions to all elements of the one or more spatial positions of the input tensor based on the determination.

[0018] The example apparatus may further include, wherein the apparatus is further caused to: determine whether one or more NLA functions are to be used on one or more elements of the input tensor; and apply at least one NLA function of the one or more NLA functions to each element of an input tensor.

[0019] The example apparatus may further include, wherein the apparatus is further caused to determine one or more weights associated with the at least one NLA function.

[0020] The example apparatus may further include, wherein: the one or more neural networks comprise one or more portions; at least one portion comprise two or more parallel branches; one or more of the two or more parallel branches comprise one or more NLA functions; an input to one or more parallel branches is same or substantially same or derived from another signal; and outputs from the one or more parallel branches are combined.

[0021] Another example apparatus includes: at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the apparatus at least to: receive or parse, from or along a bitstream, overfitted one or more features related to one or more nonlinear activation (NLA) functions comprised in one or more neural networks, wherein the one or more features are overfitted based at least on the input to an encoder; update one or more parameters of the one or more neural networks based at least on the overfitted one more features; and perform an inference of the one or more neural networks comprising the updated one or more parameters.

[0022] The example apparatus may further include, wherein the overfitted one or more features are compressed, and wherein the apparatus is further caused to decompress the overfitted one or more features.

[0023] The example apparatus may further include, wherein the one or more features comprise one or more parameters of the one or more NLA functions.

[0024] The example apparatus may further include, wherein the apparatus is further caused to: receive information whether the one or more NLA functions comprised in the one or more neural networks are to be used or not; wherein the information further comprises one or more of the following: one or more binary flags for the respective one or more NLA functions; an indication of which subset of NLA functions is to be used out of several subsets of NLA functions from; or a list of identifier values, wherein each identifier value identifies an NLA function of the one or more NLA functions.

[0025] Yet another example apparatus includes: at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the apparatus at least to: overfit one or more weight tensors of one or more neural networks to obtain overfitted one or more weight tensors, wherein the one or more weight tensors comprise one or more decomposed weight tensors; signal at least one of overfitted one or more weight tensors or data derived from the at least one of overfitted one or more weight tensors to a decoder. [0026] The example apparatus may further include of claim 22, wherein the one or more weight tensors further comprise one or more non-decomposed weight tensors.

[0027] The example apparatus may further include, wherein the apparatus is further caused to select at least one of the overfitted one or more weight tensors based on a rate-distortion performance.

[0028] The example apparatus may further include, wherein the overfitted one or more weight tensors comprise overfitted one or more decomposed weight tensors, and wherein the at least one of overfitted one or more weight tensors comprises at least one of the overfitted one or more decomposed weight tensors.

[0029] The example apparatus may further include, wherein the apparatus is further caused to decompose the one or more weight tensors to obtain the one or more decomposed weight tensors.

[0030] The example apparatus may further include, wherein the apparatus is further caused to: decompose the one or more weight tensors based on a decomposition technique; and signal information related to decomposition, wherein the information related to decomposition comprises at least one of an indication of the decomposition technique used for decomposing the one or more weight tensors, one or more parameters of the decomposition technique, or one or more parameters of the decomposed one or more weight tensors.

[0031] The example apparatus may further include, wherein the apparatus is further caused to: signal information on whether the decoder needs to perform inference by using overfitted decomposed one or more weight tensors or using overfitted recomposed one or more weight tensors.

[0032] The example apparatus may further include, wherein the apparatus is further caused to generate a weight tensor (decomposable weight tensor) of the one or more weight tensors.

[0033] The example apparatus may further include, wherein to generate the decomposable weight tensor, the apparatus is further caused to: split the weight tensor of a neural network along one or more dimensions into sub-weight tensors; concatenate at least one of multiple weight tensors or one or more sub-weight tensors of two or more neural networks along one or more dimensions; pad the weight tensor or a sub-weight tensor along one or more dimensions to a certain size to cause concatenation of at least one of the multiple weight tensors or the one or more sub-weight tensors; and reorder the weight tensor or the sub-weight tensor along one or more dimensions. [0034] Still another example apparatus includes: at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the apparatus at least to: receive overfitted one or more weight tensors or data derived from the overfitted one or more weight tensors, wherein the received overfitted one or more weight tensors comprise one or more decomposed weight; update one or more decomposed weight tensors of one or more neural networks by using the received overfitted one or more weight tensors or data derived from the overfitted one or more weight tensors; and perform inference of the one or more neural networks comprising the updated one or more decomposed weight tensors.

[0035] The example apparatus may further include, wherein the received one or more weight tensors further comprise one or more non-decomposed weight tensors.

[0036] The example apparatus may further include, wherein the one or more weight tensors are decomposed to obtain the one or more decomposed weight tensors, and wherein the apparatus is further caused to receive information related to decomposition of the one or more weight tensors, wherein the information related to decomposition comprises at least one of an indication of a decomposition technique used for decomposing the one or more weight tensors, one or more parameters of the decomposition technique, or one or more parameters of the decomposed one or more weight tensors.

[0037] The example apparatus may further include, wherein the apparatus is further caused to: receive information on whether the apparatus needs to perform inference by using the overfitted decomposed one or more weight tensors or using overfitted recomposed one or more weight tensors.

[0038] An example method includes: receiving an input at an apparatus; and overfitting one or more features related of one or more non-linear activation (NLA) functions comprised in one or more neural networks based at least on the input to the apparatus.

[0039] The example method may further include, wherein the one or more features comprise one or more parameters of the one or more NLA functions.

[0040] The example method may further include: determining whether the one or more NLA functions comprised in the one or more neural networks are to be used or not; and signaling, in or along a bitstream, information based on the determination to a decoder, wherein the information comprises one or more of the following: one or more binary flags for the respective one or more NLA functions; comprise an indication of which subset of NLA functions is to be used out of several subsets of NLA functions; or a list of identifier values, wherein each identifier value identifies an NLA function of the one or more NLA functions.

[0041] The example method may further include determining one or more weights that are used for weighting an output of each of the one or more NLA functions.

[0042] The example method may further include, wherein the one or more neural networks are comprised in at least one of a codec or one or more post-processing operations.

[0043] The example method may further include, wherein the one or more NLA functions comprise one or more parametric rectified linear unit (PReLU) functions, and wherein the one or more parameters comprise one or more slopes, and wherein each slope of the one more slopes is associated with a negative side of a PReLU function of the one or more PReLU functions.

[0044] The example method may further include: selecting at least one PReLU function of the one or more PReLU functions that are comprised within the one or more neural networks; and for each of the selected at least one PReLU function repeat following to obtain one or more updated slopes until a criterion is met: providing an input to a selected PReLU function, wherein the input comprises features extracted by one or more of the neural network layers that precede the selected PReLU function, based at least on an input to the neural network that comprises the selected PReLU function; obtaining an output based at least on the provided input; computing a gradient of the output of the selected PReLU function with respect to a slope of the selected PReLU funtion; computing an update to the slope of the selected PReLU function based at least on the computed gradient; and computing an updated slope for the selected PReLU based at least on the computed update.

[0045] The example method may further include: updating the one or more neural networks based at least on the one or more updated slopes or one or more slopes that are derived from the one or more updated slopes, to obtain one or more overfitted neural networks; and using the one or more overfitted neural networks in an inference.

[0046] The example method may further include signaling one or more of the following: the overfitted one or more parameters; an indication of the overfitted one or more parameters; or a signal derived from the overfitted one or more parameters to a decoder in or along the bitstream. [0047] The example method may further include: compressing the one or more overfitted parameters based at least on a lossy and/or a lossless codec; and signaling the compressed overfitted one or more parameters to a decoder in or along the bitstream.

[0048] The example method may further include: computing an update to the one or more parameters based on the overfitted one or more parameters; compressing the update to the one or more parameters based at least on a lossy and/or on a lossless codec; signaling the compressed update to the one or more parameters to the decoder, within or along the bitstream.

[0049] The example method may further include: determining whether the one or more NLA functions are to be used on an input tensor of one or more input tensors; and applying at least one NLA function of the one or more NLA functions to all elements of the input tensor based on the determination.

[0050] The example method may further include: determining whether the one or more NLA functions are to be used on one or more channels of the input tensor; and applying at least one NLA function of the one or more NLA functions to all elements of the one or more channels of the input tensor based on the determination.

[0051] The example method may further include: determining whether one or more NLA functions are be used on one or more spatial positions of the input tensor; and applying at least one NLA function of the one or more NLA functions to all elements of the one or more spatial positions of the input tensor based on the determination.

[0052] The example method may further include: determining whether one or more NLA functions are to be used on one or more elements of the input tensor; and applying at least one NLA function of the one or more NLA functions to each element of an input tensor.

[0053] The example method may further include determining one or more weights associated with the at least one NLA function.

[0054] The example method may further include, wherein: the one or more neural networks comprise one or more portions; at least one portion comprise two or more parallel branches; one or more of the two or more parallel branches comprise one or more NLA functions; an input to one or more parallel branches is same or substantially same or derived from another signal; and outputs from the one or more parallel branches are combined.

[0055] Another example method includes: receiving or parsing, from or along a bitstream, overfitted one or more features related to one or more non-linear activation (NLA) functions comprised in one or more neural networks, wherein the one or more features are overfitted based at least on the input to an encoder; updating one or more parameters of the one or more neural networks based at least on the overfitted one more features; and performing an inference of the one or more neural networks comprising the updated one or more parameters.

[0056] The example method may further include, wherein the overfitted one or more features are compressed, and wherein the method further comprises decompressing the overfitted one or more features.

[0057] The example method may further include, wherein the one or more features comprise one or more parameters of the one or more NLA functions.

[0058] The example method may further include: receiving information whether the one or more NLA functions comprised in the one or more neural networks are to be used or not; wherein the information further comprises one or more of the following: one or more binary flags for the respective one or more NLA functions; an indication of which subset of NLA functions is to be used out of several subsets of NLA functions; or a list of identifier values, wherein each identifier value identifies an NLA function of the one or more NLA functions.

[0059] Yet another example method includes: overfitting one or more weight tensors of one or more neural networks to obtain overfitted one or more weight tensors, wherein the one or more weight tensors comprise one or more decomposed weight tensors; and signaling at least one of overfitted one or more weight tensors or data derived from the at least one of overfitted one or more weight tensors to a decoder.

[0060] The example method may further include, wherein the one or more weight tensors further comprise one or more non-decomposed weight tensors.

[0061] The example method may further include selecting at least one of the overfitted one or more weight tensors based on a rate-distortion performance. [0062] The example method may further include, wherein the overfitted one or more weight tensors comprise overfitted one or more decomposed weight tensors, and wherein the at least one of overfitted one or more weight tensors comprises at least one of the overfitted one or more decomposed weight tensors.

[0063] The example method may further include decomposing the one or more weight tensors to obtain the one or more decomposed weight tensors.

[0064] The example method may further include: decomposing the one or more weight tensors based on a decomposition technique; and signaling information related to decomposition, wherein the information related to decomposition comprises at least one of an indication of the decomposition technique used for decomposing the one or more weight tensors, one or more parameters of the decomposition technique, or one or more parameters of the decomposed one or more weight tensors.

[0065] The example method may further include: signaling information on whether the decoder needs to perform inference by using overfitted decomposed one or more weight tensors or using overfitted recomposed one or more weight tensors.

[0066] The example method may further include generating a weight tensor (decomposable weight tensor) of the one or more weight tensors.

[0067] The example method may further include generating the decomposable weight tensor comprises: splitting the weight tensor of a neural network along one or more dimensions into subweight tensors; concatenating at least one of multiple weight tensors or one or more sub-weight tensors of two or more neural networks along one or more dimensions; padding the weight tensor or a subweight tensor along one or more dimensions to a certain size to cause concatenation of at least one of the multiple weight tensors or the one or more sub-weight tensors; and reordering the weight tensor or the sub- weight tensor along one or more dimensions.

[0068] Still another example method includes: receiving overfitted one or more weight tensors or data derived from the overfitted one or more weight tensors, wherein the received overfitted one or more weight tensors comprise one or more decomposed weight; updating one or more decomposed weight tensors of one or more neural networks by using the received overfitted one or more weight tensors or data derived from the overfitted one or more weight tensors; and performing inference of the one or more neural networks comprising the updated one or more decomposed weight tensors. [0069] The example method may further include, wherein the received one or more weight tensors further comprise one or more non-decomposed weight tensors.

[0070] The example method may further include, wherein the one or more weight tensors are decomposed to obtain the one or more decomposed weight tensors, and wherein the method further comprises receiving information related to decomposition of the one or more weight tensors, wherein the information related to decomposition comprises at least one of an indication of a decomposition technique used for decomposing the one or more weight tensors, one or more parameters of the decomposition technique, or one or more parameters of the decomposed one or more weight tensors.

[0071] The example method may further include: receiving information on whether the apparatus needs to perform inference by using the overfitted decomposed one or more weight tensors or using overfitted recomposed one or more weight tensors.

[0072] An example computer-readable medium encoded with instructions that, when executed by a computer, causing an apparatus to perform a method as described in any of the previous paragraphs.

[0073] The example computer-readable medium may further include, wherein the computer- readable medium comprises a non-transitory computer-readable medium.

[0074] A still another example apparatus includes means for performing the methods described in any of the previous paragraphs.

BRIEF DESCRIPTION OF THE DRAWINGS

[0075] The foregoing aspects and other features are explained in the following description, taken in connection with the accompanying drawings, wherein:

[0076] FIG. 1 shows schematically an electronic device employing embodiments of the examples described herein.

[0077] FIG. 2 shows schematically a user equipment suitable for employing embodiments of the examples described herein. [0078] FIG. 3 further shows schematically electronic devices employing embodiments of the examples described herein connected using wireless and wired network connections.

[0079] FIG. 4 shows schematically a block diagram of an encoder on a general level.

[0080] FIG. 5 is a block diagram showing an interface between an encoder and a decoder in accordance with the examples described herein.

[0081] FIG. 6 illustrates a system configured to support streaming of media data from a source to a client device.

[0082] FIG. 7 is a block diagram of an apparatus that may be specifically configured in accordance with an example embodiment.

[0083] FIG. 8 illustrates examples of functioning of neural networks (NNs) as components of a pipeline of a traditional codec, in accordance with an example embodiment.

[0084] FIG. 9 illustrates an example of modified video coding pipeline based on neural networks, in accordance with an example embodiment.

[0085] FIG. 10 is an example neural network -based end-to-end learned video coding system, in accordance with an example embodiment.

[0086] FIG. 11 illustrates a pipeline of video coding for machines (VCM), in accordance with an embodiment.

[0087] FIG. 12 illustrates an example of an end-to-end learned approach for the use case of video coding for machines, in accordance with an embodiment.

[0088] FIG. 13 illustrates an example of how the end-to-end learned system may be trained for the use case of video coding for machines, in accordance with an embodiment.

[0089] FIG. 14 illustrates an example of a portion of a neural network (NN ), where an input to a portion of the NN is provided to a convolutional layer, in accordance with an embodiment. [0090] FIG. 15 illustrates another example of a portion of a NN, where an input to a portion of the neural network is provided to two parallel branches, in accordance with an embodiment.

[0091] FIG. 16 illustrates an example of a portion of a NN, where an input to the portion of the neural network is provided to a convolutional layer, in accordance with an embodiment.

[0092] FIG. 17 illustrates another example of a portion of a NN, where an input to the portion of the neural network is provided to two parallel branches, in accordance with an embodiment

[0093] FIG. 18 is an example apparatus, which may be implemented in hardware, caused to perform non-linear overfitting of neural network filters and/or overfitting decomposed weight tensors, based on the examples described herein.

[0094] FIG. 19 illustrates an example method for non-linear overfitting of one or more neural network, in accordance with an embodiment.

[0095] FIG. 20 illustrates an example method for non-linear overfitting of one or more neural network, in accordance with another embodiment, in accordance with an embodiment.

[0096] FIG. 21 illustrates an example method for overfitting decomposed weight tensors, in accordance with an embodiment.

[0097] FIG. 22 illustrates an example method for overfitting decomposed weight tensors, in accordance with another embodiment.

[0098] FIG. 23 is a block diagram of one possible and non-limiting system in which the example embodiments may be practiced.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

[0099] The following acronyms and abbreviations that may be found in the specification and/or the drawing figures are defined as follows:

3GP 3 GPP file format

3GPP 3rd Generation Partnership Project 3GPP TS 3GPP technical specification

4CC four character code

4G fourth generation of broadband cellular network technology

5G fifth generation cellular network technology

5GC 5G core network

ACC accuracy

AGT approximated ground truth data

Al artificial intelligence

AIoT Al-enabled loT

ALF adaptive loop filtering a.k.a. also known as

AMF access and mobility management function

APS adaptation parameter set

AVC advanced video coding bpp bits-per-pixel

CABAC context-adaptive binary arithmetic coding

CDMA code-division multiple access

CE core experiment ctu coding tree unit

CU central unit

DASH dynamic adaptive streaming over HTTP

DCT discrete cosine transform

DSP digital signal processor

DSNN decoder-side NN

DU distributed unit eNB (or eNodeB) evolved Node B (for example, an LTE base station)

EN-DC E-UTRA-NR dual connectivity en-gNB or En-gNB node providing NR user plane and control plane protocol terminations towards the UE, and acting as secondary node in EN-DC

E-UTRA evolved universal terrestrial radio access, for example, the LTE radio access technology

FDMA frequency division multiple access f(n) fixed-pattern bit string using n bits written (from left to right) with the left bit first. Fl or Fl-C interface between CU and DU control interface

FDC finetuning-driving content gNB (or gNodeB) base station for 5G/NR, for example, a node providing NR user plane and control plane protocol terminations towards the UE, and connected via the NG interface to the 5GC

GSM Global System for Mobile communications

H.222.0 MPEG-2 Systems is formally known as ISO/IEC 13818-1 and as ITU-T Rec. H.222.0

H.26x family of video coding standards in the domain of the ITU-T

HLS high level syntax

HQ high-quality

IBC intra block copy

ID identifier

IEC International Electrotechnical Commission

IEEE Institute of Electrical and Electronics Engineers

I/F interface

IMD integrated messaging device

IMS instant messaging service loT internet of things

IP internet protocol

[RAP intra random access point

ISO International Organization for Standardization

ISOBMFF ISO base media file format

ITU International Telecommunication Union

ITU-T ITU Telecommunication Standardization Sector

JPEG joint photographic experts group

LMCS luma mapping with chroma scaling

LPNN loss proxy NN

LQ low-quality

LTE long-term evolution

LZMA Lempel-Ziv-Markov chain compression

LZMA2 simple container format that can include both uncompressed data and LZMA data

LZO Lempel-Ziv-Oberhumer compression

LZW Lempel-Ziv-Welch compression MAC medium access control mdat MediaDataBox

MME mobility management entity

MMS multimedia messaging service moov MovieBox

MP4 file format for MPEG-4 Part 14 files

MPEG moving picture experts group

MPEG-2 H.222/H.262 as defined by the ITU

MPEG-4 audio and video coding standard for ISO/IEC 14496

MSB most significant bit

MSE mean square error

NAL network abstraction layer

NDU NN compressed data unit ng or NG new generation ng-eNB or NG-eNB new generation eNB

NN neural network

NNEF neural network exchange format

NNR neural network representation

NR new radio (5G radio)

N/W or NW network

ONNX Open Neural Network eXchange

PB protocol buffers

PC personal computer

PDA personal digital assistant

PDCP packet data convergence protocol

PHY physical layer

PID packet identifier

PLC power line communication

PNG portable network graphics

PSNR peak signal-to-noise ratio

QP quantization power

RAM random access memory

RAN radio access network

RBSP raw byte sequence payload

RD loss rate distortion loss RFC request for comments

RFID radio frequency identification

RLC radio link control

RRC radio resource control

RRH remote radio head

RU radio unit

Rx receiver

SDAP service data adaptation protocol

SGD Stochastic Gradient Descent

SGW serving gateway

SMF session management function

SMS short messaging service

SPS sequence parameter set st(v) null-terminated string encoded as UTF-8 characters as specified in ISO/IEC 10646

SVC scalable video coding

SI interface between eNodeBs and the EPC

TCP-IP transmission control protocol-internet protocol

TDMA time divisional multiple access trak TrackBox

TS transport stream

TUC technology under consideration

TV television

Tx transmitter

UE user equipment ue(v) unsigned integer Exp-Golomb-coded syntax element with the left bit first

UICC Universal Integrated Circuit Card

UMTS Universal Mobile Telecommunications System u(n) unsigned integer using n bits

UPF user plane function

URI uniform resource identifier

URL uniform resource locator

UTF-8 8-bit Unicode Transformation Format

VPS video parameter set WLAN wireless local area network

X2 interconnecting interface between two eNodeBs in LTE network

Xn interface between two NG-RAN nodes

[0100] Some embodiments will now be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all, embodiments of the invention are shown. Indeed, various embodiments of the invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Like reference numerals refer to like elements throughout. As used herein, the terms ‘data,’ ‘content,’ ‘information,’ and similar terms may be used interchangeably to refer to data capable of being transmitted, received and/or stored in accordance with embodiments of the present invention. Thus, use of any such terms should not be taken to limit the spirit and scope of embodiments of the present invention.

[0101] Additionally, as used herein, the term ‘circuitry’ refers to (a) hardware-only circuit implementations (e.g., implementations in analog circuitry and/or digital circuitry); (b) combinations of circuits and computer program product(s) comprising software and/or firmware instructions stored on one or more computer readable memories that work together to cause an apparatus to perform one or more functions described herein; and (c) circuits, such as, for example, a microprocessor(s) or a portion of a microprocessor(s), that require software or firmware for operation even if the software or firmware is not physically present. This definition of ‘circuitry’ applies to all uses of this term herein, including in any claims. As a further example, as used herein, the term ‘circuitry’ also includes an implementation comprising one or more processors and/or portion(s) thereof and accompanying software and/or firmware. As another example, the term ‘circuitry’ as used herein also includes, for example, a baseband integrated circuit or applications processor integrated circuit for a mobile phone or a similar integrated circuit in a server, a cellular network device, other network device, and/or other computing device.

[0102] As defined herein, a ‘computer-readable storage medium,’ which refers to a non-transitory physical storage medium (e.g., volatile or non-volatile memory device), can be differentiated from a ‘computer-readable transmission medium,’ which refers to an electromagnetic signal. [0103] A method, apparatus and computer program product are provided in accordance with example embodiments for perform non-linear overfitting of neural network filters and/or overfitting decomposed weight tensors.

[0104] In an example, the following describes in detail suitable apparatus and possible mechanisms for non-linear overfitting of neural network filters and/or overfitting decomposed weight tensors. In this regard reference is first made to FIG. 1 and FIG. 2, where FIG. 1 shows an example block diagram of an apparatus 50. The apparatus may be an Internet of Things (loT) apparatus configured to perform various functions, for example, gathering information by one or more sensors, receiving or transmitting information, analyzing information gathered or received by the apparatus, or the like. The apparatus may comprise a video coding system, which may incorporate a codec. FIG. 2 shows a layout of an apparatus according to an example embodiment. The elements of FIG. 1 and FIG. 2 will be explained next.

[0105] The apparatus 50 may for example be a mobile terminal or user equipment of a wireless communication system, a sensor device, a tag, or a lower power device. However, it would be appreciated that embodiments of the examples described herein may be implemented within any electronic device or apparatus which may process data by neural networks.

[0106] The apparatus 50 may comprise a housing 30 for incorporating and protecting the device. The apparatus 50 may further comprise a display 32, for example, in the form of a liquid crystal display, light emitting diode display, organic light emitting diode display, and the like. In other embodiments of the examples described herein the display may be any suitable display technology suitable to display media or multimedia content, for example, an image or a video. The apparatus 50 may further comprise a keypad 34. In other embodiments of the examples described herein any suitable data or user interface mechanism may be employed. For example, the user interface may be implemented as a virtual keyboard or data entry system as part of a touch-sensitive display.

[0107] The apparatus may comprise a microphone 36 or any suitable audio input which may be a digital or analogue signal input. The apparatus 50 may further comprise an audio output device which in embodiments of the examples described herein may be any one of: an earpiece 38, speaker, or an analogue audio or digital audio output connection. The apparatus 50 may also comprise a battery (or in other embodiments of the examples described herein the device may be powered by any suitable mobile energy device such as solar cell, fuel cell or clockwork generator). The apparatus may further comprise a camera 42 capable of recording or capturing images and/or video. The apparatus 50 may further comprise an infrared port for short range line of sight communication to other devices. In other embodiments the apparatus 50 may further comprise any suitable short range communication solution such as for example a Bluetooth wireless connection or a USB/firewire wired connection.

[0108] The apparatus 50 may comprise a controller 56, a processor or a processor circuitry for controlling the apparatus 50. The controller 56 may be connected to a memory 58 which in embodiments of the examples described herein may store both data in the form of an image, audio data and video data, and/or may also store instructions for implementation on the controller 56. The controller 56 may further be connected to codec circuitry 54 suitable for carrying out coding and/or decoding of audio, image and/or video data or assisting in coding and/or decoding carried out by the controller.

[0109] The apparatus 50 may further comprise a card reader 48 and a smart card 46, for example, a UICC and UICC reader for providing user information and being suitable for providing authentication information for authentication and authorization of the user at a network.

[0110] The apparatus 50 may comprise radio interface circuitry 52 connected to the controller and suitable for generating wireless communication signals, for example, for communication with a cellular communications network, a wireless communications system or a wireless local area network. The apparatus 50 may further comprise an antenna 44 connected to the radio interface circuitry 52 for transmitting radio frequency signals generated at the radio interface circuitry 52 to other apparatus(es) and/or for receiving radio frequency signals from other apparatus(es).

[0111] The apparatus 50 may comprise a camera 42 capable of recording or detecting individual frames which are then passed to the codec 54 or the controller for processing. The apparatus may receive the video image data for processing from another device prior to transmission and/or storage. The apparatus 50 may also receive either wirelessly or by a wired connection the image for coding/decoding. The structural elements of apparatus 50 described above represent examples of means for performing a corresponding function.

[0112] With respect to FIG. 3, an example of a system within which embodiments of the examples described herein can be utilized is shown. The system 10 comprises multiple communication devices which can communicate through one or more networks. The system 10 may comprise any combination of wired or wireless networks including, but not limited to, a wireless cellular telephone network (such as a GSM, UMTS, CDMA, LTE, 4G, 5G network, and the like), a wireless local area network (WLAN) such as defined by any of the IEEE 802.x standards, a Bluetooth® personal area network, an Ethernet local area network, a token ring local area network, a wide area network, and the Internet.

[0113] The system 10 may include both wired and wireless communication devices and/or apparatus 50 suitable for implementing embodiments of the examples described herein.

[0114] For example, the system shown in FIG. 3 shows a mobile telephone network 11 and a representation of the Internet 28. Connectivity to the Internet 28 may include, but is not limited to, long range wireless connections, short range wireless connections, and various wired connections including, but not limited to, telephone lines, cable lines, power lines, and similar communication pathways.

[0115] The example communication devices shown in the system 10 may include, but are not limited to, an electronic device or apparatus 50, a combination of a personal digital assistant (PDA) and a mobile telephone 14, a PDA 16, an integrated messaging device (IMD) 18, a desktop computer 20, a notebook computer 22. The apparatus 50 may be stationary or mobile when carried by an individual who is moving. The apparatus 50 may also be located in a mode of transport including, but not limited to, a car, a truck, a taxi, a bus, a train, a boat, an airplane, a bicycle, a motorcycle or any similar suitable mode of transport.

[0116] The embodiments may also be implemented in a set-top box; for example, a digital TV receiver, which may/may not have a display or wireless capabilities, in tablets or (laptop) personal computers (PC), which have hardware and/or software to process neural network data, in various operating systems, and in chipsets, processors, DSPs and/or embedded systems offering hardware/software based coding.

[0117] Some or further apparatus may send and receive calls and messages and communicate with service providers through a wireless connection 25 to a base station 24. The base station 24 may be connected to a network server 26 that allows communication between the mobile telephone network 11 and the Internet 28. The system may include additional communication devices and communication devices of various types.

[0118] The communication devices may communicate using various transmission technologies including, but not limited to, code division multiple access (CDMA), global systems for mobile communications (GSM), universal mobile telecommunications system (UMTS), time divisional multiple access (TDMA), frequency division multiple access (FDMA), transmission control protocol- internet protocol (TCP-IP), short messaging service (SMS), multimedia messaging service (MMS), email, instant messaging service (IMS), Bluetooth, IEEE 802.11, 3GPP Narrowband loT and any similar wireless communication technology. A communications device involved in implementing various embodiments of the examples described herein may communicate using various media including, but not limited to, radio, infrared, laser, cable connections, and any suitable connection.

[0119] In telecommunications and data networks, a channel may refer either to a physical channel or to a logical channel. A physical channel may refer to a physical transmission medium such as a wire, whereas a logical channel may refer to a logical connection over a multiplexed medium, capable of conveying several logical channels. A channel may be used for conveying an information signal, for example a bitstream, from one or several senders (or transmitters) to one or several receivers.

[0120] The embodiments may also be implemented in internet of things (loT) devices. The loT may be defined, for example, as an interconnection of uniquely identifiable embedded computing devices within the existing Internet infrastructure. The convergence of various technologies has and may enable many fields of embedded systems, such as wireless sensor networks, control systems, home/building automation, and the like, to be included in the loT. In order to utilize the loT devices are provided with an IP address as a unique identifier. The loT devices may be provided with a radio transmitter, such as WLAN or Bluetooth transmitter or a RFID tag. Alternatively, the loT devices may have access to an IP-based network via a wired network, such as an Ethernet-based network or a powerline connection (PLC).

[0121] The devices/systems described in FIGs. 1 to 3 enable encoding, decoding, and/or transportation of, for example, a neural network representation and/or a media bitstream.

[0122] An MPEG-2 transport stream (TS), specified in ISO/IEC 13818-1 or equivalently in ITU- T Recommendation H.222.0, is a format for carrying audio, video, and other media as well as program metadata or other metadata, in a multiplexed stream. A packet identifier (PID) is used to identify an elementary stream (a.k.a. packetized elementary stream) within the TS. Hence, a logical channel within an MPEG-2 TS may be considered to correspond to a specific PID value.

[0123] Available media file format standards include ISO base media file format (ISO/IEC 14496- 12, which may be abbreviated ISOBMFF) and file format for NAL unit structured video (ISO/IEC 14496-15), which derives from the ISOBMFF. [0124] Video codec consists of an encoder that transforms the input video into a compressed representation suited for storage/transmission and a decoder that can decompress the compressed video representation back into a viewable form, or into a form that is suitable as an input to one or more algorithms for analysis or processing. A video encoder and/or a video decoder may also be separate from each other, for example, need not form a codec. Typically, encoder discards some information in the original video sequence in order to represent the video in a more compact form (e.g., at lower bitrate).

[0125] Typical hybrid video encoders, for example, many encoder implementations of ITU-T H.263 and H.264, encode the video information in two phases. Firstly pixel values in a certain picture area (or ‘block’) are predicted, for example, by motion compensation means (finding and indicating an area in one of the previously coded video frames that corresponds closely to the block being coded) or by spatial means (using the pixel values around the block to be coded in a specified manner). Secondly the prediction error, for example, the difference between the predicted block of pixels and the original block of pixels, is coded. This is typically done by transforming the difference in pixel values using a specified transform (for example, Discrete Cosine Transform (DCT) or a variant of it), quantizing the coefficients and entropy coding the quantized coefficients. By varying the fidelity of the quantization process, encoder can control the balance between the accuracy of the pixel representation (picture quality) and size of the resulting coded video representation (file size or transmission bitrate).

[0126] In temporal prediction, the sources of prediction are previously decoded pictures (a.k.a. reference pictures). In intra block copy (IBC; a.k.a. intra-block-copy prediction and current picture referencing), prediction is applied similarly to temporal prediction, but the reference picture is the current picture and only previously decoded samples can be referred in the prediction process. Interlayer or inter-view prediction may be applied similarly to temporal prediction, but the reference picture is a decoded picture from another scalable layer or from another view, respectively. In some cases, inter prediction may refer to temporal prediction only, while in other cases inter prediction may refer collectively to temporal prediction and any of intra block copy, inter-layer prediction, and inter-view prediction provided that they are performed with the same or similar process than temporal prediction. Inter prediction or temporal prediction may sometimes be referred to as motion compensation or motion-compensated prediction.

[0127] Inter prediction, which may also be referred to as temporal prediction, motion compensation, or motion-compensated prediction, reduces temporal redundancy. In inter prediction the sources of prediction are previously decoded pictures. Intra prediction utilizes the fact that adjacent pixels within the same picture are likely to be correlated. Intra prediction can be performed in spatial or transform domain, for example, either sample values or transform coefficients can be predicted. Intra prediction is typically exploited in intra-coding, where no inter prediction is applied.

[0128] One outcome of the coding procedure is a set of coding parameters, such as motion vectors and quantized transform coefficients. Many parameters can be entropy-coded more efficiently when they are predicted first from spatially or temporally neighboring parameters. For example, a motion vector may be predicted from spatially adjacent motion vectors and only the difference relative to the motion vector predictor may be coded. Prediction of coding parameters and intra prediction may be collectively referred to as in-picture prediction.

[0129] FIG. 4 shows a block diagram of a general structure of a video encoder. FIG. 4 presents an encoder for two layers, but it would be appreciated that presented encoder could be similarly extended to encode more than two layers. FIG. 4 illustrates a video encoder comprising a first encoder section 500 for a base layer and a second encoder section 502 for an enhancement layer. Each of the first encoder section 500 and the second encoder section 502 may comprise similar elements for encoding incoming pictures. The encoder sections 500, 502 may comprise a pixel predictor 302, 402, prediction error encoder 303, 403 and prediction error decoder 304, 404. FIG. 4 also shows an embodiment of the pixel predictor 302, 402 as comprising an inter-predictor 306, 406, an intra-predictor 308, 408, a mode selector 310, 410, a filter 316, 416, and a reference frame memory 318, 418. The pixel predictor 302 of the first encoder section 500 receives base layer picture(s)/image(s) 300 of a video stream to be encoded at both the inter-predictor 306 (which determines the difference between the image and a motion compensated reference frame) and the intra-predictor 308 (which determines a prediction for an image block based only on the already processed parts of current frame or picture). The output of both the inter-predictor and the intra-predictor are passed to the mode selector 310. The intra-predictor 308 may have more than one intra-prediction modes. Hence, each mode may perform the intra-prediction and provide the predicted signal to the mode selector 310. The mode selector 310 also receives a copy of the base layer image(s) 300. Correspondingly, the pixel predictor 402 of the second encoder section 502 receives enhancement layer picture(s)/images(s) 400 of a video stream to be encoded at both the interpredictor 406 (which determines the difference between the image and a motion compensated reference frame) and the intra-predictor 408 (which determines a prediction for an image block based only on the already processed parts of current frame or picture). The output of both the inter-predictor and the intra- predictor are passed to the mode selector 410. The intra-predictor 408 may have more than one intraprediction modes. Hence, each mode may perform the intra-prediction and provide the predicted signal to the mode selector 410. The mode selector 410 also receives a copy of the enhancement layer pictures 400.

[0130] Depending on which encoding mode is selected to encode the current block, the output of the inter-predictor 306, 406 or the output of one of the optional intra-predictor modes or the output of a surface encoder within the mode selector is passed to the output of the mode selector 310, 410. The output of the mode selector 310, 410 is passed to a first summing device 321, 421. The first summing device may subtract the output of the pixel predictor 302, 402 from the base layer image(s) 300/enhancement layer image(s) 400 to produce a first prediction error signal 320, 420 which is input to the prediction error encoder 303, 403.

[0131] The pixel predictor 302, 402 further receives from a preliminary reconstructor 339, 439 the combination of the prediction representation of the image block 312, 412 and the output 338, 438 of the prediction error decoder 304, 404. The preliminary reconstructed image 314, 414 may be passed to the intra-predictor 308, 408 and to the filter 316, 416. The filter 316, 416 receiving the preliminary representation may filter the preliminary representation and output a final reconstructed image 340, 440 which may be saved in the reference frame memory 318, 418. The reference frame memory 318 may be connected to the inter-predictor 306 to be used as the reference image against which a future base layer image 300 is compared in inter-prediction operations. Subject to the base layer being selected and indicated to be source for inter-layer sample prediction and/or inter-layer motion information prediction of the enhancement layer according to some embodiments, the reference frame memory 318 may also be connected to the inter-predictor 406 to be used as the reference image against which a future enhancement layer image(s) 400 is compared in inter-prediction operations. Moreover, the reference frame memory 418 may be connected to the inter-predictor 406 to be used as the reference image against which the future enhancement layer image(s) 400 is compared in in ter -prediction operations.

[0132] Filtering parameters from the filter 316 of the first encoder section 500 may be provided to the second encoder section 502 subject to the base layer being selected and indicated to be source for predicting the filtering parameters of the enhancement layer according to some embodiments.

[0133] The prediction error encoder 303, 403 comprises a transform unit 342, 442 and a quantizer 344, 444. The transform unit 342, 442 transforms the first prediction error signal 320, 420 to a transform domain. The transform is, for example, the DCT transform. The quantizer 344, 444 quantizes the transform domain signal, for example, the DCT coefficients, to form quantized coefficients. [0134] The prediction error decoder 304, 404 receives the output from the prediction error encoder 303, 403 and performs the opposite processes of the prediction error encoder 303, 403 to produce a decoded prediction error signal 338, 438 which, when combined with the prediction representation of the image block 312, 412 at the second summing device 339, 439, produces the preliminary reconstructed image 314, 414. The prediction error decoder may be considered to comprise a dequantizer 346, 446, which dequantizes the quantized coefficient values, for example, DCT coefficients, to reconstruct the transform signal and an inverse transformation unit 348, 448, which performs the inverse transformation to the reconstructed transform signal wherein the output of the inverse transformation unit 348, 448 contains reconstructed block(s). The prediction error decoder may also comprise a block filter which may filter the reconstructed block(s) according to further decoded information and filter parameters.

[0135] The entropy encoder 330, 430 receives the output of the prediction error encoder 303, 403 and may perform a suitable entropy encoding/variable length encoding on the signal to provide a compressed signal. The outputs of the entropy encoders 330, 430 may be inserted into a bitstream, for example, by a multiplexer 508.

[0136] FIG. 5 is a block diagram showing the interface between an encoder 501 implementing neural network based encoding 503, and a decoder 504 implementing neural network based decoding 505 in accordance with the examples described herein. The encoder 501 may embody a device, a software method or a hardware circuit. The encoder 501 has the goal of compressing an input data 511 (for example, an input video) to a compressed data 512 (for example, a bitstream) such that the bitrate measuring the size of compressed data 512 is minimized, and the accuracy of an analysis or processing algorithm is maximized. To this end, the encoder 501 uses an encoder or compression algorithm, for example to perform neural network based encoding 503, e.g., encoding the input data by using one or more neural networks.

[0137] The general analysis or processing algorithm may be part of the decoder 504. The decoder 504 uses a decoder or decompression algorithm, for example, to perform the neural network based decoding 505 (e.g., decoding by using one or more neural networks) to decode the compressed data 512 (for example, compressed video) which was encoded by the encoder 501. The decoder 504 produces decompressed data 513 (for example, reconstructed data).

[0138] The encoder 501 and decoder 504 may be entities implementing an abstraction, may be separate entities or the same entities, or may be part of the same physical device. [0139] The analysis/processing algorithm may be any algorithm, traditional or learned from data. In the case of an algorithm which is learned from data, in some embodiments it is assumed that this algorithm can be modified or updated, for example, by using optimization via gradient descent. An example of the learned algorithm is a neural network.

[0140] An out-of-band transmission, signaling, or storage may refer to the capability of transmitting, signaling, or storing information in a manner that associates the information with a video bitstream. The out-of-band transmission may use a more reliable transmission mechanism compared to the protocols used for carrying coded video data, such as slices. The out-of-band transmission, signaling or storage can additionally or alternatively be used e.g. for ease of access or session negotiation. For example, a sample entry of a track in a file conforming to the ISO Base Media File Format may comprise parameter sets, while the coded data in the bitstream is stored elsewhere in the file or in another file. Another example of out-of-band transmission, signaling, or storage comprises including information, such as NN and/or NN updates in a file format track that is separate from track(s) containing coded video data.

[0141] The phrase along the bitstream (e.g. indicating along the bitstream) or along a coded unit of a bitstream (e.g. indicating along a coded tile) may be used in claims and described embodiments to refer to transmission, signaling, or storage in a manner that the ‘out-of-band’ data is associated with, but not included within, the bitstream or the coded unit, respectively. The phrase decoding along the bitstream or along a coded unit of a bitstream or alike may refer to decoding the referred out-of-band data (which may be obtained from out-of-band transmission, signaling, or storage) that is associated with the bitstream or the coded unit, respectively. For example, the phrase along the bitstream may be used when the bitstream is contained in a container file, such as a file conforming to the ISO Base Media File Format, and certain file metadata is stored in the file in a manner that associates the metadata to the bitstream, such as boxes in the sample entry for a track containing the bitstream, a sample group for the track containing the bitstream, or a timed metadata track associated with the track containing the bitstream. In another example, the phrase along the bitstream may be used when the bitstream is made available as a stream over a communication protocol and a media description, such as a streaming manifest, is provided to describe the stream.

[0142] An elementary unit for the output of a video encoder and the input of a video decoder, respectively, may be a network abstraction layer (NAL) unit. For transport over packet-oriented networks or storage into structured files, NAL units may be encapsulated into packets or similar structures. A bytestream format encapsulating NAL units may be used for transmission or storage environments that do not provide framing structures. The bytestream format may separate NAL units from each other by attaching a start code in front of each NAL unit. To avoid false detection of NAL unit boundaries, encoders may run a byte-oriented start code emulation prevention algorithm, which may add an emulation prevention byte to the NAL unit payload if a start code would have occurred otherwise. In order to enable straightforward gateway operation between packet and stream-oriented systems, start code emulation prevention may be performed regardless of whether the bytestream format is in use or not. A NAL unit may be defined as a syntax structure containing an indication of the type of data to follow and bytes containing that data in the form of a raw byte sequence payload interspersed as necessary with emulation prevention bytes. A raw byte sequence payload (RBSP) may be defined as a syntax structure containing an integer number of bytes that is encapsulated in a NAL unit. An RBSP is either empty or has the form of a string of data bits containing syntax elements followed by an RBSP stop bit and followed by zero or more subsequent bits equal to 0.

[0143] In some coding standards, NAL units consist of a header and payload. The NAL unit header indicates the type of the NAL unit. In some coding standards, the NAL unit header indicates a scalability layer identifier (e.g. called nuh_layer_id in H.265/HEVC and H.266/VVC), which could be used e.g. for indicating spatial or quality layers, views of a multiview video, or auxiliary layers (such as depth maps or alpha planes). In some coding standards, the NAL unit header includes a temporal sublayer identifier, which may be used for indicating temporal subsets of the bitstream, such as a 30- frames-per-second subset of a 60-frames-per-second bitstream.

[0144] NAL units may be categorized into Video Coding Layer (VCL) NAL units and non-VCL NAL units. VCL NAL units are typically coded slice NAL units.

[0145] A non-VCL NAL unit may be, for example, one of the following types: a video parameter set (VPS), a sequence parameter set (SPS), a picture parameter set (PPS), an adaptation parameter set (APS), a supplemental enhancement information (SEI) NAL unit, an access unit delimiter, an end of sequence NAL unit, an end of bitstream NAL unit, or a filler data NAL unit. Parameter sets may be needed for the reconstruction of decoded pictures, whereas many of the other non-VCL NAL units are not necessary for the reconstruction of decoded sample values.

[0146] Some coding formats specify parameter sets that may carry parameter values needed for the decoding or reconstruction of decoded pictures. A parameter may be defined as a syntax element of a parameter set. A parameter set may be defined as a syntax structure that contains parameters and that can be referred to from or activated by another syntax structure, for example, using an identifier. [0147] Some types of parameter sets are briefly described in the following, but it needs to be understood, that other types of parameter sets may exist and that embodiments may be applied, but are not limited to, the described types of parameter sets.

[0148] Parameters that remain unchanged through a coded video sequence may be included in a sequence parameter set. Alternatively, an SPS may be limited to apply to a layer that references the SPS, e.g. an SPS may remain valid for a coded layer video sequence. In addition to the parameters that may be needed by the decoding process, the sequence parameter set may optionally contain video usability information (VUI), which includes parameters that may be important for buffering, picture output timing, rendering, and resource reservation.

[0149] A picture parameter set contains such parameters that are likely to be unchanged in several coded pictures. A picture parameter set may include parameters that can be referred to by the VCL NAL units of one or more coded pictures.

[0150] A video parameter set (VPS) may be defined as a syntax structure containing syntax elements that apply to zero or more entire coded video sequences and may contain parameters applying to multiple layers. The VPS may provide information about the dependency relationships of the layers in a bitstream, as well as many other information that are applicable to all slices across all layers in the entire coded video sequence.

[0151] A video parameter set RBSP may include parameters that can be referred to by one or more sequence parameter set RBSPs.

[0152] The relationship and hierarchy between a video parameter set (VPS), a sequence parameter set (SPS), and a picture parameter set (PPS) may be described as follows. A VPS resides one level above an SPS in the parameter set hierarchy and in the context of scalability. The VPS may include parameters that are common for all slices across all layers in the entire coded video sequence. The SPS includes the parameters that are common for all slices in a particular layer in the entire coded video sequence, and may be shared by multiple layers. The PPS includes the parameters that are common for all slices in a particular picture and are likely to be shared by all slices in multiple pictures.

[0153] An adaptation parameter set (APS) may be specified in some coding formats, such as H.266/VVC. An APS may be applied to one or more image segments, such as slices. In H.266/VVC, an APS may be defined as a syntax structure containing syntax elements that apply to zero or more slices as determined by zero or more syntax elements found in slice headers or in a picture header. An APS may comprise a type (aps_params_type in H.266/VVC) and an identifier (aps_adaptation_parameter_set_id in H.266/VVC). The combination of an APS type and an APS identifier may be used to identify a particular APS. H.266/VVC comprises three APS types: an adaptive loop filtering (ALF), a luma mapping with chroma scaling (LMCS), and a scaling list APS types. The ALF APS(s) are referenced from a slice header (thus, the referenced ALF APSs can change slice by slice), and the LMCS and scaling list APS(s) are referenced from a picture header (thus, the referenced LMCS and scaling list APSs can change picture by picture). In H.266/VVC, the APS RBSP has the following syntax:

[0154] Video coding specifications may enable the use of supplemental enhancement information (SEI) messages or alike. Some video coding specifications include SEI NAL units, and some video coding specifications contain both prefix SEI NAL units and suffix SEI NAL units. A prefix SEI NAL unit can start a picture unit or alike; and a suffix SEI NAL unit can end a picture unit or alike. Hereafter, an SEI NAL unit may equivalently refer to a prefix SEI NAL unit or a suffix SEI NAL unit. An SEI NAL unit includes one or more SEI messages, which are not required for the decoding of output pictures but may assist in related processes, such as picture output timing, post-processing of decoded pictures, rendering, error detection, error concealment, and resource reservation.

[0155] Several SEI messages are specified in H.264/AVC, H.265/HEVC, H.266/VVC, and H.274/VSEI standards, and the user data SEI messages enable organizations and companies to specify SEI messages for specific use. The standards may contain the syntax and semantics for the specified SEI messages but a process for handling the messages in the recipient might not be defined. Consequently, encoders may be required to follow the standard specifying a SEI message when they create SEI message(s), and decoders might not be required to process SEI messages for output order conformance. One of the reasons to include the syntax and semantics of SEI messages in standards is to allow different system specifications to interpret the supplemental information identically and hence interoperate. It is intended that system specifications can require the use of particular SEI messages both in the encoding end and in the decoding end, and additionally the process for handling particular SEI messages in the recipient can be specified.

[0156] The method and apparatus of an example embodiment may be utilized in a wide variety of systems, including systems that rely upon the compression and decompression of media data and possibly also the associated metadata. In at least an embodiment, however, the method and apparatus are configured to train or finetune a decoder-side neural network. In this regard, FIG. 6 depicts an example of such a system 600 that includes a source 602 of media data and associated metadata. The source 602 may be, in an embodiment, a server. However, the source may be embodied in other manners when desired. The source 602 is configured to stream the media data and associated metadata to a client device 604. The client device may be embodied by a media player, a multimedia system, a video system, a smart phone, a mobile telephone or other user equipment, a personal computer, a tablet computer or any other computing device configured to receive and decompress the media data and process associated metadata. In the illustrated embodiment, media data and metadata are streamed via a network 606, such as any of a wide variety of types of wireless networks and/or wireline networks. The client device is configured to receive structured information containing media, metadata and any other relevant representation of information containing the media and the metadata and to decompress the media data and process the associated metadata (e.g. for proper playback timing of decompressed media data). [0157] An apparatus 700 is provided in accordance with an example embodiment as shown in FIG. 7. Inan embodiment, the apparatus of FIG. 7 may be embodied by the source 602, such as a file writer which, in turn, may be embodied by a server, that is configured to stream a compressed representation of the media data and associated metadata. In an alternative embodiment, the apparatus may be embodied by the client device 604, such as a file reader which may be embodied, for example, by any of the various computing devices described above. In either of these embodiments and as shown in FIG. 7, the apparatus of an example embodiment includes, is associated with or is in communication with a processing circuitry 702, one or more memory devices 704, a communication interface 706 and optionally a user interface.

[0158] The processing circuitry 702 may be in communication with the memory device 704 via a bus for passing information among components of the apparatus 700. The memory device may be non- transitory and may include, for example, one or more volatile and/or non-volatile memories. In other words, for example, the memory device may be an electronic storage device (e.g., a computer readable storage medium) comprising gates configured to store data (e.g., bits) that may be retrievable by a machine (e.g., a computing device like the processing circuitry). The memory device may be configured to store information, data, content, applications, instructions, or the like for enabling the apparatus to carry out various functions in accordance with an example embodiment of the present disclosure. For example, the memory device could be configured to buffer input data for processing by the processing circuitry. Additionally or alternatively, the memory device could be configured to store instructions for execution by the processing circuitry.

[0159] The apparatus 700 may, in some embodiments, be embodied in various computing devices as described above. However, in some embodiments, the apparatus may be embodied as a chip or chip set. In other words, the apparatus may comprise one or more physical packages (e.g., chips) including materials, components and/or wires on a structural assembly (e.g., a baseboard). The structural assembly may provide physical strength, conservation of size, and/or limitation of electrical interaction for component circuitry included thereon. The apparatus may therefore, in some cases, be configured to implement an embodiment of the present disclosure on a single chip or as a single ‘system on a chip.’ As such, in some cases, a chip or chipset may constitute means for performing one or more operations for providing the functionalities described herein.

[0160] The processing circuitry 702 may be embodied in a number of different ways. For example, the processing circuitry may be embodied as one or more of various hardware processing means such as a coprocessor, a microprocessor, a controller, a digital signal processor (DSP), a processing element with or without an accompanying DSP, or various other circuitry including integrated circuits such as, for example, an ASIC (application specific integrated circuit), an FPGA (field programmable gate array), a microcontroller unit (MCU), a hardware accelerator, a special-purpose computer chip, or the like. As such, in some embodiments, the processing circuitry may include one or more processing cores configured to perform independently. A multi-core processing circuitry may enable multiprocessing within a single physical package. Additionally or alternatively, the processing circuitry may include one or more processors configured in tandem via the bus to enable independent execution of instructions, pipelining and/or multithreading.

[0161] In an example embodiment, the processing circuitry 702 may be configured to execute instructions stored in the memory device 704 or otherwise accessible to the processing circuitry. Alternatively or additionally, the processing circuitry may be configured to execute hard coded functionality. As such, whether configured by hardware or software methods, or by a combination thereof, the processing circuitry may represent an entity (e.g., physically embodied in circuitry) capable of performing operations according to an embodiment of the present disclosure while configured accordingly. Thus, for example, when the processing circuitry is embodied as an ASIC, FPGA or the like, the processing circuitry may be specifically configured hardware for conducting the operations described herein. Alternatively, as another example, when the processing circuitry is embodied as an executor of instructions, the instructions may specifically configure the processing circuitry to perform the algorithms and/or operations described herein when the instructions are executed. However, in some cases, the processing circuitry may be a processor of a specific device (e.g., an image or video processing system) configured to employ an embodiment of the present invention by further configuration of the processing circuitry by instructions for performing the algorithms and/or operations described herein. The processing circuitry may include, among other things, a clock, an arithmetic logic unit (ALU) and logic gates configured to support operation of the processing circuitry.

[0162] The communication interface 706 may be any means such as a device or circuitry embodied in either hardware or a combination of hardware and software that is configured to receive and/or transmit data, including video bitstreams. In this regard, the communication interface may include, for example, an antenna (or multiple antennas) and supporting hardware and/or software for enabling communications with a wireless communication network. Additionally or alternatively, the communication interface may include the circuitry for interacting with the antenna(s) to cause transmission of signals via the antenna(s) or to handle receipt of signals received via the antenna(s). In some environments, the communication interface may alternatively or also support wired communication. As such, for example, the communication interface may include a communication modem and/or other hardware/software for supporting communication via cable, digital subscriber line (DSL), universal serial bus (USB) or other mechanisms.

[0163] In some embodiments, the apparatus 700 may optionally include a user interface that may, in turn, be in communication with the processing circuitry 702 to provide output to a user, such as by outputting an encoded video bitstream and, in some embodiments, to receive an indication of a user input. As such, the user interface may include a display and, in some embodiments, may also include a keyboard, a mouse, a joystick, a touch screen, touch areas, soft keys, a microphone, a speaker, or other input/output mechanisms. Alternatively or additionally, the processing circuitry may comprise user interface circuitry configured to control at least some functions of one or more user interface elements such as a display and, in some embodiments, a speaker, ringer, microphone and/or the like. The processing circuitry and/or user interface circuitry comprising the processing circuitry may be configured to control one or more functions of one or more user interface elements through computer program instructions (e.g., software and/or firmware) stored on a memory accessible to the processing circuitry (e.g., memory device, and/or the like).

[0164] Fundamentals of neural networks

[0165] A neural network (NN) is a computation graph consisting of several layers of computation. Each layer consists of one or more units, where each unit performs a computation. A unit is connected to one or more other units, and a connection may be associated with a weight. The weight may be used for scaling the signal passing through an associated connection. Weights are learnable parameters, for example, values which can be learned from training data. There may be other learnable parameters, such as those of batch-normalization layers.

[0166] Couple of examples of architectures for neural networks are feed-forward and recurrent architectures. Feed-forward neural networks are such that there is no feedback loop, each layer takes input from one or more of the previous layers, and provides its output as the input for one or more of the subsequent layers. Also, units inside a certain layer take input from units in one or more of preceding layers and provide output to one or more of following layers.

[0167] Initial layers, those close to the input data, extract semantically low-level features, for example, edges and textures in images, and intermediate and final layers extract more high-level features. After the feature extraction layers there may be one or more layers performing a certain task, for example, classification, semantic segmentation, object detection, denoising, style transfer, super- resolution, and the like. In recurrent neural networks, there is a feedback loop, so that the neural network becomes stateful, for example, it is able to memorize information or a state.

[0168] Neural networks are being utilized in an ever-increasing number of applications for many different types of devices, for example, mobile phones, chat bots, loT devices, smart cars, voice assistants, and the like. Some of these applications include, but are not limited to, image and video analysis and processing, social media data analysis, device usage data analysis, and the like.

[0169] One of the properties of neural networks, and other machine learning tools, is that they are able to learn properties from input data, either in a supervised way or in an unsupervised way. Such learning is a result of a training algorithm, or of a meta-level neural network providing the training signal.

[0170] In general, the training algorithm consists of changing some properties of the neural network so that its output is as close as possible to a desired output. For example, in the case of classification of objects in images, the output of the neural network can be used to derive a class or category index which indicates the class or category that the object in the input image belongs to. Training usually happens by minimizing or decreasing the output error, also referred to as the loss. Examples of losses are mean squared error, cross-entropy, and the like. In recent deep learning techniques, training is an iterative process, where at each iteration the algorithm modifies the weights of the neural network to make a gradual improvement in the network’s output, for example, gradually decrease the loss.

[0171] Training a neural network is an optimization process, but the final goal is different from the typical goal of optimization. In optimization, the only goal is to minimize a function. In machine learning, the goal of the optimization or training process is to make the model learn the properties of the data distribution from a limited training dataset. In other words, the goal is to learn to use a limited training dataset in order to learn to generalize to previously unseen data, for example, data which was not used for training the model. This is usually referred to as generalization. In practice, data is usually split into at least two sets, the training set and the validation set. The training set is used for training the network, for example, to modify its learnable parameters in order to minimize the loss. The validation set is used for checking the performance of the network on data, which was not used to minimize the loss, as an indication of the final performance of the model. In particular, the errors on the training set and on the validation set are monitored during the training process to understand the following: - If the network is learning at all - in this case, the training set error should decrease, otherwise the model is in the regime of underfitting.

- If the network is learning to generalize - in this case, also the validation set error needs to decrease and be not too much higher than the training set error. For example, the validation set error should be less than 20% higher than the training set error. If the training set error is low, for example 10% of its value at the beginning of training, or with respect to a threshold that may have been determined based on an evaluation metric, but the validation set error is much higher than the training set error, or it does not decrease, or it even increases, the model is in the regime of overfitting. This means that the model has just memorized properties of the training set and performs well only on that set, but performs poorly on a set not used for training or tuning of its parameters.

[0172] Lately, neural networks have been used for compressing and de-compressing data such as images. The most widely used architecture for such task is the auto-encoder, which is a neural network consisting of two parts: a neural encoder and a neural decoder. In various embodiments, these neural encoder and neural decoder would be referred to as encoder and decoder, even though these refer to algorithms which are learned from data instead of being tuned manually. The encoder takes an image as an input and produces a code, to represent the input image, which requires less bits than the input image. This code may have been obtained by a binarization or quantization process after the encoder. The decoder takes in this code and reconstructs the image which was input to the encoder.

[0173] Such encoder and decoder are usually trained to minimize a combination of bitrate and distortion, where the distortion may be based on one or more of the following metrics: mean squared error (MSE), peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), or the like. These distortion metrics are meant to be correlated to the human visual perception quality, so that minimizing or maximizing one or more of these distortion metrics results into improving the visual quality of the decoded image as perceived by humans.

[0174] In various embodiments, terms ‘model’, ‘neural network’, ‘neural net’ and ‘network’ may be used interchangeably, and also the weights of neural networks may be sometimes referred to as learnable parameters or as parameters.

[0175] Fundamentals of video/image coding

[0176] Video codec consists of an encoder that transforms the input video into a compressed representation suited for storage/transmission and a decoder that can decompress the compressed video representation back into a viewable form. Typically, an encoder discards some information in the original video sequence in order to represent the video in a more compact form, for example, at lower bitrate.

[0177] Typical hybrid video codecs, for example ITU-T H.263 and H.264, encode the video information in two phases. Firstly, pixel values in a certain picture area (or ‘block’) are predicted, for example, by motion compensation means or circuits (by finding and indicating an area in one of the previously coded video frames that corresponds closely to the block being coded) or by spatial means or circuit (by using the pixel values around the block to be coded in a specified manner). Secondly the prediction error, e.g. the difference between the predicted block of pixels and the original block of pixels, is coded. This is typically done by transforming the difference in pixel values using a specified transform (e.g. discrete cosine transform (DCT) or a variant of it), quantizing the coefficients and entropy coding the quantized coefficients. By varying the fidelity of the quantization process, the encoder may control the balance between the accuracy of the pixel representation (e.g., picture quality) and size of the resulting coded video representation (e.g., file size or transmission bitrate).

[0178] In other example, the pixel values may be predicted by using spatial prediction techniques. This prediction technique uses the pixel values around the block to be coded in a specified manner. Secondly, the prediction error, for example, the difference between the predicted block of pixels and the original block of pixels is coded. This is typically done by transforming the difference in pixel values using a specified transform, for example, discrete cosine transform (DCT) or a variant of it; quantizing the coefficients; and entropy coding the quantized coefficients. By varying the fidelity of the quantization process, encoder can control the balance between the accuracy of the pixel representation, for example, picture quality and size of the resulting coded video representation, for example, file size or transmission bitrate.

[0179] Inter prediction, which may also be referred to as temporal prediction, motion compensation, or motion-compensated prediction, exploits temporal redundancy. In inter prediction the sources of prediction are previously decoded pictures.

[0180] Intra prediction utilizes the fact that adjacent pixels within the same picture are likely to be correlated. Intra prediction can be performed in spatial or transform domain, for example, either sample values or transform coefficients can be predicted. Intra prediction is typically exploited in intracoding, where no inter prediction is applied. [0181] One outcome of the coding procedure is a set of coding parameters, such as motion vectors and quantized transform coefficients. Many parameters can be entropy-coded more efficiently when they are predicted first from spatially or temporally neighboring parameters. For example, a motion vector may be predicted from spatially adjacent motion vectors and only the difference relative to the motion vector predictor may be coded. Prediction of coding parameters and intra prediction may be collectively referred to as in-picture prediction.

[0182] The decoder reconstructs the output video by applying prediction techniques similar to the encoder to form a predicted representation of the pixel blocks. For example, using the motion or spatial information created by the encoder and stored in the compressed representation and prediction error decoding, which is inverse operation of the prediction error coding recovering the quantized prediction error signal in spatial pixel domain. After applying prediction and prediction error decoding techniques the decoder sums up the prediction and prediction error signals, for example, pixel values to form the output video frame. The decoder and encoder can also apply additional filtering techniques to improve the quality of the output video before passing it for display and/or storing it as prediction reference for the forthcoming frames in the video sequence.

[0183] In typical video codecs the motion information is indicated with motion vectors associated with each motion compensated image block. Each of these motion vectors represents the displacement of the image block in the picture to be coded in the encoder side or decoded in the decoder side and the prediction source block in one of the previously coded or decoded pictures.

[0184] In order to represent motion vectors efficiently, the motion vectors are typically coded differentially with respect to block specific predicted motion vectors. In typical video codecs, the predicted motion vectors are created in a predefined way, for example, calculating the median of the encoded or decoded motion vectors of the adjacent blocks.

[0185] Another way to create motion vector predictions is to generate a list of candidate predictions from adjacent blocks and/or co-located blocks in temporal reference pictures and signaling the chosen candidate as the motion vector predictor. In addition to predicting the motion vector values, the reference index of previously coded/decoded picture can be predicted. The reference index is typically predicted from adjacent blocks and/or or co-located blocks in temporal reference picture.

[0186] Moreover, typical high efficiency video codecs employ an additional motion information coding/decoding mechanism, often called merging/merge mode, where all the motion field information, which includes motion vector and corresponding reference picture index for each available reference picture list, is predicted and used without any modification/correction. Similarly, predicting the motion field information is carried out using the motion field information of adjacent blocks and/or co-located blocks in temporal reference pictures and the used motion field information is signaled among a list of motion field candidate list filled with motion field information of available adjacent/co-located blocks.

[0187] In typical video codecs, the prediction residual after motion compensation is first transformed with a transform kernel, for example, DCT and then coded. The reason for this is that often there still exists some correlation among the residual and transform can in many cases help reduce this correlation and provide more efficient coding.

[0188] Typical video encoders utilize Lagrangian cost functions to find optimal coding modes, for example, the desired macroblock mode and associated motion vectors. This kind of cost function uses a weighting factor X to tie together the exact or estimated image distortion due to lossy coding methods and the exact or estimated amount of information that is required to represent the pixel values in an image area:

C = D + R - equation 1

[0189] In equation 1, C is the Lagrangian cost to be minimized, D is the image distortion, for example, mean squared error with the mode and motion vectors considered, and R is the number of bits needed to represent the required data to reconstruct the image block in the decoder including the amount of data to represent the candidate motion vectors.

[0190] A design principle has been followed for SEI message specifications: the SEI messages are generally not extended in future amendments or versions of the standard.

[0191] Filters in video codecs

[0192] Conventional image and video codecs may use a set of filters to enhance the visual quality of the predicted and error-compensated visual content and can be applied either in-loop or out-of-loop, or both. In the case of in-loop filters, a filter applied on one block in the currently-encoded or currently decoded frame will affect the encoding or decoding of another block in the same frame and/or in another frame which is predicted or processed based at least on the current frame. An in-loop filter can affect the bitrate and/or the visual quality. An enhanced block may cause a smaller residual, e.g., a smaller difference between original block and filtered block, thus using less bits in the bitstream output by the encoder. An out-of-loop filter, or post-processing filter, may be applied on a frame or part of a frame after it has been reconstructed; the filtered visual content may not be used for decoding other content.

[0193] Information on Neural Network based Image/Video Coding

[0194] Recently, neural networks (NNs) have been used in the context of image and video compression, by following mainly two approaches.

[0195] In one approach, NNs are used to replace or are used as an addition to one or more of the components of a traditional codec such as VVC/H.266. Here, ‘traditional’ means those codecs whose components and parameters are typically not learned from data by means of a training process, for example, those codecs whose components are not neural networks. Some examples of uses of neural networks within a traditional codec include but are not limited to:

Additional in-loop filter, for example, by having the NN as an additional in-loop filter with respect to the traditional loop filters;

Single in-loop filter, for example, by having the NN replacing all traditional in-loop filters; Intra-frame prediction, for example, as an additional intra-frame prediction mode, or replacing the traditional intra-frame prediction;

Inter-frame prediction, for example, as an additional inter-frame prediction mode, or replacing the traditional inter-frame prediction;

Transform and/or inverse transform, for example, as an additional transform and/or inverse transform, or replacing the traditional transform and/or inverse transform; and

Probability model for the arithmetic codec, for example, as an additional probability model, or replacing the traditional probability model.

[0196] FIG. 8 illustrates examples of functioning of NNs as components of a pipeline of traditional codec, in accordance with an embodiment. In particular, FIG. 8 illustrates an encoder, which also includes a decoding loop. FIG. 8 is shown to include components described below:

A luma intra pred block or circuit 801. This block or circuit performs intra prediction in the luma domain, for example, by using already reconstructed data from the same frame. The operation of the luma intra pred block or circuit 801 may be performed by a deep neural network such as a convolutional auto-encoder.

A chroma intra pred block or circuit 802. This block or circuit performs intra prediction in the chroma domain, for example, by using already reconstructed data from the same frame. The chroma intra pred block or circuit 802 may perform cross-component prediction, for example, predicting chroma from luma. The operation of the chroma intra pred block or circuit 802 may be performed by a deep neural network such as a convolutional autoencoder.

An intra pred block or circuit 803 and an inter-pred block or circuit 804. These blocks or circuit perform intra prediction and in ter -prediction, respectively. The intra pred block or circuit 803 and the inter-pred block or circuit 804 may perform the prediction on all components, for example, luma and chroma. The operations of the intra pred block or circuit 803 and the inter-pred block or circuit 804 may be performed by two or more deep neural networks such as convolutional auto-encoders.

A probability estimation block or circuit 805 for entropy coding. This block or circuit performs prediction of probability for the next symbol to encode or decode, which is then provided to the entropy coding module 812, such as an arithmetic coding module, to encode or decode the next symbol. The operation of the probability estimation block or circuit 805 may be performed by a neural network.

A transform and quantization (T/Q) block or circuit 806. These are actually two blocks or circuits. The transform and quantization block or circuit 806 may perform a transform of input data to a different domain, for example, the FFT transform would transform the data to frequency domain. The transform and quantization block or circuit 806 may quantize its input values to a smaller set of possible values. In the decoding loop, there may be inverse quantization block or circuit and inverse transform block or circuit Q '/T ^-1 806a. One or both of the transform block or circuit and quantization block or circuit may be replaced by one or two or more neural networks. One or both of the inverse transform block or circuit and inverse quantization block or circuit 813 may be replaced by one or two or more neural networks.

An in-loop filter block or circuit 807. Operations of the in-loop filter block or circuit 807 is performed in the decoding loop, and it performs filtering on the output of the inverse transform block or circuit, or on the reconstructed data, in order to enhance the reconstructed data with respect to one or more predetermined quality metrics. This filter may affect both the quality of the decoded data and the bitrate of the bitstream output by the encoder. The operation of the in-loop filter block or circuit 807 may be performed by a neural network, such as a convolutional auto-encoder. In examples, the operation of the inloop filter may be performed by multiple steps or filters, where the one or more steps may be performed by neural networks. A post-processing filter block or circuit 808. The post-processing filter block or circuit 808 may be performed only at decoder side, as it may not affect the encoding process. The postprocessing filter block or circuit 808 filters the reconstructed data output by the in-loop filter block or circuit 807, in order to enhance the reconstructed data. The post-processing filter block or circuit 808 may be replaced by a neural network, such as a convolutional auto-encoder.

A resolution adaptation block or circuit 809: this block or circuit may downsample the input video frames, prior to encoding. Then, in the decoding loop, the reconstructed data may be upsampled, by the upsampling block or circuit 810, to the original resolution. The operation of the resolution adaptation block or circuit 809 block or circuit may be performed by a neural network such as a convolutional auto-encoder.

An encoder control block or circuit 811. This block or circuit performs optimization of encoder’ s parameters, such as what transform to use, what quantization parameters (QP) to use, what intra-prediction mode (out of N intra-prediction modes) to use, and the like. The operation of the encoder control block or circuit 811 may be performed by a neural network, such as a classifier convolutional network, or such as a regression convolutional network. An ME/MC block or circuit 814 performs motion estimation and/or motion compensation, which are two key operations to be performed when performing inter-frame prediction. ME/MC stands for motion estimation / motion compensation

[0197] In another approach, commonly referred to as ‘end-to-end learned compression’, NNs are used as the main components of the image/video codecs. In this second approach, there are following two example options:

[0198] Option 1: re-use the video coding pipeline but replace most or all the components with NNs. Referring to FIG. 9, it illustrates an example of modified video coding pipeline based on neural networks, in accordance with an embodiment. An example of neural network may include, but is not limited, a compressed representation of a neural network. FIG. 9 is shown to include following components:

A neural transform block or circuit 902: this block or circuit transforms the output of a summation/subtraction operation 903 to a new representation of that data, which may have lower entropy and thus be more compressible.

A quantization block or circuit 904: this block or circuit quantizes an input data 901 to a smaller set of possible values. An inverse transform and inverse quantization blocks or circuits 906. These blocks or circuits perform the inverse or approximately inverse operation of the transform and the quantization, respectively.

An encoder parameter control block or circuit 908. This block or circuit may control and optimize some or all the parameters of the encoding process, such as parameters of one or more of the encoding blocks or circuits.

An entropy coding block or circuit 910. This block or circuit may perform lossless coding, for example, based on entropy. One popular entropy coding technique is arithmetic coding. A neural intra-codec block or circuit 912. This block or circuit may be an image compression and decompression block or circuit, which may be used to encode and decode an intra frame. An encoder 914 may be an encoder block or circuit, such as the neural encoder part of an auto-encoder neural network. A decoder 916 may be a decoder block or circuit, such as the neural decoder part of an auto-encoder neural network. An intra-coding block or circuit 918 may be a block or circuit performing some intermediate steps between encoder and decoder, such as quantization, entropy encoding, entropy decoding, and/or inverse quantization.

A deep loop filter block or circuit 920. This block or circuit performs filtering of reconstructed data, in order to enhance it.

A decode picture buffer block or circuit 922. This block or circuit is a memory buffer, keeping the decoded frame, for example, reconstructed frames 924 and enhanced reference frames 926 to be used for inter prediction.

An inter-prediction block or circuit 928. This block or circuit performs inter-frame prediction, for example, predicts from frames, for example, frames 932, which are temporally nearby. An ME/MC 930 performs motion estimation and/or motion compensation, which are two key operations to be performed when performing inter-frame prediction. ME/MC stands for motion estimation / motion compensation.

[0199] In order to train the neural networks of this system, a training objective function, referred to as ‘training loss’ , is typically utilized, which usually comprises one or more terms, or loss terms, or simply losses. Although here the Option 2 and FIG. 10 considered as example for describing the training objective function, a similar training objective function may also be used for training the neural networks for the systems in FIG. 6 and FIG. 7. In an example, the training loss comprises a reconstruction loss term and a rate loss term. The reconstruction loss encourages the system to decode data that is similar to the input data, according to some similarity metric. Following are some examples of reconstruction losses are: a loss derived from mean squared error (MSE); a loss derived from multi-scale structural similarity (MS-SSIM), such as 1 minus MS- SSIM, or 1 - MS-SSIM; losses derived from the use of a pretrained neural network. For example, error(f 1 , f2), where fl and f2 are the features extracted by a pretrained neural network for the input (uncompressed) data and the decoded (reconstructed) data, respectively, and error() is an error or distance function, such as LI norm or L2 norm; and losses derived from the use of a neural network that is trained simultaneously with the end- to-end learned codec. For example, adversarial loss can be used, which is the loss provided by a discriminator neural network that is trained adversarially with respect to the codec, following the settings proposed in the context of generative adversarial networks (GANs) and their variants.

[0200] The rate loss encourages the system to compress the output of the encoding stage, such as the output of the arithmetic encoder. ‘Compressing’ for example, means reducing the number of bits output by the encoding stage.

[0201] When an entropy-based lossless encoder is used, such as the arithmetic encoder, the rate loss typically encourages the output of the Encoder NN to have low entropy. The rate loss may be computed on the output of the Encoder NN, or on the output of the quantization operation, or on the output of the probability model. Following are some examples of rate losses are the following:

A differentiable estimate of the entropy;

A sparsification loss, for example, a loss that encourages the output of the Encoder NN or the output of the quantization to have many zeros. Examples are L0 norm, LI norm, LI norm divided by L2 norm; and

A cross-entropy loss applied to the output of a probability model, where the probability model may be a NN used to estimate the probability of the next symbol to be encoded by the arithmetic encoder.

[0202] For training one or more neural networks that are part of a codec, such as one or more neural networks in FIG. 8 and/or FIG. 9, one or more of reconstruction losses may be used, and one or more of rate losses may be used. The loss terms may then be combined for example as a weighted sum to obtain the training objective function. Typically, the different loss terms are weighted using different weights, and these weights determine how the final system performs in terms of rate-distortion loss. For example, when more weight is given to one or more of the reconstruction losses with respect to the rate losses, the system may learn to compress less but to reconstruct with higher accuracy as measured by a metric that correlates with the reconstruction losses. These weights are usually considered to be hyperparameters of the training session and may be set manually by the operator designing the training session, or automatically for example by grid search or by using additional neural networks.

[0203] For the sake of explanation, video is considered as data type in various embodiments. However, it would be understood that the embodiments are also applicable to other media items, for example, images and audio data.

[0204] Option 2 is illustrated in FIG. 10, and it includes of a different type of codec architecture. Referring to FIG. 10, it illustrates an example neural network-based end-to-end learned video coding system, in accordance with an example embodiment. As shown FIG. 10, a neural network-based end- to-end learned video coding system 1000 includes an encoder 1001, a quantizer 1002, a probability model 1003, an entropy codec 1004, for example, an arithmetic encoder 1005 and an arithmetic decoder 1006, a dequantizer 1007, and a decoder 1008. The encoder 1001 and the decoder 1008 are typically two neural networks, or mainly comprise neural network components. The probability model 1003 may also mainly comprise neural network components. The quantizer 1002, the dequantizer 1007, and the entropy codec 1004 are typically not based on neural network components, but they may also potentially comprise neural network components. In some embodiments, the encoder, quantizer, probability model, entropy codec, arithmetic encoder, arithmetic decoder, dequantizer, and decoder, may also be referred to as an encoder component, quantizer component, probability model component, entropy codec component, arithmetic encoder component, arithmetic decoder component, dequantizer component, and decoder component respectively.

[0205] On the encoding side, the encoder 1001 takes a video/image as an input 1009 and converts the video/image in original signal space into a latent representation that may comprise a more compressible representation of the input. The latent representation may be normally a 3-dimensional tensor for image compression, where 2 dimensions represent spatial information, and the third dimension contains information at that specific location.

[0206] Consider an example, in which the input data is an image, when the input image is a 128x128x3 RGB image (with horizontal size of 128 pixels, vertical size of 128 pixels, and 3 channels for the Red, Green, Blue color components), and when the encoder downsamples the input tensor by 2 and expands the channel dimension to 32 channels, then the latent representation is a tensor of dimensions (or ‘shape’) 64x64x32 (e.g., with horizontal size of 64 elements, vertical size of 64 elements, and 32 channels). Please note that the order of the different dimensions may differ depending on the convention which is used. In some embodiments, for the input image, the channel dimension may be the first dimension, so for the above example, the shape of the input tensor may be represented as 3x128x128, instead of 128x128x3.

[0207] In the case of an input video (instead of just an input image), another dimension in the input tensor may be used to represent temporal information.

[0208] The quantizer 1002 quantizes the latent representation into discrete values given a predefined set of quantization levels. The probability model 1003 and the arithmetic encoder 1005 work together to perform lossless compression for the quantized latent representation and generate bitstreams to be sent to the decoder side. Given a symbol to be encoded to the bitstream, the probability model 1003 estimates the probability distribution of all possible values for that symbol based on a context that is constructed from available information at the current encoding/decoding state, such as the data that has already encoded/decoded. The arithmetic encoder 1005 encodes the input symbols to bitstream using the estimated probability distributions.

[0209] On the decoding side, opposite operations are performed. The arithmetic decoder 1006 and the probability model 1003 first decode symbols from the bitstream to recover the quantized latent representation. Then, the dequantizer 1007 reconstructs the latent representation in continuous values and pass it to the decoder 1008 to recover the input video/image. The recovered input video/image is provided as an output 1010. Note that the probability model 1003, in this system 1000, is shared between the arithmetic encoder 1005 and the arithmetic decoder 1006. In practice, this means that a copy of the probability model 1003 is used at the arithmetic encoder 1005 side, and another exact copy is used at the arithmetic decoder 1006 side.

[0210] In this system 1000, the encoder 1001, the probability model 1003, and the decoder 1008 are normally based on deep neural networks. The system 1000 is trained in an end-to-end manner by minimizing the following rate-distortion loss function, which may be referred to simply as training loss, or loss:

L=D+/.R - equation 2

[0211] In equation 2, D is the distortion loss term, R is the rate loss term, and X is the weight that controls the balance between the two losses. [0212] The distortion loss term may be referred to also as reconstruction loss. It encourages the system to decode data that is similar to the input data, according to some similarity metric. Examples of reconstruction losses are: a loss derived from mean squared error (MSE); a loss derived from multi-scale structural similarity (MS-SSIM), such as 1 minus MS- SSIM, or 1 - MS-SSIM; losses derived from the use of a pretrained neural network. For example, error(f 1 , f2), where fl and f2 are the features extracted by a pretrained neural network for the input (uncompressed) data and the decoded (reconstructed) data, respectively, and error() is an error or distance function, such as LI norm or L2 norm; and losses derived from the use of a neural network that is trained simultaneously with the end- to-end learned codec. For example, adversarial loss can be used, which is the loss provided by a discriminator neural network that is trained adversarially with respect to the codec, following the settings proposed in the context of generative adversarial networks (GANs) and their variants.

[0213] Multiple distortion losses may be used and integrated into D.

[0214] Minimizing the rate loss encourages the system to compress the quantized latent representation so that the quantized latent representation can be represented by a smaller number of bits. The rate loss may be computed on the output of the encoder NN, or on the output of the quantization operation, or on the output of the probability model. In an example embodiment, the rate loss may comprise multiple rate losses. Example of rate losses are the following: a differentiable estimate of the entropy of the quantized latent representation, which indicates the number of bits necessary to represent the encoded symbols, for example, bits- per-pixel (bpp); a sparsification loss, for example, a loss that encourages the output of the Encoder NN or the output of the quantization to have many zeros. Examples are L0 norm, LI norm, LI norm divided by L2 norm; and a cross-entropy loss applied to the output of a probability model, where the probability model may be a NN used to estimate the probability of the next symbol to be encoded by the arithmetic encoder 1005. [0215] A similar training loss may be used for training the systems illustrated in FIG. 8 and FIG. 9.

[0216] For training one or more neural networks that are part of a codec, such as one or more neural networks in FIG. 8, FIG. 9 and/or FIG. 10, one or more of reconstruction losses may be used, and one or more of the rate losses may be used. All the loss terms may then be combined for example as a weighted sum to obtain the training objective function. Typically, the different loss terms are weighted using different weights, and these weights determine how the final system performs in terms of rate-distortion loss. For example, when more weight is given to one or more of the reconstruction losses with respect to the rate losses, the system may learn to compress less but to reconstruct with higher accuracy as measured by a metric that correlates with the reconstruction losses. These weights are usually considered to be hyper-parameters of the training session and may be set manually by the operator designing the training session, or automatically for example by grid search or by using additional neural networks.

[0217] In an example embodiment, the rate loss and the reconstruction loss may be minimized jointly at each iteration. In another example embodiment, the rate loss and the reconstruction loss may be minimized alternately, e.g., in one iteration the rate loss is minimized and in the next iteration the reconstruction loss is minimized, and so on. In yet another example embodiment, the rate loss and the reconstruction loss may be minimized sequentially, e.g., first one of the two losses is minimized for a certain number of iterations, and then the other loss is minimized for another number of iterations. These different ways of minimizing rate loss and reconstruction loss may also be combined.

[0218] It is to be understood that even in end-to-end learned approaches, there may be components which are not learned from data, such as an arithmetic codec.

[0219] For lossless video/image compression, the system 1000 contains the probability model 1003, the arithmetic encoder 1005, and the arithmetic decoder 1006. The system loss function contains the rate loss, since the distortion loss is always zero, in other words, no loss of information.

[0220] Video Coding for Machines (VCM)

[0221] Reducing the distortion in image and video compression is often intended to increase human perceptual quality, as humans are considered to be the end users, e.g. consuming or watching the decoded images or videos. Recently, with the advent of machine learning, especially deep learning, there is a rising number of machines (e.g., autonomous agents) that analyze or process data independently from humans and may even take decisions based on the analysis results without human intervention. Examples of such analysis are object detection, scene classification, semantic segmentation, video event detection, anomaly detection, pedestrian tracking, and the like. Example use cases and applications are self-driving cars, video surveillance cameras and public safety, smart sensor networks, smart TV and smart advertisement, person re-identification, smart traffic monitoring, drones, and the like. Accordingly, when decoded data is consumed by machines, a quality metric for the decoded data may be defined, which may be different from a quality metric for human perceptual quality. Also, dedicated algorithms for compressing and decompressing data for machine consumption may be different than those for compressing and decompressing data for human consumption. The set of tools and concepts for compressing and decompressing data for machine consumption is referred to here as Video Coding for Machines.

[0222] The receiver or decoder-side device may have multiple ‘machines’ or neural networks (NNs) for analyzing or processing decoded data. These multiple machines may be used in a certain combination which is for example determined by an orchestrator sub-system. The multiple machines may be used for example in temporal succession, based on the output of the previously used machine, and/or in parallel. For example, a video which was compressed and then decompressed may be analyzed by one machine (NN) for detecting pedestrians, by another machine (another NN) for detecting cars, and by another machine (another NN) for estimating the depth of objects in the frames.

[0223] An ‘encoder-side device’ may encode input data, such as a video, into a bitstream which represents compressed data. The bitstream is provided to a ‘decoder-side device’ . The term ‘receiverside’ or ’decoder-side’ refers to a physical or abstract entity or device which performs decoding of compressed data, and the decoded data may be input to one or more machines, circuits or algorithms. The one or more machines may not be part of the decoder. The one or more machines may be run by the same device running the decoder or by another device which receives the decoded data from the device running the decoder. Different machines may be run by different devices.

[0224] The encoded video data may be stored into a memory device, for example, as a file. The stored file may later be provided to another device.

[0225] Alternatively, the encoded video data may be streamed from one device to another.

[0226] In various embodiments, machine and neural network may be used interchangeably, and may mean any process or algorithm (e.g., learned from data or not) which analyzes or processes data for a certain task. Further, the term ‘receiver-side’ or ‘decoder-side’ refers to a physical or abstract entity or device which contains one or more machines, and runs these one or more machines on some encoded and eventually decoded video representation which is encoded by another physical or abstract entity or device, e.g., ‘encoder-side device’. In some embodiments, the encoder-side and decoder-side may be present in the same physical or abstract entity or device.

[0227] FIG. 11 illustrates a pipeline of video coding for machines (VCM), in accordance with an embodiment. A VCM encoder 1102 encodes the input video into a bitstream 1104. A bitrate 1106 may be computed 1108 from the bitstream 1104 in order to evaluate the size of the bitstream 1104. A VCM decoder 1110 decodes the bitstream 1104 output by the VCM encoder 1102. An output of the VCM decoder 1110 may be referred, for example, as decoded data for machines 1112. This data may be considered as the decoded or reconstructed video. However, in some implementations of the pipeline of VCM, the decoded data for machines 1112 may not have same or similar characteristics as the original video which was input to the VCM encoder 1102. For example, this data may not be easily understandable by a human, if the human watches the decoded video from a suitable output device such as a display. The output of the VCM decoder 1110 is then input to one or more task neural network (task-NN). For the sake of illustration, FIG. 11 is shown to include three example task-NNs, a task-NN 1114 for object detection, a task-NN 1116 for image segmentation, a task-NN 1118 for object tracking, and a non-specified one, a task-NN 1120 for performing task X. The goal of VCM is to obtain a low bitrate while guaranteeing that the task-NNs still perform well in terms of the evaluation metric associated with each task.

[0228] One of the possible approaches to realize video coding for machines is an end-to-end learned approach. FIG. 12 illustrates an example of an end-to-end learned approach, in accordance with an embodiment. In this approach, a VCM encoder 1202 and a VCM decoder 1204 mainly consist of neural networks. The video is input to a neural network encoder 1206. The output of the neural network encoder 1206 is input to a lossless encoder 1208, such as an arithmetic encoder, which outputs a bitstream 1210. The lossless codec may take an additional input from a probability model 1212, both in the lossless encoder 1208 and in a lossless decoder 1214, which predicts the probability of the next symbol to be encoded and decoded. The probability model 1212 may also be learned, for example it may be a neural network. At a decoder-side, the bitstream 1210 is input to the lossless decoder 1214, such as an arithmetic decoder, whose output is input to a neural network decoder 1216. The output of the neural network decoder 1216 is a decoded data for machines 1218, that may be input to one or more task-NNs, a task-NN 1220 for object detection, a task-NN 1222 for object segmentation, a task-NN 1224 for object tracking, and a non-specified one, a task-NN 1226 for performing task X. [0229] FIG. 13 illustrates an example of how the end-to-end learned system may be trained, in accordance with an embodiment. For the sake of simplicity, only one task-NN is illustrated. However, it may be understood that multiple task-NNs may be similarly used in the training process. A rate loss 1302 may be computed 1304 from the output of a probability model 1306. The rate loss 1302 provides an approximation of the bitrate required to encode the input video data, for example, by a neural network encoder 1308. A task loss 1310 may be computed 1312 from a task output 1314 of a task-NN 1316.

[0230] The rate loss 1302 and the task loss 1310 may then be used to train 1318 the neural networks used in the system, such as the neural network encoder 1308, probability model, a neural network decoder 1320. Training may be performed by first computing gradients of each loss with respect to the trainable parameters of the neural networks that are contributing or affecting the computation of that loss. The gradients are then used by an optimization method, such as Adam, for updating the trainable parameters of the neural networks. It is to be understood that, in alternative or in addition to one or more task losses and/or one or more rate losses, the training process may use additional losses which may not be directly related to one or more specific tasks, such as losses derived from pixel-wise distortion metrics (for example, MSE, MS-SSIM).

[0231] The machine tasks may be performed at decoder side (instead of at encoder side) for multiple reasons, for example, the encoder-side device may not have the capabilities (e.g. computational, power, or memory) for running the neural networks that perform these tasks, or some aspects or the performance of the task neural networks may have changed or improved by the time that the decoder-side device needs the tasks results (e.g., different or additional semantic classes, better neural network architecture). Also, there may be a need for customization, where different clients may run different neural networks for performing these machine learning tasks.

[0232] Neural Network Based Filtering

[0233] In some video codecs, a neural network may be used as filter in the decoding loop, and it may be referred to as neural network loop filter, or neural network in-loop filter. The NN loop filter may replace other loop filters of an existing video codec or may represent an additional loop filter with respect to the already present loop filters in an existing video codec.

[0234] In the context of image and video enhancement, a neural network may be used as postprocessing filter, for example, applied to the output of an image or video decoder in order to remove or reduce coding artifacts. [0235] Some of the proposed embodiments relates to neural networks used as part of the decoding operations (such as a NN loop filter, or an intra-frame prediction NN, or an inter-frame prediction NN) or as part of post-processing operations (e.g., a NN post-processing filter). The embodiments also related to signaling of information related to those NNs, where the information is signaled from an encoder to a decoder.

[0236] The following example system may be used in several embodiments to illustrate or describe the idea. The example system comprises a VVC/H.266 compliant codec and a post-processing NN (NN post-filter), where the NN post-filter is used on the output of the decoder in order to enhance the quality of the output of the decoder (e.g., a decoded frame). Quality may be measured in terms of a metric that may include one or more of the following:

Mean-squared error (MSE);

Peak signal- to-noise ratio (PSNR);

Mean Average Precision (mAP) computed based on the output of a task NN (such as an object detection NN) when the input is the output of the post-processing NN; or Other task-related metric, for tasks such as object tracking, video activity classification, video anomaly detection, and the like.

[0237] The enhancement may result into a coding gain, which may be expressed, for example, in terms of Bjontegaard delta rate (BD-rate) or BD-PSNR.

[0238] Information on overfitting

[0239] At encoding phase, when an input needs to be encoded (such as an image or a video sequence), an encoder may change one or more parameters of one or more neural networks comprised in a codec, and/or one or more signals produced by one or more neural networks comprised in a codec, based at least on the input to the encoder and on the output of the one or more neural networks comprised in the codec, in order to improve a rate-distortion performance of the codec. It at least some embodiments described herein, this operation may be referred to as ‘optimizing’, ‘adapting’, ‘finetuning’, ‘updating’, or ’overfitting’ the one or more parameters and/or the one or more signals. In the literature, this operation may be referred to as content-based adaptation, where the content comprises an input to the encoder. The one or more parameters that may be overfitted by the encoder may comprise, but are not limited to, one or more of the following:

One or more trainable parameters or weights of one or more neural networks that are comprised in an encoder; One or more trainable parameters or weights of one or more neural networks that are comprised in a decoder; or

One or more parameters or weights of one or more neural networks that are comprised in one or more post-processing operations.

[0240] In one example, the one or more of trainable parameters or weights that are overfitted by the encoder are one or more bias parameters comprised in one or more convolutional layers of a postprocessing filter.

[0241] The one or more signals that may be overfitted by the encoder may comprise, but are not limited to, the output of an end-to-end learned encoder neural network. In one example, the one or more signals comprise a latent tensor output by an end-to-end learned encoder neural network.

[0242] The optimization may be performed at encoder-side, and may comprise one or more optimization iterations, where one optimization iterations may comprise one or more of the following operations:

Computing a loss function based on an input to the encoder (or a signal derived from the input to the encoder) and on an output of one or more neural networks (or a signal derived from an output of the one or more neural networks);

Computing one or more gradients of the computed loss function with respect to one or more parameters of one or more neural networks comprised in the codec;

• And/or computing one or more gradients of the computed loss function with respect to one or more signals produced by one or more neural networks comprised in the codec; or

Updating the one or more parameters and/or the one or more signals.

[0243] The optimization may be performed until a stopping criterion is met. In one example, the optimization is performed until a predetermined number of iterations has been performed. In another example, the optimization is performed until a predetermined value of the loss function, or a predetermined value of a performance level of the codec, has been obtained.

[0244] Once the optimization is complete, the overfitted one or more parameters of one or more neural networks and/or the overfitted one or more signals produced by one or more neural networks may be used in an inference phase for encoding or decoding or post-processing. [0245] When the one or more parameters or the one or more signals to be optimized are comprised in the decoder or in the post-processing operations, an update to those parameters or signals (such update may be referred to as weight-update for simplicity) may need to be encoded and signaled to the decoderside. The bitrate of the bitstream representing such signaling may represent an additional bitrate (also referred to as bitrate overhead) with respect to the bitrate of the bitstream representing the encoded image or video. In order to increase a rate-distortion performance of a codec, it may be advantageous to decrease the bitrate overhead. This may be achieved by a bitrate reduction process, which may comprise, but may not be limited to, one or more of the following:

Selecting a subset of the parameters and/or signals of one or more neural networks comprised in the decoder or in the post-processing operations, and overfitting the selected subset; or

Compressing the weight-update using a lossy and/or a lossless codec.

[0246] Information on decomposed tensors and on tensor decomposition

[0247] In neural networks, several types of decomposed tensors may be used to represent the weight tensors

[0248] One of the advantages of decomposed weight tensors is that the sum of the number of elements of the decomposed weight tensors is smaller than the number of elements of the original weight tensor. This may lead to a lower computational and memory complexity of the NN inference and, sometimes, also of the NN training.

[0249] Examples of decomposed tensors used in NNs are:

Depth-wise separable convolutions: each kernel is applied only to a single input channel.

Tensors obtained by means of canonical polyadic (CP) decomposition. These comprise the following components:

• A convolutional layer with kernels of spatial size equal to 1x1 and a lower number of kernels (and thus smaller number of output channels) than its input tensor. The output of this component is a tensor with a reduced number of channels with respect to its input tensor.

• Two separable (both in depth and in spatial dimensions) convolutional layers.

• A convolutional layer with kernels of spatial size equal to 1x1 and a higher number of kernels (and thus higher number of output channels) than its input tensor. Tensors obtained by means of Tucker decomposition. These comprise the following:

• A convolutional layer with kernels of spatial size equal to 1x1 and a lower number of kernels (and thus smaller number of output channels) than its input tensor. The output of this component is a tensor with a reduced number of channels with respect to its input tensor.

• Two (regular) convolutional layers

• A convolutional layer with kernels of spatial size equal to 1x1 and a higher number of kernels (and thus higher number of output channels) than its input tensor.

Matrix (e.g., comprising the weights of a fully connected layer) obtained by computing the Singular Value Decomposition (SVD) of an input tensor and then truncating to top N singular values.

[0250] In some examples, given an input tensor, it is possible to obtain decomposed tensors.

[0251] In an example, it is possible to obtain depth-wise separable convolutions from an input trained weight tensor by using the network decoupling method in (last accessed on October 10, 2022).

[0252] In another example, CP decomposition may be used. In another example, Tucker decomposition may be used.

[0253] In some examples, training directly a NN comprising decomposed weight tensors may not always be possible, or may be less efficient (e.g., in terms of training time) than training a similar NN comprising non-decomposed weights tensors.

[0254] Overfitting one or more parameters or signals of one or more neural networks comprised in a codec or in one or more post-processing operations may improve a rate-distortion performance of the codec or of the one or more post-processing operations. However, prior art approaches have targeted the overfitting of linear operations, for example one or more of the following:

The convolutional layer’s weights;

The bias parameters; or

The multiplier parameters. [0255] It is known that non-linear operations are more expressive or powerful for modeling functions; this is one of the strengths of neural networks compared to linear modeling techniques. Overfitting non-linear operations may achieve better improvements of a rate-distortion performance compared to overfitting linear operations.

[0256] However, one of the problems not addressed by prior art overfitting techniques is the overfitting of non-linear operations. This is one of the problems addressed by at least some of the embodiments described herein.

[0257] Further, another example problem is that, in order to obtain good rate-distortion performance improvement, the encoded weight-update may require a high bitrate, which in turn may hinder the coding gains (e.g., in terms of BD-rate). Finding new ways to decrease the bitrate overhead represented by the encoded weight-update is an open problem and is another example problem addressed by at least some of the embodiments described herein.

[0258] In an embodiment, an encoder may overfit one or more parameters of one or more nonlinear functions comprised in one or more neural networks, based at least on an input to the encoder.

[0259] In one embodiment, an encoder may determine whether one or more non-linear activation (NLA) functions comprised in one or more neural networks shall be used or not.

[0260] In one embodiment, an encoder may determine one or more weights that may be used for weighting the output of respective one or more NLA functions in one or more neural networks.

[0261] Following sections provide more details and embodiments.

[0262] Preliminary information

[0263] In at least some of the embodiments, compressing and decompressing data by using a codec is considered. For the sake of simplicity, in at least some of the embodiments, video is considered as the data type. However, the proposed embodiments may be extended to other types of data such as images, audio, and the like.

[0264] An encoder-side device performs a compression or encoding operation of an input video by using a video encoder. The output of the video encoder is a bitstream representing the compressed video. A decoder-side device performs decompression or decoding operation of the compressed video by using a video decoder. The output of the video decoder may be referred to as decoded video. The decoded video may be post-processed by one or more post-processing operations, such as a postprocessing filter. The output of the one or more post-processing operations may be referred to as postprocessed video.

[0265] The encoder-side device may also include at least some decoding operations, for example, in a coding loop, and/or at least some post-processing operations. In an example, the encoder may include all the decoding operations and any post-processing operations.

[0266] The encoder-side device and the decoder-side device may be comprised within the same physical device, or within different physical devices.

[0267] The encoder, the encoder-side device, the decoder, and/or the decoder-side device may comprise one or more neural networks. Some examples of such neural networks are the following:

A post-processing NN filter (also referred to here as post-filter, or NN post-filter, or post-filter NN), which takes as input at least one of the outputs of an end-to-end learned decoder or of a conventional decoder (e.g., a decoder not comprising neural networks or other components learned from data) or of a hybrid decoder (e.g., a decoder comprising one or more neural networks or other components learned from data).

A NN in-loop filter (also referred to here as in-loop NN filter, or NN loop filter, or loop NN filter), used within an end-to-end learned decoder, or within a hybrid decoder.

A learned probability model (e.g., a NN) that is used for providing estimates of probabilities of symbols to be encoded and/or decoded by a lossless coding module, within an end-to-end learned codec or within a hybrid codec.

An encoder neural network for an end-to-end learned codec.

A decoder neural network for an end-to-end learned codec.

[0268] In at least some of the embodiments described herein, the example of one or more neural networks representing one or more post-processing filters is considered. However, at least some of the embodiments may be applied also to neural networks representing other operations performed at decoder side, such as an in-loop filter, a learned probability model, a decoder neural network.

[0269] Overfitting the parameters of parametric non-linear functions [0270] In an embodiment, an encoder may overfit one or more parameters of one or more nonlinear functions comprised in one or more neural networks based at least on an input to the encoder, where the one or more neural networks may be comprised in a codec and/or in one or more postprocessing operations.

[0271] In an example, the one or more non-linear functions may be parametric rectified linear units (PReLUs), and the one or more parameters are the slopes of the negative side of the PReLU functions. The equation describing the PReLU function is as follows:

[0272] Where x represents an input to the PReLU function, a represents the slope of the negative side of the PReLU function, f(x) represents the output of the PReLU function when the input is x. When the input x is less than or equal to 0, the output of the PReLU function is equal to x multiplied by a slope a. When the input x is greater than 0, the output of the PReLU function is equal to x.

[0273] Following graphs illustrate difference between a ReLU and a PReLU. For example, for ReLU /(x) = 0 for x < 0; for PReLU /(x) = ax for x < 0.

[0274] The slope a is the parameter of the PReLU function that may be overfitted by the encoder. In particular, the encoder may perform one or more of the following operations:

Select one or more PReLU functions that are comprised within one or more neural networks; For each of the selected one or more PReLU functions, provide an input. For example, when the one or more neural networks comprise a post-processing NN filter, the input to such a filter may be a decoded video frame that is output by a video decoder. Then, the input to each of the selected one or more PReLU functions may be features extracted by one or more of the neural network layers the precede that PReLU function, based at least on an input to the neural network that comprises that PReLU function;

For each of the selected one or more PReLU functions, obtain an output based at least on the provided input;

For each of the selected one or more PReLU functions, compute a gradient of its output with respect to the slope of that PReLU function;

For each of the selected one or more PReLU functions, compute an update to the slope based at least on the computed gradient;

For each of the selected one or more PReLU functions, compute an updated slope based at least on the computed update;

Repeat one or more of the previous steps until a criterion is met, to obtain one or more updated slopes (also referred to as one or more overfitted slopes);

The one or more neural networks are updated based at least on the one or more updated slopes or on one or more slopes that are derived from the one or more updated slopes, to obtain one or more overfitted neural networks; and/or

The one or more overfitted neural networks may be used in an inference, for example for filtering a decoded video frame.

[0275] The overfitted one or more parameters (e.g., the overfitted slopes), an indication of the overfitted one or more parameters, or a signal derived from the overfitted one or more parameters (e.g., a compressed representation) may be signaled from the encoder to the decoder in or along the bitstream. The encoder may perform one or more of the following operations:

Compressing the overfitted one or more parameters based at least on a lossy and/or on a lossless codec (this codec may be a different codec than the codec within which the one or more neural networks may be comprised); or

Signaling the compressed overfitted one or more parameters to the decoder, in or along the bitstream.

[0276] In an example, the decoder may perform one or more of the following operations: Receiving or parsing the compressed overfitted one or more parameters, from or along the bitstream; Decompressing the compressed overfitted one or more parameters, based at least on a codec;

Updating one or more parameters of one or more neural networks based at least on the decompressed overfitted one or more parameters; or

Performing an inference of the one or more neural networks comprising the updated one or more parameters.

[0277] In an embodiment, the encoder may perform the following operations:

Computing an update to the one or more parameters based on the overfitted one or more parameters;

Compressing the update to the one or more parameters based at least on a lossy and/or on a lossless codec (this codec may be a different codec than the codec within which the one or more neural networks may be comprised); or

Signaling the compressed update to the one or more parameters to the decoder, within or along the bitstream.

[0278] In one example, the decoder may perform one or more of the following operations: Receiving or parsing the compressed update to the one or more parameters, from or along the bitstream;

Decompressing the compressed update to the one or more parameters, based at least on a codec;

Updating one or more parameters of one or more neural networks based at least on the decompressed update to the one or more parameters; or

Performing an inference of the one or more neural networks comprising the updated one or more parameters.

[0279] Overfitting the usage of non-linear functions

[0280] In an embodiment, one or more neural networks may comprise one or more non-linear activation (NLA) functions. An encoder may determine whether one or more of the one or more NLA functions shall be used or not. The encoder may signal to the decoder information of whether one or more NLA functions shall be used. In one example, the signaled information may comprise one or more binary flags for the respective one or more NLA functions. In another example, the signaled information may comprise an indication of which subset of NLA functions is to be used out of several subsets of NLA functions. In yet another example, the signaled information may comprise a list of identifier values, where each identifier value identifies an NLA function. The mapping of identifier values to NLA functions may, for example, be pre-defined in a coding standard or specification. In another example, an identifier value, such as a URI, may not be pre-defined but may uniquely identify the NLA function. In addition to identifying an NLA function, the signaled information may comprise parameter values for the NLA function, such as one or more parameter values indicative of the slopes of the negative side of the PReLU function. The signaled information may be carried in or along the bitstream. In an embodiment, the signaled information is carried in an APS that has a type (aps_params_type) indicating that the APS comprises NLA functions.

[0281] In an embodiment, one or more of the one or more NLA functions are applied to all elements of an input tensor. Thus, the encoder may determine (and signal) whether one or more NLA functions shall be used on the respective one or more input tensors.

[0282] In another embodiment, one or more of the one or more NLA functions are applied to all elements of one or more channels of an input tensor. Thus, the encoder may determine (and signal) whether one or more NLA functions shall be used on the respective one or more channels of an input tensor.

[0283] In another embodiment, one or more of the one or more NLA functions are applied to all elements at one or more spatial positions of an input tensor. Thus, the encoder may determine (and signal) whether one or more NLA functions shall be used on the respective one or more spatial positions of an input tensor.

[0284] In another embodiment, one or more of the one or more NLA functions are applied to each element of an input tensor. Thus, the encoder may determine (and signal) whether one or more NLA functions shall be used on the respective one or more elements of an input tensor. In this embodiment, the encoder decides whether the associated NLA function shall be used or not separately for each element of an input tensor.

[0285] In an embodiment, a combination of the above mentioned embodiments may be also possible.

[0286] In an embodiment, the encoder may signal which subset of the NLA functions applies with an identified or inferred neural network inference. For example, the encoder may signal in or along the bitstream, such as in the picture header, the APS identifier that comprises the NLA functions to be used with neural-network-based in-loop filtering. The neural network used for in-loop filtering may be pre-defined, inferred (by an encoder and/or a decoder), indicated in or along the bitstream (by an encoder), or decoded from or along the bitstream (by a decoder).

[0287] In an embodiment, the encoder may signal which NLA function among the indicated or inferred subset of the NLA functions are to be used per one or more channels of the input tensor, per one or more spatial positions of the input tensor, or per element of the input tensor. In an example, an encoder signals a list of indices among the indicated or inferred subset of the NLA functions, where each signaled index identifies the NLA function to be used for the respective channel. In another example, an encoder signals a list of indices among the indicated or inferred subset of the NLA functions, where each signaled index identifies the NLA function to be used for the respective spatial position or element. In yet another example, an encoder signals a list of pairs, each comprising an index among the indicated or inferred subset of the NLA functions and a count of spatial positions or elements, where each signaled pair identifies the NLA function to be used for the count of spatial positions or elements in a pre-defined order within the input tensor.

[0288] In an example, the one or more neural networks may comprise one or more portions, where at least one portion may comprise two or more parallel branches. One or more of the two or more parallel branches comprise one or more NLA functions, and the input to parallel branches is same or substantially same or may be derived from another signal, and the outputs from the parallel branches are combined. For one or more of the parallel branches, an encoder may determine whether one or more NLA functions comprised in the one or more parallel branches shall be used, based at least on an input to the encoder and on an output of the one or more neural networks. Based on the determination, the encoder may signal one or more binary flags to a decoder.

[0289] FIG. 14 illustrates an example of a portion of a NN 1401, where an input to the portion 1402 is provided to a convolutional layer (Conv) 1404, in accordance with an embodiment. The output of Conv 1404 is a tensor, Input to NLA functions 1406, which is input to two parallel branches, where each parallel branch comprises at least a NLA function. It is to be noted that each of the parallel branches may comprise additional operations than a NLA function. A first parallel branch comprises a PReLU function 1408, a second parallel branch comprises a gaussian error linear unit (GeLU) function 1410. One of the two NLA functions, and thus one of the two parallel branches, may be selected by using a selection module or circuit 1414, according to information that is signaled from the encoder, ‘signaling from encoder’ 1412. Based on such selection done by a selection module or circuit 1414, the output, ‘output from portion’ 1416 may be either the output of the first branch or the output of the second branch. [0290] FIG. 15 illustrates another example of a portion of a NN 1501, where an input to the portion 1502 is provided to two parallel branches, in accordance with an embodiment. In this example, a first parallel branch comprises a convolutional layer ‘Convl’ 1504 and a PReLU function 1506, a second parallel branch comprises a convolutional layer ‘Conv2’ 1508 and a GeLU function 1510. One of the two parallel branches may be selected, by using selection module or circuit 1512, according to information that is signaled from the encoder, ‘signaling from encoder’ 1514. Based on such selection, an output ‘output from portion’ 1516 may be either the output of the first branch or the output of the second branch.

[0291] Overfitting the weighting of non-linear functions

[0292] In an embodiment, one or more neural networks may comprise one or more non-linear activation (NLA) functions. One or more weights may be used for weighting the output of respective one or more NLA functions in one or more neural networks. In an embodiment, a decoder side device may determine the one or more weights. In another embodiment, an encoder may determine the one or more weights. The encoder may signal to the decoder information about the determined one or more weights. The signaled information may comprise the determined one or more weights, or data derived from the determined one or more weights, or indications of the determined one or more weights, or an indication of a predetermined set of one or more weights. The signaled information may be carried within or along the bitstream. In one example, the decoder side device comprises or has access to one or more predetermined sets of one or more weights, where each of the one or more predetermined sets is associated to (or can be identified by means of) an identifier. The encoder signals an identifier of an optimal predetermined set to the decoder. The decoder uses the identifier to retrieve (e.g., via a look-up table) the associated predetermined set. The one or more weights comprised in the retrieved predetermined set is then used for weighting the output of one or more NLA functions in one or more neural networks.

[0293] In an embodiment, one or more of the one or more NLA functions are applied to all elements of an input tensor. One or more weights may be used for weighting the respective one or more NLA functions that are applied to respective one or more input tensors. In an embodiment, a decoder may determine the one or more weights. In another embodiment, an encoder may determine the one or more weights, and signal the determined one or more weights to a decoder. In one example, a neural network comprises a first neural network layer or block that outputs two tensors, two non-linear activation function (NLA) layers that are applied to the respective two tensors output by the first neural network layer or block, a weighting operation, a convolutional layer. An input data is input to the first neural network layer or block. The two tensors output by the first neural network layer or block are input to the respective two non-linear activation function layers. The two tensors output by the nonlinear activation function layers are input to the weighting operation. The weighting operation weights the two input tensors based at least on two weights, where the two weights may have been received from an encoder, or may have been determined at decoder side based on information received from an encoder. The output of the weighting operation is input to the convolutional layer. The output of the convolutional layer represents the final output of the neural network.

[0294] In another embodiment, one or more of the one or more NLA functions are applied to all elements of one or more channels of an input tensor. One or more weights are used for weighting the respective one or more NLA functions that are applied to respective one or more channels of an input tensor. In an embodiment, a decoder determines the one or more weights. In another embodiment, an encoder determines the one or more weights.

[0295] In another embodiment, one or more of the one or more NLA functions are applied to all elements at one or more spatial positions of an input tensor. One or more weights are used for weighting the respective one or more NLA functions that are applied to respective one or more spatial positions of an input tensor. In an embodiment, a decoder determines the one or more weights. In another embodiment, an encoder determines the one or more weights.

[0296] In another embodiment, one or more of the one or more NLA functions are applied to each element of an input tensor. One or more weights are used for weighting the respective one or more NLA functions that are applied to respective one or more elements of an input tensor. In an embodiment, a decoder determines the one or more weights. In another embodiment, an encoder determines the one or more weights.

[0297] In an embodiment, a combination of the above mentioned embodiments may be also possible.

[0298] In an example, the one or more neural networks may comprise one or more portions, where at least one portion may comprise two or more parallel branches. The one or more of the two or more parallel branches comprise one or more NLA functions, and the input to parallel branches is same or substantially same or may be derived from another signal, and the outputs from the parallel branches are combined. For one or more of the parallel branches, an encoder may determine one or more respective weights for weighting the output of one or more NLA functions comprised in the one or more parallel branches, based at least on an input to the encoder and on an output of the one or more neural networks. Based on the determination, the encoder may signal the determined one or more weights or data derived from the determined one or more weights to a decoder.

[0299] FIG. 16 illustrates an example of a portion of a NN 1601, where a input to the portion 1602 is provided to a convolutional layer ‘Conv’ 1604, in accordance with an embodiment. An output of ‘Conv’ 1606 is a tensor ‘input to NLA functions’, which is input to two parallel branches, where each parallel branch comprises a NLA function. A first parallel branch comprises a PReLU function 1608, a second parallel branch comprises a GeLU function 1610. The output of each of the two NLA functions may be weighted, by weighting modules or circuits 1612 and 1614, according to information that is signaled from the encoder ‘signaling from encoder’ 1616. The weighted outputs may then be combined, using a combination module or circuit 1618, for example, by a summation operation. An output of the combination module or circuit 1618 represents an output of the portion of NN 1620.

[0300] FIG. 17 illustrates another example of a portion of a NN 1701, where an input to the portion 1702 is provided to two parallel branches, in accordance with an embodiment. In this example, a first parallel branch comprises a convolutional layer ‘Convl’ 1704 and a PReLU function 1706, a second parallel branch comprises a convolutional layer ‘Conv2’ 1708 and a GeLU function 1710. The output of each of the two NLA functions may be weighted, by weighting modules or circuits 1712 and 1714, according to information that is signaled from the encoder ‘signaling from encoder’ 1716. The weighted outputs may then be combined, by using combination module or circuit 1718, for example, by a summation operation. An output of the combination module or circuit 1718 represents an output of the portion of NN 1720.

[0301] In an embodiment, an encoder may perform one or more of the following operations: Overfitting one or more decomposed weights tensors of one or more neural networks. Signaling data derived from the overfitted one or more decomposed weight tensors to a decoder.

[0302] The decoder may perform one or more of the following operations:

Using the signaled data to update one or more decomposed weight tensors of one or more neural networks.

Performing inference of one or more neural networks comprising the updated one or more decomposed weight tensors.

[0303] In an embodiment, an encoder may perform one or more of the following operations: Decomposing one or more weight tensors of one or more neural networks Overfitting the decomposed one or more weight tensors.

Signaling data derived from the overfitted decomposed one or more weight tensors to a decoder.

[0304] The decoder may perform one or more of the following operations:

Decomposing one or more weight tensors of one or more neural networks.

Using the signaled data to update the decomposed one or more weight tensors.

Determining updated recomposed one or more weight tensors based at least on the updated decomposed weight tensors and on a recomposition technique. An example recomposition technique may comprise multiplying the decomposed tensors.

Performing inference of one or more neural networks comprising the updated recomposed one or more weight tensors or the updated decomposed one or more weight tensors.

[0305] In an embodiment, an encoder may perform one or more of the following operations: Overfitting one or more weight tensors of one or more neural networks.

Decomposing the overfitted one or more weight tensors.

Signaling data derived from the decomposed overfitted one or more weight tensors.

[0306] The decoder may perform one or more of the following operations:

Decomposing one or more weight tensors of one or more neural networks.

Using the signaled data to update the decomposed one or more weight tensors.

Determining updated recomposed one or more weight tensors based at least on the updated decomposed weight tensors and on a recomposition technique.

Performing inference of one or more neural networks comprising the updated recomposed one or more weight tensors or the updated decomposed one or more weight tensors.

[0307] Following paragraphs provide more details on the above mentioned embodiments and additional embodiments.

[0308] Overfitting the decomposed weight tensors already present in a NN

[0309] It is assumed that one or more neural networks comprise one or more decomposed weight tensors. The one or more decomposed weight tensors may have been obtained in an offline stage by means of a tensor decomposition technique, or may be part of the original design of the architecture of the one or more neural networks.

[0310] In an embodiment, an encoder may perform one or more of the following operations: Overfitting one or more decomposed weights tensors of one or more neural networks. Signaling data derived from the overfitted one or more decomposed weight tensors to a decoder. For example, signaling an encoded weight update.

[0311] The decoder may perform one or more of the following operations:

Using the signaled data (e.g., an encoded weight update) or data derived from the signaled data (e.g., a decoded weight update) to update one or more decomposed weight tensors of one or more neural networks.

Performing inference of one or more neural networks comprising the updated one or more decomposed weight tensors.

[0312] In one embodiment, an encoder may perform one or more of the following operations: Overfitting one or more weight tensors of one or more neural networks, based at least on some input data. For example, the input data may be data to be encoded by the encoder.. The one or more weight tensors may comprise one or more decomposed weight tensors, and/or one or more non-decomposed weight tensors.

Selecting one or more of the overfitted one or more weight tensors, based on a ratedistortion performance. For example, selecting the overfitted weight tensors that provide the lower rate-distortion cost.

Signaling data derived from the selected overfitted one or more weight tensors to a decoder. For example, signaling an encoded weight update.

[0313] The decoder may perform one or more of the following operations:

Using the signaled data (e.g., an encoded weight update) or data derived from the signaled data (e.g., a decoded weight update) to update one or more weight tensors of one or more neural networks, where the one or more weight tensors may comprise one or more decomposed weight tensors, and/or one or more non-decomposed weight tensors

Performing inference of one or more neural networks comprising the updated one or more weight tensors. [0314] Decomposing and then overfitting

[0315] In one embodiment, an encoder may perform one or more of the following operations: Decomposing one or more weight tensors of one or more neural networks, based at least on a tensor decomposition technique, obtaining decomposed one or more weight tensors. Alternatively, the encoder may already have available the decomposed weight tensors, for example, when decomposition was already performed earlier by the encoder or if the decomposed weight tensors were determined in an offline stage and provided to the encoder.

Overfitting the decomposed one or more weight tensors, based at least on some input data. For example, the input data may be data to be encoded by the encoder.

Signaling data derived from the overfitted decomposed one or more weight tensors to a decoder. For example, signaling an encoded weight update.

Signaling information about the decomposition. Such information may comprise an indication of the technique used for decomposing the one or more weight tensors, one or more parameters of the decomposition technique, and/or one or more parameters (e.g., properties such as size) of the decomposed one or more weight tensors.

Signaling information on whether the decoder shall perform inference using updated decomposed one or more weight tensors or using updated recomposed one or more weight tensors.

[0316] The decoder may perform one or more of the following operations: Decomposing one or more weight tensors of one or more neural networks, based on the signaled information about the decomposition. Alternatively, the decoder may already have available the decomposed weight tensors, for example, when decomposition was already performed earlier by the decoder or when the decomposed weight tensor were determined in an offline stage and provided to the decoder.

Using at least a portion of the signaled data (e.g., an encoded weight update) or data derived from the signaled data (e.g., a decoded weight update) to update the decomposed one or more weight tensors.

Determining updated recomposed one or more weight tensors based at least on the updated decomposed weight tensors and on a recomposition technique.

Performing inference of one or more neural networks comprising the updated recomposed one or more weight tensors or the updated decomposed one or more weight tensors. [0317] Overfitting and then decomposing

[0318] In one embodiment, an encoder may perform one or more of the following operations: Overfitting one or more weight tensors of one or more neural networks, based at least on some input data. For example, the input data may be data to be encoded by the encoder.

Decomposing the overfitted one or more weight tensors, based at least on a tensor decomposition technique, obtaining decomposed overfitted one or more weight tensors.

Signaling data derived from the decomposed overfitted one or more weight tensors. For example, signaling an encoded weight update.

Signaling information about the decomposition. Such information may comprise an indication of the technique used for decomposing the one or more weight tensors, one or more parameters of the decomposition technique, and/or one or more parameters (e.g., properties such as size) of the decomposed one or more weight tensors.

Signaling information on whether the decoder shall perform inference using updated decomposed one or more weight tensors or using updated recomposed one or more weight tensors.

[0319] The decoder may perform one or more of the following operations:

Decomposing one or more weight tensors of one or more neural networks. Alternatively, the decoder may already have available the decomposed weight tensors, for example, when decomposition was already performed earlier by the decoder or if the decomposed weight tensor were determined in an offline stage and provided to the decoder.

Using at least a portion of the signaled data (e.g., an encoded weight update) or data derived from the signaled data (e.g., a decoded weight update) to update the decomposed one or more weight tensors.

Determining updated recomposed one or more weight tensors based at least on the updated decomposed weight tensors and on a recomposition technique.

Performing inference of one or more neural networks comprising the updated recomposed one or more weight tensors or the updated decomposed one or more weight tensors. [0320] Generation of decomposable weight tensors

[0321] In any of the previous embodiments, a weight tensor to be decomposed, named as decomposable weight tensor, may be generated by based on one or more of the following: splitting the weight tensor of a neural network along one or more dimensions into subweight tensors. concatenating multiple weight tensors and/or sub-weight tensors of more than one filters along one or more dimensions. padding a weight tensor or a sub-weight tensor along one or more dimensions to a certain size so the weight tensors and/or sub-weight tensors may be concatenated. reordering a weight tensor or a sub-weight tensor along one or more dimensions.

[0322] In an example, the encoder and decoder may generate a decomposable weight tensor according to a pre-determined procedure. The encoder overfits the generated decomposable weight tensor and signal the weight updates to the decoder. The decoder may apply the weight updates to the decomposable weight tenor and recover the updated weight tensors of NN filters according to the predetermined procedure.

[0323] In another example, the encoder may determine the procedure to generate a decomposable weight tensor and the weight updates of the decomposable weight tensor by optimizing a loss function at the encoding stage. The encoder may signal the one or more parameters of the procedure and the weight updates to the decoder. The decoder may perform the procedure that the encoder signaled to generate the decomposable weight tensor and apply the weight updates to it. After the weight updates are applied, the decoder may recover the weight tensors of NN filters from the updated decomposable weight tensor according to the procedure signaled by the encoder.

[0324] FIG. 18 is an example apparatus 1800, which may be implemented in hardware, caused to implement mechanisms for non-linear overfitting of one or more neural networks and/or overfitting decomposed weight tensors, based on the examples described herein. The apparatus 1800 comprises at least one processor 1802, at least one non-transitory memory 1804 including computer program code 1805, wherein the at least one memory 1804 and the computer program code 1805 are configured to, with the at least one processor 1802, cause the apparatus 1800 to implement mechanisms for non-linear overfitting of neural network filters and/or overfitting decomposed weight tensors 1806, based on the examples described herein. In an embodiment, the at least one neural network or the portion of the at least one neural network may be used at a decoder-side for decoding or reconstructing one or more media items.

[0325] The apparatus 1800 optionally includes a display 1808 that may be used to display content during rendering. The apparatus 1800 optionally includes one or more network (NW) interfaces (I/F(s)) 1810. The NW I/F(s) 1810 may be wired and/or wireless and communicate over the Internet/other network(s) via any communication technique. The NW I/F(s) 1810 may comprise one or more transmitters and one or more receivers. The N/W I/F(s) 1810 may comprise standard well-known components such as an amplifier, filter, frequency-converter, (de)modulator, and encoder/decoder circuitry(ies) and one or more antennas.

[0326] The apparatus 1800 may be a remote, virtual or cloud apparatus. The apparatus 1800 may be either a coder or a decoder, or both a coder and a decoder. The at least one memory 1804 may be implemented using any suitable data storage technology, such as semiconductor based memory devices, flash memory, magnetic memory devices and systems, optical memory devices and systems, fixed memory and removable memory. The at least one memory 1804 may comprise a database for storing data. The apparatus 1800 need not comprise each of the features mentioned, or may comprise other features as well. The apparatus 1800 may correspond to or be another embodiment of the apparatus 50 shown in FIG. 1 and FIG. 2, any of the apparatuses shown in FIG. 3, or apparatus 700 of FIG. 7. The apparatus 1800 may correspond to or be another embodiment of the apparatuses shown in FIG. 20, including UE 110, RAN node 170, or network element(s) 190.

[0327] FIG. 19 illustrates an example method 1900 for non-linear overfitting of one or more neural network, in accordance with an embodiment. As shown in block 1806 of FIG. 18, the apparatus 1800 includes means, such as the processing circuitry 1802 or the like, for non-linear overfitting of one or more neural networks. At 1902, the method 1900 includes receiving an input at an apparatus. At 1904, the method 1900 includes overfitting one or more features related to of one or more non-linear activation (NLA) functions comprised in one or more neural networks based at least on the input to the apparatus. In an embodiment, the one or more features comprise one or more parameters of the one or more NLA functions. In an embodiment, the method 1900 may further includes determining whether the one or more NLA functions comprised in the one or more neural networks are to be used or not; and signaling, in or along a bitstream, information based on the determination to a decoder, wherein the information comprises one or more of the following: one or more binary flags for the respective one or more NLA functions, wherein the one or more flags comprise an indication of which subset of NLA functions is to be used out of several subsets of NLA functions from the one or more NLA functions; or a list of identifier values, wherein each identifier value identifies an NLA function of the one or more functions.

[0328] FIG. 20 illustrates an example method 2000 for non-linear overfitting of one or more neural network, in accordance with another embodiment, in accordance with an embodiment. As shown in block 1806 of FIG. 18, the apparatus 1800 includes means, such as the processing circuitry 1802 or the like, for non-linear overfitting of one or more neural networks. At 2002, the method 2000 includes Receiving or parsing, from or along a bitstream, overfitted one or more features related to one or more non-linear activation (NLA) functions comprised in one or more neural networks, wherein the one or more features are overfitted based at least on the input to an encoder. At 2004, the method 2000 includes Updating one or more parameters of the one or more neural networks based at least on the overfitted one more features At 2006, the method 2000 includes performing an inference of the one or more neural networks comprising the updated one or more parameters. In an embodiment, the overfitted one or more features are compressed, and the method 2000 may further include decompressing the overfitted one or more features. In an embodiment, the one or more features comprise one or more parameters of the one or more NLA functions.

[0329] In an embodiment, the method 2000 may further include receiving information whether the one or more NLA functions comprised in the one or more neural networks are to be used or not; wherein the information further comprises one or more of the following: one or more binary flags for the respective one or more NLA functions, wherein the one or more flags comprise an indication of which subset of NLA functions is to be used out of several subsets of NLA functions from the one or more NLA functions; or a list of identifier values, wherein each identifier value identifies an NLA function of the one or more functions.

[0330] FIG. 21 illustrates an example method 2100 for overfitting decomposed weight tensors, in accordance with an embodiment. As shown in block 1806 of FIG. 18, the apparatus 1800 includes means, such as the processing circuitry 1802 or the like, for overfitting decomposed weight tensors. At 2102, the method 2100 includes overfitting one or more weight tensors of one or more neural networks to obtain overfitted one or more weight tensors, wherein the one or more weight tensors comprise one or more decomposed weight tensors. At 2102, the method 2100 includes signaling at least one of overfitted one or more weight tensors or data derived from the at least one of overfitted one or more weight tensors to a decoder. In an embodiment, the overfitted one or more weight tensors comprise overfitted one or more decomposed weight tensors, and wherein the at least one of overfitted one or more weight tensors comprises at least one of the overfitted one or more decomposed weight tensors [0331] FIG. 22 illustrates an example method 2200 for overfitting decomposed weight tensors, in accordance with another embodiment. As shown in block 1806 of FIG. 18, the apparatus 1800 includes means, such as the processing circuitry 1802 or the like, for overfitting decomposed weight tensors. At 2202, the method 2200 includes receiving overfitted one or more weight tensors or data derived from the overfitted one or more weight tensors, wherein the received overfitted one or more weight tensors comprise one or more decomposed weight. At 2204, the method 2200 includes updating one or more decomposed weight tensors of one or more neural networks by using the received overfitted one or more weight tensors or data derived from the overfitted one or more weight tensors. At 2206, the method 2200 includes performing inference of the one or more neural networks comprising the updated one or more decomposed weight tensors.

[0332] In an embodiment, wherein the one or more weight tensors are decomposed to obtain the one or more decomposed weight tensors, and the method 2200 may further include receiving information related to decomposition of the one or more weight tensors, wherein the information related to decomposition comprises at least one of an indication of a decomposition technique used for decomposing the one or more weight tensors, one or more parameters of the decomposition technique, or one or more parameters of the decomposed one or more weight tensors.

[0333] Referring to FIG. 23, this figure shows a block diagram of one possible and non-limiting example in which the examples may be practiced. A user equipment (UE) 110, radio access network (RAN) node 170, and network element(s) 190 are illustrated. In the example of FIG. 1, the user equipment (UE) 110 is in wireless communication with a wireless network 100. A UE is a wireless device that can access the wireless network 100. The UE 110 includes one or more processors 120, one or more memories 125, and one or more transceivers 130 interconnected through one or more buses 127. Each of the one or more transceivers 130 includes a receiver, Rx, 132 and a transmitter, Tx, 133. The one or more buses 127 may be address, data, or control buses, and may include any interconnection mechanism, such as a series of lines on a motherboard or integrated circuit, fiber optics or other optical communication equipment, and the like. The one or more transceivers 130 are connected to one or more antennas 128. The one or more memories 125 include computer program code 123. The UE 110 includes a module 140, comprising one of or both parts 140-1 and/or 140-2, which may be implemented in a number of ways. The module 140 may be implemented in hardware as module 140-1, such as being implemented as part of the one or more processors 120. The module 140-1 may be implemented also as an integrated circuit or through other hardware such as a programmable gate array. In another example, the module 140 may be implemented as module 140-2, which is implemented as computer program code 123 and is executed by the one or more processors 120. For instance, the one or more memories 125 and the computer program code 123 may be configured to, with the one or more processors 120, cause the user equipment 110 to perform one or more of the operations as described herein. The UE 110 communicates with RAN node 170 via a wireless link 111.

[0334] The RAN node 170 in this example is a base station that provides access by wireless devices such as the UE 110 to the wireless network 100. The RAN node 170 may be, for example, a base station for 5G, also called New Radio (NR). In 5G, the RAN node 170 may be a NG-RAN node, which is defined as either a gNB or an ng-eNB. A gNB is a node providing NR user plane and control plane protocol terminations towards the UE, and connected via the NG interface to a 5GC (such as, for example, the network element(s) 190). The ng-eNB is a node providing E-UTRA user plane and control plane protocol terminations towards the UE, and connected via the NG interface to the 5GC. The NG- RAN node may include multiple gNBs, which may also include a central unit (CU) (gNB-CU) 196 and distributed unit(s) (DUs) (gNB-DUs), of which DU 195 is shown. Note that the DU may include or be coupled to and control a radio unit (RU). The gNB-CU is a logical node hosting radio resource control (RRC), SDAP and PDCP protocols of the gNB or RRC and PDCP protocols of the en-gNB that controls the operation of one or more gNB-DUs. The gNB-CU terminates the Fl interface connected with the gNB-DU. The Fl interface is illustrated as reference 198, although reference 198 also illustrates a link between remote elements of the RAN node 170 and centralized elements of the RAN node 170, such as between the gNB-CU 196 and the gNB-DU 195. The gNB-DU is a logical node hosting RLC, MAC and PHY layers of the gNB or en-gNB, and its operation is partly controlled by gNB-CU. One gNB- CU supports one or multiple cells. One cell is supported by only one gNB-DU. The gNB-DU terminates the Fl interface 198 connected with the gNB-CU. Note that the DU 195 is considered to include the transceiver 160, for example, as part of a RU, but some examples of this may have the transceiver 160 as part of a separate RU, for example, under control of and connected to the DU 195. The RAN node 170 may also be an eNB (evolved NodeB) base station, for LTE (long term evolution), or any other suitable base station or node.

[0335] The RAN node 170 includes one or more processors 152, one or more memories 155, one or more network interfaces (N/W I/F(s)) 161, and one or more transceivers 160 interconnected through one or more buses 157. Each of the one or more transceivers 160 includes a receiver, Rx, 162 and a transmitter, Tx, 163. The one or more transceivers 160 are connected to one or more antennas 158. The one or more memories 155 include computer program code 153. The CU 196 may include the processor(s) 152, memories 155, and network interfaces 161. Note that the DU 195 may also contain its own memory/memories and processor(s), and/or other hardware, but these are not shown. [0336] The RAN node 170 includes a module 150, comprising one of or both parts 150-1 and/or 150-2, which may be implemented in a number of ways. The module 150 may be implemented in hardware as module 150-1, such as being implemented as part of the one or more processors 152. The module 150-1 may be implemented also as an integrated circuit or through other hardware such as a programmable gate array. In another example, the module 150 may be implemented as module 150-2, which is implemented as computer program code 153 and is executed by the one or more processors 152. For instance, the one or more memories 155 and the computer program code 153 are configured to, with the one or more processors 152, cause the RAN node 170 to perform one or more of the operations as described herein. Note that the functionality of the module 150 may be distributed, such as being distributed between the DU 195 and the CU 196, or be implemented solely in the DU 195.

[0337] The one or more network interfaces 161 communicate over a network such as via the links 176 and 131. Two or more gNBs 170 may communicate using, for example, link 176. The link 176 may be wired or wireless or both and may implement, for example, an Xn interface for 5G, an X2 interface for LTE, or other suitable interface for other standards.

[0338] The one or more buses 157 may be address, data, or control buses, and may include any interconnection mechanism, such as a series of lines on a motherboard or integrated circuit, fiber optics or other optical communication equipment, wireless channels, and the like. For example, the one or more transceivers 160 may be implemented as a remote radio head (RRH) 195 for LTE or a distributed unit (DU) 195 for gNB implementation for 5G, with the other elements of the RAN node 170 possibly being physically in a different location from the RRH/DU, and the one or more buses 157 could be implemented in part as, for example, fiber optic cable or other suitable network connection to connect the other elements (for example, a central unit (CU), gNB-CU) of the RAN node 170 to the RRH/DU 195. Reference 198 also indicates those suitable network link(s).

[0339] It is noted that description herein indicates that ‘cells’ perform functions, but it should be clear that equipment which forms the cell may perform the functions. The cell makes up part of a base station. That is, there can be multiple cells per base station. For example, there could be three cells for a single carrier frequency and associated bandwidth, each cell covering one-third of a 360 degree area so that the single base station’s coverage area covers an approximate oval or circle. Furthermore, each cell can correspond to a single carrier and a base station may use multiple carriers. So if there are three 120 degree cells per carrier and two carriers, then the base station has a total of 6 cells. [0340] The wireless network 100 may include a network element or elements 190 that may include core network functionality, and which provides connectivity via a link or links 181 with a further network, such as a telephone network and/or a data communications network (for example, the Internet). Such core network functionality for 5G may include access and mobility management function(s) (AMF(S)) and/or user plane functions (UPF(s)) and/or session management function(s) (SMF(s)). Such core network functionality for LTE may include MME (Mobility Management Entity )/SGW (Serving Gateway) functionality. These are merely example functions that may be supported by the network element(s) 190, and note that both 5G and LTE functions might be supported. The RAN node 170 is coupled via a link 131 to the network element 190. The link 131 may be implemented as, for example, an NG interface for 5G, or an SI interface for LTE, or other suitable interface for other standards. The network element 190 includes one or more processors 175, one or more memories 171, and one or more network interfaces (N/W I/F(s)) 180, interconnected through one or more buses 185. The one or more memories 171 include computer program code 173. The one or more memories 171 and the computer program code 173 are configured to, with the one or more processors 175, cause the network element 190 to perform one or more operations.

[0341] The wireless network 100 may implement network virtualization, which is the process of combining hardware and software network resources and network functionality into a single, softwarebased administrative entity, a virtual network. Network virtualization involves platform virtualization, often combined with resource virtualization. Network virtualization is categorized as either external, combining many networks, or parts of networks, into a virtual unit, or internal, providing network-like functionality to software containers on a single system. Note that the virtualized entities that result from the network virtualization are still implemented, at some level, using hardware such as processors 152 or 175 and memories 155 and 171, and also such virtualized entities create technical effects.

[0342] The computer readable memories 125, 155, and 171 may be of any type suitable to the local technical environment and may be implemented using any suitable data storage technology, such as semiconductor based memory devices, flash memory, magnetic memory devices and systems, optical memory devices and systems, fixed memory and removable memory. The computer readable memories 125, 155, and 171 may be means for performing storage functions. The processors 120, 152, and 175 may be of any type suitable to the local technical environment, and may include one or more of general purpose computers, special purpose computers, microprocessors, digital signal processors (DSPs) and processors based on a multi-core processor architecture, as non-limiting examples. The processors 120, 152, and 175 may be means for performing functions, such as controlling the UE 110, RAN node 170, network element(s) 190, and other functions as described herein. [0343] In general, the various embodiments of the user equipment 110 can include, but are not limited to, cellular telephones such as smart phones, tablets, personal digital assistants (PDAs) having wireless communication capabilities, portable computers having wireless communication capabilities, image capture devices such as digital cameras having wireless communication capabilities, gaming devices having wireless communication capabilities, music storage and playback appliances having wireless communication capabilities, Internet appliances permitting wireless Internet access and browsing, tablets with wireless communication capabilities, as well as portable units or terminals that incorporate combinations of such functions.

[0344] One or more of modules 140-1, 140-2, 150-1, and 150-2 may be configured to perform non-linear overfitting of neural network filters and/or overfitting decomposed weight tensors. Computer program code 173 may also be configured to perform non-linear overfitting of neural network filters and/or overfitting decomposed weight tensors.

[0345] As described above, FIGs. 19 to 22 include a flowchart of an apparatus (e.g. 50, 100, 602, 604, 700, or 1800), method, and computer program product according to certain example embodiments. It will be understood that each block of the flowcharts, and combinations of blocks in the flowcharts, may be implemented by various means, such as hardware, firmware, processor, circuitry, and/or other devices associated with execution of software including one or more computer program instructions. For example, one or more of the procedures described above may be embodied by computer program instructions. In this regard, the computer program instructions which embody the procedures described above may be stored by a memory (e.g. 58, 125, 704, or 1804) of an apparatus employing an embodiment of the present invention and executed by processing circuitry (e.g. 56, 120, 702, or 1802) of the apparatus. As will be appreciated, any such computer program instructions may be loaded onto a computer or other programmable apparatus (e.g., hardware) to produce a machine, such that the resulting computer or other programmable apparatus implements the functions specified in the flowchart blocks. These computer program instructions may also be stored in a computer-readable memory that may direct a computer or other programmable apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture, the execution of which implements the function specified in the flowchart blocks. The computer program instructions may also be loaded onto a computer or other programmable apparatus to cause a series of operations to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide operations for implementing the functions specified in the flowchart blocks.

[0346] A computer program product is therefore defined in those instances in which the computer program instructions, such as computer-readable program code portions, are stored by at least one non- transitory computer-readable storage medium with the computer program instructions, such as the computer-readable program code portions, being configured, upon execution, to perform the functions described above, such as in conjunction with the flowchart(s) of FIGs. 19 to 22. In other embodiments, the computer program instructions, such as the computer-readable program code portions, need not be stored or otherwise embodied by a non-transitory computer-readable storage medium, but may, instead, be embodied by a transitory medium with the computer program instructions, such as the computer- readable program code portions, still being configured, upon execution, to perform the functions described above.

[0347] Accordingly, blocks of the flowcharts support combinations of means for performing the specified functions and combinations of operations for performing the specified functions for performing the specified functions. It will also be understood that one or more blocks of the flowcharts, and combinations of blocks in the flowcharts, may be implemented by special purpose hardware-based computer systems which perform the specified functions, or combinations of special purpose hardware and computer instructions.

[0348] In some embodiments, certain ones of the operations above may be modified or further amplified. Furthermore, in some embodiments, additional optional operations may be included. Modifications, additions, or amplifications to the operations above may be performed in any order and in any combination.

[0349] In the above, some example embodiments have been described with reference to an SEI message or an SEI NAL unit. It needs to be understood, however, that embodiments can be similarly realized with any similar structures or data units. Where example embodiments have been described with SEI messages contained in a structure, any independently parsable structures could likewise be used in embodiments. Specific SEI NAL unit and a SEI message syntax structures have been presented in example embodiments, but it needs to be understood that embodiments generally apply to any syntax structures with a similar intent as SEI NAL units and/or SEI messages. [0350] In the above, some embodiments have been described in relation to a particular type of a parameter set (namely adaptation parameter set). It needs to be understood, however, that embodiments could be realized with any type of parameter set or other syntax structure in the bitstream.

[0351] In the above, some example embodiments have been described with the help of syntax of the bitstream. It needs to be understood, however, that the corresponding structure and/or computer program may reside at the encoder for generating the bitstream and/or at the decoder for decoding the bitstream.

[0352] In the above, where example embodiments have been described with reference to an encoder, it needs to be understood that the resulting bitstream and the decoder have corresponding elements in them. For example, when an embodiment is described in relation to an encoder signaling information in or along the bitstream, it needs to be understood that a respective embodiment for decoding comprises decoding information from or along the bitstream. Likewise, where example embodiments have been described with reference to a decoder, it needs to be understood that the encoder has structure and/or computer program for generating the bitstream to be decoded by the decoder.

[0353] Many modifications and other embodiments of the inventions set forth herein will come to mind to one skilled in the art to which these inventions pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the inventions are not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended claims. Moreover, although the foregoing descriptions and the associated drawings describe example embodiments in the context of certain example combinations of elements and/or functions, it should be appreciated that different combinations of elements and/or functions may be provided by alternative embodiments without departing from the scope of the appended claims. In this regard, for example, different combinations of elements and/or functions than those explicitly described above are also contemplated as may be set forth in some of the appended claims. Accordingly, the description is intended to embrace all such alternatives, modifications and variances which fall within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

[0354] It should be understood that the foregoing description is only illustrative. Various alternatives and modifications may be devised by those skilled in the art. For example, features recited in the various dependent claims could be combined with each other in any suitable combination(s). In addition, features from different embodiments described above could be selectively combined into a new embodiment. Accordingly, the description is intended to embrace all such alternatives, modifications and variances which fall within the scope of the appended claims.

[0355] References to a ‘computer’, ‘processor’, etc. should be understood to encompass not only computers having different architectures such as single/multi-processor architectures and sequential (Von Neumann)/parallel architectures but also specialized circuits such as field-programmable gate arrays (FPGA), application specific circuits (ASIC), signal processing devices and other processing circuitry. References to computer program, instructions, code etc. should be understood to encompass software for a programmable processor or firmware such as, for example, the programmable content of a hardware device such as instructions for a processor, or configuration settings for a fixed-function device, gate array or programmable logic device, and the like.

[0356] As used herein, the term ‘circuitry’ or ‘’circuit’ may refer to any of the following: (a) hardware circuit implementations, such as implementations in analog and/or digital circuitry, and (b) combinations of circuits and software (and/or firmware), such as (as applicable): (i) a combination of processor(s) or (ii) portions of processor(s)/software including digital signal processor(s), software, and memory(ies) that work together to cause an apparatus to perform various functions, and (c) circuits, such as a microprocessor(s) or a portion of a microprocessor(s), that require software or firmware for operation, even if the software or firmware is not physically present. This description of ‘circuitry’ or ‘circuit’ applies to uses of this term in this application. As a further example, as used herein, the term ‘circuitry’ would also cover an implementation of merely a processor (or multiple processors) or a portion of a processor and its (or their) accompanying software and/or firmware. The term ‘circuitry’ or ‘circuit’ would also cover, for example and if applicable to the particular element, a baseband integrated circuit or applications processor integrated circuit for a mobile phone or a similar integrated circuit in a server, a cellular network device, or another network device.