Method for distributed learning in a communication network

Abstract

A method (100) for distributed learning of a temporal neural network in a communication network. The method is performed by a first node of the communication network, the first node associated to a pre-synaptic neuron of the temporal neural network. The method comprises receiving (S101), from a second node of the communication system, the second node associated to a post-synaptic neuron of the temporal neural network, an indication that a hidden state of the post- synaptic neuron has changed. The method comprises transmitting (S102), to the second node, a pre-synaptic stimuli and receiving (S103), with a scheduled acknowledgement message associated to the transmitted pre-synaptic stimuli, a hidden state information related to the post-synaptic neuron. Further disclosed are related apparatuses, computer programs, and computer program products.

Description

[0001]METHOD FOR DISTRIBUTED LEARNING IN A COMMUNICATION NETWORK TECHNICAL FIELD The disclosure relates to methods and apparatuses for distributed learning in acommunication network, and more specifically to training and inference efficiency ofcommunication and computation in distributed learning for temporal neural networks.Also disclosed are related apparatuses, computer programs, and computer program products. BACKGROUND As telecommunication networks increase in size and more devices are able to connect to networks, the demands on forecasting abilities at network nodesincrease. Neural networks (NNs), a machine learning architecture inspired byadvancements in neuroscience, are particularly suited for some types of flexible forecasting / classification problems which may arise. However, telecommunication networks becoming larger and more decentralized means that the network node,where the training and forecasting may be needed, either lacks access to therequired data, as datasets cannot be transferred in some cases. Therefore,distributed learning methods such as split learning have become an increasinglyfavored solution. However, neural networks are trained and used by implementing alarge number of connections, called synapses, between nodes, called neurons, andnaïve distributed learning of the neural network may thus incur a largecommunication overhead. This challenge is addressed by temporal neural networkssuch as, for example, liquid time constant neural networks (LTC NNs) by virtue ofbeing sparse i.e. by comprising relatively few synapses through which messages canbe sent. Additionally, temporal NNs also adapt to some data-drift scenarios ininference time via near-instant feedback on a transmitted signal without need for anadditional training phase.Developing distributed methods for training adaptive temporal neural networks suchas LTC NNs for continuous time problems in communication networks is therefore ofgreat interest due to the increasing efforts in model provisioning in the MachineLearning Operations (MLOps) paradigm – small number of adaptive models arepreferable. SUMMARYAn object of the disclosure is to provide methods for communication-efficientdistributed learning of temporal neural networks in communication systems.According to a first aspect, there is a method for distributed learning of a temporalneural network in a communication network. The method is performed by a first nodeof the communication network, the first node associated to a pre-synaptic neuron ofthe temporal neural network. The method comprises receiving, from a second nodeof the communication system, the second node associated to a post-synaptic neuronof the temporal neural network, an indication that a hidden state of the post-synapticneuron has changed. The method comprises transmitting, to the second node, a pre-synaptic stimuli and receiving, with a scheduled acknowledgement messageassociated to the transmitted pre-synaptic stimuli, a hidden state information related to the post-synaptic neuron.According to an embodiment of the first aspect, the method further comprisesselectively delivering activations from pre-synaptic neuron to the post-synaptic neuron based on estimated hidden state information of the post-synaptic neuron. According to an embodiment of the first aspect, the communication network is a telecommunication network. According to an embodiment of the first aspect, the first node and the second node are geographically distinct nodes of a telecommunication network and the request response message is a hybrid automatic repeat request, HARQ, message. According to an embodiment of the first aspect, the first node is a network function or an application function, or an external application function and the second node is a network function or an application function or an external application function. According to an embodiment of the first aspect, the first node and the second node are part of an open radio access network, O-RAN, and the request response message is one of: aresponse request message between near real-time radio interface and core,RIC, and non-real time RIC via the A1 interface; a response request message between non-real time RIC and an evolved nodeB, eNB, via the O1 interface; or a response request message between near real-time RIC and a radio access node via the E2 interface.According to an embodiment of the first aspect, the method further comprisesdetermining, based on at least an estimated communication cost for transmitting a pre-synaptic stimuli and the most recently received hidden state, when to transmit a new pre-synaptic stimuli. According to a second aspect, there is a method for distributed learning of atemporal neural network in a communication network, the method performed by asecond node of the communication network. The second node is associated with apost-synaptic neuron of the temporal neural network. The method comprisesreceiving, from a first node of the telecommunication system, the first nodeassociated with a pre-synaptic neuron of the temporal neural network, a pre-synapticstimuli. The method comprises transmitting, with an acknowledgement message associated with the received pre-synaptic stimuli, a hidden state information to the first node, wherein the hidden state information is related to the post-synaptic neuron.According to an embodiment of the second aspect, the temporal neural network isone of: a recurrent neural network, RNN; a liquid time constant, LTC, network; or acontinuous time recurrent neural network. According to an embodiment of the second aspect, the communication network is a telecommunication network. According to an embodiment of the second aspect, the method further comprises estimating a hidden state information related to the post-synaptic neuron. According to an embodiment of the second aspect, the method further comprises transmitting, to the first node, an indication that a state of the post-synaptic neuronhas changed; and receiving, from the first node, a second pre-synaptic stimuli inresponse to the transmitted indication. According to an embodiment of the second aspect, the indication that a state of the post-synaptic neuron has changed comprises an indication that the state of the post- synaptic neuron has decayed. According to an embodiment of the second aspect, the first node and the second node are geographically distinct nodes of a telecommunication network and the acknowledgement message is a hybrid automatic repeat request, HARQ, message. According to an embodiment of the second aspect, the first node is a network function or an application function and the second node is a network function or an application function or any other external application function. According to an embodiment of the second aspect, the first node and the second node are part of an open radio access network, O-RAN, and the request responsemessage is one of: a response request message between near real-time radiointerface and core, RIC, and non-real time RIC via the A1 interface; a response request message between non-real time RIC and an evolved nodeB, eNB, via theO1 interface; or a response request message between near real-time RIC and aradio access node via the E2 interface. According to a third aspect, there is an apparatus for distributed learning of atemporal neural network, in a communication network. The apparatus is comprisedin a first node of the communication network, the first node associated to a pre-synaptic neuron of the temporal neural network. The apparatus is configured toreceive, from a second node of the communication system, the second nodeassociated to a post-synaptic neuron of the temporal neural network, an indicationthat a hidden state of the post-synaptic neuron has changed. The apparatus is configured to transmit, to the second node, a pre-synaptic stimuli. The apparatus isconfigured to receive, with a scheduled acknowledgement message associated tothe transmitted pre-synaptic stimuli, a hidden state information related to the post- synaptic neuron.According to an embodiment of the third aspect, the apparatus is further configuredto selectively deliver activations from pre-synaptic neuron to the post-synapticneuron based on estimated hidden state information of the post-synaptic neuron. According to an embodiment of the third aspect, the communication network is a telecommunication network.According to an embodiment of the third aspect, wherein the first node and thesecond node are geographically distinct nodes of a telecommunication network and the request response message is a hybrid automatic repeat request, HARQ, message. According to an embodiment of the third aspect, the first node is a network function or an application function, or an external application function and the second node is a network function or an application function or an external application function. According to an embodiment of the third aspect, the first node and the second node are part of an open radio access network, O-RAN, and the request responsemessage is one of: a response request message between near real-time radiointerface and core, RIC, and non-real time RIC via the A1 interface; a responserequest message between non-real time RIC and an evolved nodeB, eNB, via theO1 interface; or a response request message between near real-time RIC and aradio access node via the E2 interface.According to an embodiment of the third aspect, the apparatus is further configuredto determine, based on at least an estimated communication cost for transmitting apre-synaptic stimuli and the most recently received hidden state, when to transmit a new pre-synaptic stimuli. According to a fourth aspect, there is an apparatus for distributed learning of atemporal neural network in a communication network. The apparatus is comprised ina second node of the communication network. The second node is associated with apost-synaptic neuron of the temporal neural network. The apparatus is configured toreceive, from a first node of the communication network, the first node associatedwith a pre-synaptic neuron of the temporal neural network, a pre-synaptic stimuli.The apparatus is configured to transmit, with an acknowledgement message associated with the received pre-synaptic stimuli, a hidden state information to the first node, wherein the hidden state information is related to the post-synaptic neuron.According to an embodiment of the fourth aspect, the temporal neural network is oneof: a recurrent neural network; a liquid time constant, LTC, network; or a continuoustime recurrent neural network. According to an embodiment of the fourth aspect, the communication network is a telecommunication network.According to an embodiment of the fourth aspect, the apparatus is further configuredto estimate a hidden state information related to the post-synaptic neuron.According to an embodiment of the fourth aspect, the apparatus is further configuredto: transmit, to the first node, an indication that a state of the post-synaptic neuronhas changed; and receive, from the first node, a second pre-synaptic stimuli inresponse to the transmitted indication. According to an embodiment of the fourth aspect, the indication that a state of the post-synaptic neuron has changed comprises an indication that the state of the post- synaptic neuron has decayed. According to an embodiment of the fourth aspect, the first node and the second node are geographically distinct nodes of a telecommunication network and the request response message is a hybrid automatic repeat request, HARQ, message. According to an embodiment of the fourth aspect, the first node is a network function or an application function and the second node is a network function or an application function or any other external application function. According to an embodiment of the fourth aspect, the first node and the second node are part of an open radio access network, O-RAN, and the request response message is one of: a response request message between near real-time radio interface and core, RIC, and non-real time RIC via the A1 interface; a response request message between non-real time RIC and an evolved nodeB, eNB, via the O1 interface; or a response request message between near real-time RIC and a radio access node via the E2 interface.According to a fifth aspect, there is a computer program comprising machinereadable instructions which, on execution by a processor of an apparatus, cause the apparatus to perform a method according to any embodiment of the first aspect.According to a sixth aspect, there is a computer program product comprising a non-transient storage medium, on which a computer program according to the fifth aspectis stored.According to a seventh aspect, there is a computer program comprising machinereadable instructions which, on execution by a processor of an apparatus, cause the apparatus to perform a method according to any embodiment of the second aspect.According to an eighth aspect, there is a computer program product comprising anon-transient storage medium, on which a computer program according to theseventh aspect is stored.BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 illustrates an example of a method according to the disclosure.Fig. 2 illustrates an example of a method according to the disclosure.Fig. 3 illustrates an example of a communication flow according to thedisclosure. Fig. 4 illustrates an example of a communication flow according to thedisclosure. Fig. 5 illustrates an example of a communication flow according to thedisclosure. Fig.6 illustrates an example of an apparatus according to the disclosure. Fig. 7 illustrates an example of a communication system according to thedisclosure.Fig. 8 illustrates an example of a radio access node according to thedisclosure. Fig. 9 illustrates an example of the logical components of a virtualizationenvironment according to the disclosure.Fig. 10a is a line graph of the performance results of different neural networksaccording to the disclosure. Fig. 10b is a line graph of the performance results of different neural networksaccording to the disclosure. Fig. 10c is a line graph of the performance results of different neural networksaccording to the disclosure. Fig. 10d is a line graph of the performance results of different neural networksaccording to the disclosure. DETAILED DESCRIPTION OF THE DRAWINGSFig. 1 illustrates an example of a method 100 according to the disclosure. Themethod 100 is for distributed learning of a temporal neural network (TNN) in acommunication network. A TNN is any artificial neural network characterized bytemporal characteristics such as processing input data based on arrival time instead of pooling input data and processing the input data at fixed points in time. TNNs are particularly suited for modelling systems which evolve over time.The class of TNNs include, for example, recurrent neural networks (RNNs). An RNNis a type of artificial neural network characterized by a recurrent flow of informationbetween layers of nodes, so that the output of some nodes may be fed back as inputto those same nodes in the network, thus affecting the future input to the samenodes. The recurrent flow of information provides a memory-like function for theRNNs. Other TNNs include liquid time constraint (LTC) NNs and temporal graphcollaborative transformers. A neural network is an architecture for machine learning comprising a set of nodes and a set of connections between the nodes. The nodes may be referred to asartificial neurons, or simply neurons, of the neural network. The connections betweenthe neurons may be referred to as synapses. A synapse can transmit signals from afirst neuron to a second neuron, wherein the signal may comprise a real number, avector or one-dimensional array of real numbers, or a matrix or a two-dimensionalarray of real numbers, or a tensor or a multi-dimensional array of real numbers. The neurons of the neural network may be arranged in layers, the layers comprising at least an input layer, a first hidden layer, and an output layer, the input layercomprising at least one input neuron. The input neuron receives an input to beprocessed by the neural network. The input may comprise a real number, a vector orone-dimensional array of real numbers, or a matrix or two-dimensional array of realnumbers, or a tensor or a multi-dimensional array of real numbers. The input neuronmay apply a mathematical function to the input to obtain an output of the inputneuron. The mathematical function may comprise a non-linear and / or discontinuousfunction. The output of the input neuron may then be transmitted by a synapseconnected to the input neuron.Each neuron in the input layer is connected, by a synapse, to at least one neuron inthe first hidden layer. Preferably, each neuron in the input layer may be connected toeach of the neurons of the first hidden layer by a corresponding synapse. That is, afirst neuron in the input layer may be associated to each of ^ neurons of the firsthidden layer by ^ synapses. If there are ^ neurons in the input layer, the input layerand the first hidden layer are connected by ^^ synapses.The neural network may comprise more than one hidden layer. Neural networks comprising at least two hidden layers of neurons may be referred to as deep neuralnetworks. In the architecture of a deep neural network, each neuron of a hiddenlayer is connected by at least one synapse to a neuron of the next hidden layer.The output of a neuron in the input layer may comprise a real number, or a one- ormulti-dimensional array of real numbers. The output is transmitted by the synapsesto the neurons in the first hidden layer. The output transmitted by a synapse may bereferred to as a signal. The signal received by a neuron of the first hidden layer ofthe neural network may be processed by the neuron applying some mathematicalfunction to the received signal. Each neuron of the first hidden layer may receivemultiple signals, each received signal corresponding to one neuron in the input layer. The neuron of the first hidden layer may then apply a mathematical function which takes multiple input values, thereby obtaining a single processed value or array of values from the multiple received signals. In embodiments, the mathematicalfunction may be non-linear and / or discontinuous.The single processed value or array of values may be transmitted as a signal by thesynapses connecting the first hidden layer to the next hidden layer of neurons. In some embodiments, the first hidden layer is connected to the final layer of the neural network, referred to as the output layer.In some embodiments, the neural network may comprise ^ > 1 hidden layers. The ^hidden layers are connected sequentially by synapses and collectively functionsimilarly to the first hidden layer, each hidden layer receiving at least one inputsignal, processing the input signal / signals, and outputting a signal to be transmittedto the next layer. The ^^^hidden layer of the neural network is connected to the output layer. Each neuron of the output layer processes the signals it receives, and outputs a final output of the neural network.Additionally, each synapse has a respective associated weight, wherein the weightmay be a real number. The associated weight may be interpreted as a weight of a signal emanating from the neuron and / or a weight of a signal transmitted by thesynapse. A neuron may have an associated first threshold so that an incoming signalis disregarded if the input value modulated by the signal strength is below the firstthreshold. Alternatively or in addition, the neuron may have an associated second threshold so that an output value is only transmitted if the output value modulated bythe weight of the synapse is above the second threshold.Learning a neural network comprises a process of refining initial weights associatedto the synapses of the neural network. Refining the weights may comprise empiricalrisk minimization on a labelled training data set, wherein the weights are graduallyrefined to minimize the discrepancy between predicted values and actual values ofthe training data set. In implementations, the weight updates may be performedusing backpropagation algorithms.In a distributed implementation of a neural network, the set of synapses and the setof neurons are distributed over at least two physical computing nodes, so that some subset of the neurons and some subset of the synapses are realized in one memory and the remaining neurons and the remaining synapses are realized in a physically distinct memory. In such distributed implementations, some synapses may be implemented as logical functions within a computational node, but synapses connecting a first neuron implemented in a first computing node to a second neuron implemented in a second computing node may be implemented partly as a physicalcommunication link. A signal transmitted through such a synapse necessarily has to be transmitted by means of a signal from the first computing node to the second computing node.In TNNs, the synapses allow signals to flow both forward and backward along thesynapse.The method 100 is now presented in more detail. The method is performed by a firstnetwork node in the communication network, where the first network node isassociated to a pre-synaptic neuron of the TNN. In an TNN, two neurons connected by a synapse may be referred to as a pre-synaptic neuron and a post-synapticneuron relative the synapse, where the pre-synaptic neuron transmits output forwardalong the synapse and the post-synaptic neuron transmits output backwards alongthe synapse. That is, the synapse has a well-defined direction and the terms pre-synaptic and post-synaptic are relative to the well-defined direction. Note that thesame neuron may be a pre-synaptic neuron relative a first synapse and a post- synaptic neuron relative a second synapse.In a live communication network implementation of the method, time series datarelated to the system may be sampled in asynchronous time, in the sense that anevent from, for example, a base station in a communication network or an Internet ofThings, IoT, sensor may be registered at any time. Asynchronous sampling contrastswith synchronous sampling, where events can only be recorded at predefined periodic time steps. In asynchronous sampling, the time series data may be irregularly sampled for example because an IoT sensor samples only when certain (irregularly spaced) events occur. Continuous time models, such as continuous time neural networks, are able to accept input at any time and are better suited for use with asynchronously sampleddata. Therefore, continuous time neural networks may provide improved adaptivecomputation over discrete time neural networks. Additionally, due to the lack ofdiscretization, continuous time neural networks may also provide improved learningof the temporal dynamics of the related real time system over discrete time neuralnetworks. In particular, continuous time neural networks may provide betterextrapolation capabilities for real time systems than discrete time neural networks.The mapping ^ from the inputs of a continuous neural network to the hidden states,may be defined in terms of ordinary differential equations, ODEs, where the right-hand side of the equation may be referred to as the state evolution function:where ^(^) is the hidden state vector as a function of the time ^, ^(^) is the input attime ^, and ^ is a vector comprising the parameters (e.g. weights) of the neuralnetwork. Hence, one forward-pass, i.e. a single evaluation of the state evolutionfunction with a fixed input, to update the parameters may be written as:^(^ + ^^) = ^(^) + ^^ ^(^(^), ^(^), ^, ^)where the gradients ^^ may be computed using the ordinary differential equationdescribing the state evolution and backward propagation through time as: The parameters can then be updated as: ^^^^ : = ^^^^ + ^^^for some step size ^ > 0.In some continuous time recurrent neural networks, the ODEs comprise anadditional parameter ^, which provides a more stable neural network by boundingthe state evolution function, thereby preventing extreme state values: Such a class of continuous time recurrent neural networks are the LTC networkswhich were first introduced in Hasani, R., Lechner, M., Amini, A., Rus, D., & Grosu,R. (2021). Liquid Time-constant Networks. Proceedings of the AAAI Conference onArtificial Intelligence, 35(9), 7657-7666. https: / / doi.org / 10.1609 / aaai.v35i9.16936.LTC networks have shown outstanding performance over the state of the art in taskssuch as navigation of unknown territory with drones, see “Liquid” Neural NetworkAdapts on the Go. IEEE spectrum.2023. https: / / spectrum.ieee.org / amp / liquid-neural-networks-2659899772, retrieved 2024-03-01. . Moreover, LTC networks are afoundational building block of neural circuit policy, NCP, architectures. An advantageof the NCP architecture is a connection topology between inter-neurons andcommand neurons with 90% sparsity in the inter-neurons, enabling less storage andmemory requirements than the state of the art. An LTC network is trained in two steps, using an ODE solver and backwardpropagation through time. However, due to their sparse nature, LTC networks learnquicker on smaller data samples than the state of the art. Thereby, the computational complexity of both the ODE solver and the backward propagation through time is balanced by a reduced number of training rounds and iterations. Additionally, LTCnetworks are adaptive without retraining or finetuning, thus greatly reducing anyassociated computational overhead. The NCP architecture inherits these advantages from LTC networks. An NCParchitecture comprises four hidden layers of specific LTC networks (sensory, inter-neuron, command, and motor) where intermediate neurons are highly sparse innumber and the synapses are highly recurrent.In the ODEs determining an LTC, the state evolution function is scaled by a biasingparameter ^ as shown below: Note that, in this ODE, the coefficient of the hidden states ^(^) is time-varying, incontrast to the continuous time recurrent neural network where the coefficient is aconstant. Additionally, an LTC comprises a variable time constant ^ = ^^^^ which isitself learned from the input data: The variable time constant ensures that, even if the inputs in some training iterationsare abnormally high or low, the states of the network remain bounded. In particular,the state of the individual neurons becomes bounded. This liquidity of the time constant allows for adaptability without risk of highly anomalous data causing catastrophic forgetting. The liquidity is realized using a negative feedback mechanism within the synapse of two neurons (a pre-synaptic neuron and a post- synaptic neuron).It is therefore desirable to develop solutions for the implementation of LTC networksin communication systems. Due to the nature of available computational resources, it is of interest to develop distributed learning implementations of LTC networks. In the state of the art, there are implementations of long-term short-term memory models in the scope of federated learning, where model parameters are exchanged between the client and server nodes sequentially to obtain averaged models at the client nodes. However, LTC networks are unsuited for this type of sequential federated learning, since a forward pass operation from a pre-synaptic neuron requires immediate feedback from the corresponding post-synaptic neuron, so the feedback can be used to update the pre-synaptic neuron, and so on. Methods according to the disclosure are therefore particularly suited for LTC networks.Returning to Fig. 1, the method 100 comprises receiving S101, from a second nodeof the communication network associated to a post-synaptic neuron of the TNN, an indication that a hidden state of the post-synaptic neuron has decayed.The method 100 comprises transmitting S102, to the second node, a pre-synapticstimulus. The pre-synaptic stimulus may comprise the hidden state of the pre- synaptic neuron. The hidden state may additionally comprise the hidden state of the pre-synaptic neuron modified by the current weight of the pre-synaptic neuron and / or the current weight of the synapse connecting the pre-synaptic neuron and the post- synaptic neuron. The first method 100 comprises receiving S103, with a scheduled acknowledgement message associated to the transmitted pre-synaptic stimulus, a hidden state information related to the post-synaptic neuron. The hidden state information related to the post-synaptic neuron may comprise an updated hidden state information of the post-synaptic neuron. The hidden state information may comprise an updated hidden state information related to the updated hidden state modified by the current weight of the post-synaptic neuron and / or the synapse connecting the pre-synaptic neuron and the post-synaptic neuron. The acknowledgement message is an acknowledgement message associated to the received pre-synaptic stimulus. In embodiments, the acknowledgement message may be a scheduled acknowledgement message according to a standard for communication. In embodiments, the standard for communication may be a telecommunications standard such as a standard set by the 3rdGeneration Partnership Program, 3GPP. For example, the standard may be a standard for Long- Term Evolution, LTE, communication, 5G New Radio, NR, communication, or any future standard. By way of further example, the standard may be a short-range wireless standard such as a WiFi standard set by the Institute of Electrical and Electronics Engineers, IEEE, or other suitable standardizing bodies. By way of further example, the standard may be a combination of multiple standards in a hybridnetwork comprising for example both WiFi communication links and 5G NRcommunication links. An acknowledgement message is a signal passed between communicating devices in a communication system to signify receipt of a message. In some communicationsystems, the acknowledgement message may additionally signify that the receivedmessage could be decoded and / or demodulated correctly, where the correctness ofthe decoding may be determined using checksums or more generally errorcorrecting codes. In some communication systems, an acknowledgement messageis expected by the sending device within a specific timeframe, and if no acknowledgement message is received the message is retransmitted. In other communication systems, a negative-acknowledgement message is transmitted if an expected message did not arrive, and / or if a received message could not bedecoded / demodulated correctly. In other communication systems, a hybridacknowledgement message protocol may be used, wherein both failure to send anacknowledgement message within a predefined timeframe and sending a negative- acknowledgement cause the sending device to retransmit the message. An acknowledgement message may be a part of an automatic repeat request, ARQ,protocol. The hidden state information may for example be piggybacked on thepayload of a scheduled acknowledgement message in a hybrid automatic repeatrequest, HARQ, protocol between geographically distinct first node and second nodecommunicating using a NR standard or an LTE standard.The HARQ message may be a synchronous HARQ message or an asynchronousHARQ message. The HARQ message may be an uplink HARQ message or adownlink HARQ message. In embodiments, the first node and the second node may comprise nodes in an Internet of Things, IoT, network. The IoT network may comprise devices communicating over wireless links, where the wireless links may implement an IoT over cellular protocol such as Narrowband LTE, NB-LTE, machine-typecommunication, MTC, or device to device, D2D, communication. Alternatively or inaddition, the wireless links may implement low rate wireless personal area network, WPAN, communication such as SigFox, ZigBee, or XBee. Alternatively or in addition,the wireless links may implement an application protocol such as Web Socket,Message Queuing Telemetry Transport, MQTT, or Constrained Application Protocol,CoAP. Alternatively, the first node may be a network function of an application function and the second node may be a network function or an application function or any other external consumer in a telecommunications network. A network function is a logical component of a communication network, typically realized by means of server virtualization, so that a network function is implementedwithin one or more virtual machines. Network functions may comprise, for example,Policy Control Function (PCF), Session Management Function (SMF), User Plane Function (UPF), and Access and Mobility Function (AMF).An external application function in a network may be a (virtualized) 3rd partyapplication function with some access to the telecommunication network. Theexternal consumer may, for example, provide control for drones or delivery robots and as such have access to network data through a data collection function (e.g.network data analytics function in NR) which may be processed and / or used to trainmachine learning algorithms supporting the external consumer.The acknowledgement message between network and / or application functions maycomprise a Naf_Event_Exposure_Notify or a Nnf_Event_Exposure_Notify message. Alternatively, the first node and the second node may be open radio access network (ORAN) nodes, and the acknowledgement message may be a response request message between a near real-time radio interface and core, RIC, and non-real time RIC via the A1 interface. Alternatively, the acknowledgement message may be a response request message between non-real time RIC and an evolved nodeB (eNB) or a next generation nodeB (gNB), or a radio access node according to any futurestandard via the O1 interface. Alternatively, the acknowledgement message may bea response request message between near real-time RIC and a radio access nodevia the E2 interface. An ORAN node is a node in a telecommunications network which supports an ORAN specification (e.g. a specification published by the O-RAN Alliance or any similar organization) and may operate alone or together with other nodes to implement one or more functionalities of any node in the telecommunications network, including oneor more network nodes and / or core network nodes. The ORAN node may support aspecification by, for example, supporting an interface defined by the ORANspecification, including an A1, O1, E2, X2, or Xn interface, an open fronthaul userplane interface, or an open fronthaul management plane interface. Moreover, an ORAN node may be a logical node in a physical node. The ORAN node may be implemented in a virtualization environment in which one or more network functions is virtualized. For example, the virtualization environment may include an O-cloud computing platform orchestrated by a Service Management and Orchestration Framework via an O2 interface defined by the O-RAN alliance or comparable technologies. Alternatively, the first node may be an ORAN node and the second node may be a network node. Alternatively, the first node may be a network node and the second node may be an ORAN node. Returning to Fig.1, the method 100 may further comprise updating S104 the hidden state of the pre-synaptic neuron in response to the received hidden state of the post- synaptic neuron. The method 100 may further comprise transmitting S105 the new pre-synaptic stimulus at an optimal time, where the optimal time is determined based on at least an estimated communication const for transmitting a pre-synaptic stimulus and the most recent hidden state. Optimizing when to transmit a new pre-synaptic stimulus may comprise using an optimizer in the form of a trained machine learning algorithm at the first node, which takes as input the estimated communication cost for transmitting the pre-synaptic stimulus and the most recent hidden state and outputs a predicted optimal time to transmit the pre-synaptic stimuli.Alternatively or in addition, the first node may comprise an outlier detectormechanism, preventing the first node from transmitting an outlier value as a pre- synaptic stimulus to the second node. Fig.2 depicts a second method 200 according to the disclosure. The second method200 is a method for distributed learning of a TNN in a communication network. Themethod is performed by a second node of the communication network, where thefirst second is associated to a post-synaptic neuron of the TNN.The second method 200 comprises receiving S201, from a first node of thecommunication system, where the first node is associated to a pre-synaptic neuron of the TNN, a pre-synaptic stimulus. The first node of the communication system and the second node of the communication system are connected by a communication link, through which a synapse from the first node to the second node is realized. The communication link may be a wired link or a wireless link. The pre-synaptic stimulus is an output from the first node generated by processing training data and / or prior feedback from one or more pre-synaptic neurons. That is, the pre-synaptic stimulus is a signal transmitted along the forward direction of the synapse.The second method 200 comprises transmitting S202, with an acknowledgementmessage associated with the received pre-synaptic stimulus, a hidden state information to the first node, wherein the hidden state information is related to thepost-synaptic neuron. The hidden state information ℎ^ at some time ^ can bedetermined by a simple look-up of the value of and the value can then betransmitted along with an acknowledgement message or otherwise encoded in anacknowledgement message. By way of example, the hidden state information maybe appended to the payload of an ACK message in L2 communication.In some embodiments, receiving S201 a pre-synaptic stimulus may occur at pre- determined time intervals, where the length of the pre-determined time interval may depend on at least the use case and the layer at which the distributed learning is performed. By way of example, learning in the radio or media access control (MAC) layers may comprise time intervals in the range of milliseconds to a few seconds. In higher layers of the network, learning may comprise time intervals in the order of seconds to minutes. In other embodiments, the TNN is a liquid time constant neural network, LTC network, and the receiving S201 a pre-synaptic stimulus may occur at any time. The method 200 may further comprise calculating S203 a hidden state information of the post-synaptic neuron. Calculating the hidden state information may comprise using the mathematical function associated to the post-synaptic neuron with the received pre-synaptic stimulus to update a hidden state of the post-synaptic neuron. The updated hidden state information of the post-synaptic neuron may be transmitted with the acknowledgement message to the pre-synaptic neuron. The method 200 may further comprise transmitting S204 to the first node an indication that a state of the post-synaptic neuron has changed. A state of the post- synaptic neuron is said to have changed if it has not been updated in a period of time exceeding a pre-determined update threshold. In embodiments, the state changing may comprise the state decaying. The state of the post-synaptic neuron is said to have decayed if the input to the hidden state comprises input from a closed loop of neurons, i.e. the input comprises no new information. Equivalently, the state of the post-synaptic neuron is said to have decayed if it has not exceeded a state threshold within a pre-determined time update threshold, that is, the state has remained static for a time period exceeding the pre-determined state update threshold. The method 200 may further comprise receiving S205, from the first node, a second pre-synaptic stimulus in response to the transmitted indication that a state of the post-synaptic stimuli has decayed. In embodiments, the second pre-synaptic stimulus may be transmitted as part of an acknowledgement message associated to the transmitted indication. Three examples of embodiments of the methods 100, 200 and how the two methods may be performed simultaneously by a first node and a second node will now be discussed in more detail, to enable the person skilled in the art to practice theteachings of the disclosure. References in parenthesis refer to the correspondingmethod steps of Fig.1 and Fig.2. Fig.3 is a signaling diagram illustrating a communication flow between a first node300a and a second node 300b in a communication network. The first node 300a isassociated with a pre-synaptic neuron of a TNN and the second node 300b is associated with a post-synaptic neuron of the TNN.When the first node 300a receives S101 a state change indication for a neuron (thepre-synaptic neuron?) comprises therein, the first node 300a transmits (S102) S301a message comprising an indication of the pre-synaptic stimulus of the pre-synapticneuron to the second node 300b. The transmitted message may comprise aNnwdaf_ModelTraining_Subscribe message. After receiving S201 the pre-synapticmessage, the second node calculates (S203) S302 a hidden state information of thepost-synaptic neuron and transmits (S202) S303 an acknowledgement messagecomprising an indication of the retrieved hidden state information of the post-synapticneuron. The acknowledgement message may comprise aNnwdaf_ModelTraining_Notify message. The first node 300a checks S304 whetherthere are new pre-synaptic stimuli available to be transmitted, which may result inrepeating step S301. The second node 300b checks S305 whether the current stateof the post-synaptic neuron has decayed. The checking S304 and S305 may beperformed at predetermined time intervals. When the current state is determined tohave decayed, the second node 300b transmits S306 an indication to the first node300a that the hidden state has decayed. The transmitted indication may comprise aNnwdaf_ModelTraining_Subscribe message. The first node responds to the decayindication by transmitting S307 a new pre-synaptic stimulus to the second node300b. In response to receiving the new pre-synaptic stimulus the second node 300bchecks S308 the hidden state of the post-synaptic neuron and transmits S309 thehidden state with an acknowledgement message related to the received new pre-synaptic stimulus. The acknowledgement message may comprise aNnwday_ModelTraining_Notify message.Fig. 4 is a signaling diagram illustrating a communication flow between a first node400a and a second node 400b in a communication network. The first node 400a is associated to a pre-synaptic neuron of a TNN and the second node 400b is associated with a post-synaptic neuron of the TNN. The signaling diagram illustratesan embodiment implemented in an IoT network following a Message QueuingTelemetry Transport (MQTT) protocol, as defined by the OASIS standardorganization. When the first node 400a receives S101 a state change indication for apost-synaptic neuron of the second node 400b, the first node transmits (S102) S401a pre-synaptic stimulus related to the pre-synaptic neuron in the first node to thesecond node 400b. The transmitted message may be an MQTT Publish message.After receiving (S201) the pre-synaptic stimulus message, the second nodecalculates (S203) the hidden state information of the post-synaptic neuron andtransmits (S202) S402 the hidden state to the first node with an acknowledgementmessage. The acknowledgement message may be an MQTT Publish message andthe hidden state information may be added to the payload of the MQTT Publishmessage. The first node 400a, in response to receiving the hidden state information,estimates S403 a communication cost associated to transmitting a new pre-synapticstimulus to the second node as a function of at least current latency and linkutilization. The estimate may be a projected estimate over some future time period. The first node checks S404 if new pre-synaptic stimuli are available. The first nodedetermines (S105) S405, based on at least the estimated cost of a transmission, thehidden state of the pre-synaptic neuron, and the new pre-synaptic stimulus, totransmit S406 a new pre-synaptic stimulus. The new pre-synaptic stimulus may betransmitted with an MQTT Publish message.Fig. 5 is a signaling diagram illustrating a communication flow between a first node500a and a second node 500b in a communication network. The first node 500a is associated to a pre-synaptic neuron of a TNN and the second node 500b isassociated to a post-synaptic neuron of a TNN. The communication flow relates to athird embodiment in the form of a cloud-implementation of a method according to thedisclosure.In this embodiment, a plurality of application functions and network functions areimplemented with computational abilities and memory abilities to train local machinelearning models. Each network function and each application function may therefore comprise one or more neurons and the synapses may be implemented over thenetwork exposure function (NEF). The first node 500a comprises a gNB and thesecond node 500b comprises an access and mobility function (AMF). The first nodeand the second node communicate using Internet Protocol (IP) such as IP version 6(IPv6) according to the IEEE.The embodiment comprises the second node 500b determining S501 that a state ofa post-synaptic neuron has decayed. The embodiment comprises the second node500b transmitting (S204) S502 a decay indication to the first node 500a. Thetransmitted message may comprise a Nnwdaf_MLMModelMonitor_Notify requestmessage, where the decay indication is added to the payload of the message. Thefirst node obtains S503 a new pre-synaptic stimulus. The obtained pre-synapticstimulus is transmitted (S102) S504. The message transmitting the new pre-synapticstimulus may comprise a Nnwdaf_MLMModelMonitor_Notify response message.The second node calculates (S203) S505 the hidden state information and transmits(S202) S506 the hidden state information with an acknowledgement message. Theacknowledgement message may comprise a Nnwdaf_MLMModelMonitor_Notifyresponse message.Fig.6 is an illustration of an apparatus 600 which may execute methods 100, 200according to the disclosure. Instances of the apparatus 600 may together implementembodiments such as the embodiments of Figs 3-5, where the apparatus maycomprise the first node or the second node. The apparatus comprises a memory601, on which a computer program 602 comprising computer readable instructions which, on execution by a processor 604, cause the apparatus to perform methods 100, 200. Alternatively or in addition, the memory 601 may comprise a computer program product 603 on which the computer program 602 is stored. The apparatus 600 may be comprised in a network node of a communication system 700 (Fig.7). By way of example, the apparatus 600 may be comprised in a radio access node 800 (Fig.8).Fig. 7 is an illustration of an example of a communication system 700 in whichmethods according to the disclosure may be implemented. The communicationsystem 700 comprises a host 701 in communication with a telecommunicationnetwork 702. The telecommunication network 702 comprises a core network 706,the core network comprising a core network node 708. The core network is in communication with an access network 704, where the access network comprises network nodes 710A, 710B. The network nodes are in communication with one or more user equipments, UEs, 712A, 712B. Alternatively or in addition, the network nodes 710A, 710B may be in communication with a hub 714, where the hub is in communication with one or more UEs 712C, 712D. Additionally, UEs may be in communication with other UEs. The telecommunication network may employ any telecommunication standard as defined by a suitable standardizing body and theUEs may communicate for example by a suitable device-to-device protocol such asvehicle-to-vehicle communication as defined in the 5G NR standard or a short-rangewireless protocol such as Bluetooth.Fig. 8 is an illustration of an example of a radio access node 800 which may performmethods according to the disclosure. The radio access node may be a network node710A, 710B in the communication system 700. The radio access node acommunication interface 806. The communication interface comprises an antenna 810 receiving input from radio front-end circuitry 818, the radio front-end circuitrycomprising a filter 820 and an amplifier 822. The communication interface mayfurther comprise a port / terminal 816. The communication interface is powered by a power source 806. The communication interface may be controlled by processing circuitry 805, the processing circuitry comprising radio frequency transceiver circuitry812 and baseband circuitry 814. The processing circuitry may be powered by thepower source 808. The processing circuitry may further have access to a memory 804, and the memory may additionally be powered by the power source 808.Fig. 9 is a schematic of the logical components of a virtualization environment 900which may implement some or all of the functions of a network node in a distributedmanner, and which may perform methods according to the disclosure. Thevirtualization environment may comprise an application / virtual appliance / virtual node / server instance 902. The virtualization environment may further comprise hardware904 in the form of, for example, server hosts. The virtualization environment mayfurther comprise a virtualization layer 906. The virtualization environment may furthercomprise one or more virtual machines 908A, 908B. The virtualization environmentmay further comprise a management and orchestration function 910, orchestrating the virtualization and managing the interactions between the different logical components.Figs. 10a-d illustrate a comparison between the performance of different temporalneural networks. Three TNNs chosen for the comparison are LTC networks, LSTMnetworks, and CTRNNs, and the purpose of the demonstration is to show adaptability from a source data set to a target data set. Fig.10a shows the performance of each of the three methods when the training data comes from the source domain and the test data come from the source domain. Fig.10b shows the performance of each of the three models when the training data comes from the target domain and the test data comes from the source domain. Fig.10c shows the performance of each of the three models when the training data comes from the source domain and the test data comes from the target domain.Figs. 10a-c illustrate that the LTC network converges to a lower mean average erroron a test set of data than the LSTM network and the CTRNN in considerably fewertraining epochs. Fig.10d shows that the test accuracy of the LTC network is superior to the test accuracy of the LSTM network and the CTRNN even when the LTCnetwork is trained on 4284 samples and the LTSM network and CTRNN are trainedon 7284 samples.

Claims

CLAIMS 1. A method (100) for distributed learning of a temporal neural network, in acommunication network, the method performed by a first node of the communicationnetwork, the first node associated to a pre-synaptic neuron of the temporal neuralnetwork, the method comprising: receiving (S101), from a second node of the communication system, thesecond node associated to a post-synaptic neuron of the temporal neural network,an indication that a hidden state of the post-synaptic neuron has changed; transmitting (S102), to the second node, a pre-synaptic stimuli;receiving (S103), with a scheduled acknowledgement message associated tothe transmitted pre-synaptic stimuli, a hidden state information related to the post- synaptic neuron.

2. The method (100) according to claim 1, further comprising selectivelydelivering (S104) activations from pre-synaptic neuron to the post-synaptic neuronbased on estimated hidden state information of the post-synaptic neuron.

3. The method (100) according to claim 1 or 2, wherein the communicationnetwork is a telecommunication network.

4. The method (100) according to claim 1 or 2, wherein the first node and thesecond node are geographically distinct nodes of a telecommunication network and the request response message is a hybrid automatic repeat request, HARQ, message.

5. The method (100) according to claim 1 or 2, wherein the first node is anetwork function or an application function, or an external application function andthe second node is a network function or an application function or an external application function.

6. The method (100) according to claim 1 or 2, wherein the first node and thesecond node are part of an open radio access network, O-RAN, and the request response message is one of: a response request message between near real-time radio interface and core, RIC, and non-real time RIC via the A1 interface; a response request message between non-real time RIC and an evolved nodeB, eNB, via the O1 interface; or a response request message between near real-time RIC and a radio access node via the E2 interface.

7. The method (100) according to any one of claims 1-6, further comprising:determining (S105), based on at least an estimated communication cost fortransmitting a pre-synaptic stimuli and the most recently received hidden state, when to transmit a new pre-synaptic stimuli.

8. A method (200) for distributed learning of a temporal neural network in acommunication network, the method performed by a second node of thecommunication network, the second node associated with a post-synaptic neuron ofthe temporal neural network, the method comprising:receiving (S201), from a first node of the telecommunication system, the firstnode associated with a pre-synaptic neuron of the temporal neural network, a pre-synaptic stimuli; transmitting (S202), with an acknowledgement message associated with the received pre-synaptic stimuli, a hidden state information to the first node, wherein the hidden state information is related to the post-synaptic neuron.

9. The method (200) according to claim 8, wherein the temporal neuralnetwork is one of: a recurrent neural network, RNN; aliquid time constant, LTC, network; ora continuous time recurrent neural network.

10. The method (200) according to claim 8 or 9, wherein the communicationnetwork is a telecommunication network.

11. The method (200) according to any one of claims 8-10, further comprisingestimating (S203) a hidden state information related to the post-synaptic neuron.

12. The method according to any one of claims 8-11, further comprising: transmitting (S204), to the first node, an indication that a state of the post-synaptic neuron has changed; andreceiving (S205), from the first node, a second pre-synaptic stimuli in response to the transmitted indication.

13. The method (200) according to claim 12, wherein the indication that astate of the post-synaptic neuron has changed comprises an indication that the stateof the post-synaptic neuron has decayed.

14. The method (200) according to any one of claims 11-13, wherein the firstnode and the second node are geographically distinct nodes of a telecommunicationnetwork and the acknowledgement message is a hybrid automatic repeat request,HARQ, message.

15. The method (200) according to any one of claims 11-13, wherein the first node is a network function or an application function and the second node is a network function or an application function or any other external application function.

16. The method (200) according to any one of claims 11-13, wherein the first node and the second node are part of an open radio access network, O-RAN, and the request response message is one of: a response request message between near real-time radio interface and core, RIC, and non-real time RIC via the A1 interface; a response request message between non-real time RIC and an evolved nodeB, eNB, via the O1 interface; or aresponse request message between near real-time RIC and a radio accessnode via the E2 interface.

17. An apparatus (600) for distributed learning of a temporal neural network,in a communication network, the apparatus comprised in a first node of the communication network, the first node associated to a pre-synaptic neuron of thetemporal neural network, the apparatus configured to:receive, from a second node of the communication system, the second nodeassociated to a post-synaptic neuron of the temporal neural network, an indicationthat a hidden state of the post-synaptic neuron has changed; transmit, to the second node, a pre-synaptic stimuli; receive, with a scheduled acknowledgement message associated to the transmitted pre-synaptic stimuli, a hidden state information related to the post- synaptic neuron.

18. The apparatus according to claim 17, further configured to selectively deliver activations from pre-synaptic neuron to the post-synaptic neuron based on estimated hidden state information of the post-synaptic neuron.

19. The apparatus (600) according to claim 17 or 18, wherein thecommunication network is a telecommunication network.

20. The apparatus (600) according to claim 17 or 18, wherein the first nodeand the second node are geographically distinct nodes of a telecommunication network and the request response message is a hybrid automatic repeat request, HARQ, message.

21. The apparatus (600) according to claim 17 or 18, wherein the first node isa network function or an application function, or an external application function andthe second node is a network function or an application function or an external application function.

22. The apparatus (600) according to claim 17 or 18, wherein the first nodeand the second node are part of an open radio access network, O-RAN, and the request response message is one of: a response request message between near real-time radio interface and core, RIC, and non-real time RIC via the A1 interface; a response request message between non-real time RIC and an evolved nodeB, eNB, via the O1 interface; or a response request message between near real-time RIC and a radio access node via the E2 interface.

23. The apparatus (600) according to any one of claims 17-22, furtherconfigured to: determine, based on at least an estimated communication cost for transmitting a pre-synaptic stimuli and the most recently received hidden state, when to transmit a new pre-synaptic stimuli.

24. An apparatus (600) for distributed learning of a temporal neural network ina communication network, the apparatus comprised in a second node of the communication network, the second node associated with a post-synaptic neuron ofthe temporal neural network, the apparatus configured to:receive (S101), from a first node of the telecommunication system, the firstnode associated with a pre-synaptic neuron of the temporal neural network, a pre-synaptic stimuli; transmit (S102), with an acknowledgement message associated with the received pre-synaptic stimuli, a hidden state information to the first node, wherein the hidden state information is related to the post-synaptic neuron.

25. The apparatus (600) according to claim 24, wherein the temporal neuralnetwork is one of: a recurrent neural network, RNN; a liquid time constant, LTC, network; or a continuous time recurrent neural network.

26. The apparatus according to claim 8 or 9, wherein the communication network is a telecommunication network.

27. The apparatus (600) according to any one of claims 24-26, furtherconfigured to estimate (S103) a hidden state information related to the post-synaptic neuron.

28. The apparatus (600) according to any one of claims 24-27, furtherconfigured to: transmit (S104), to the first node, an indication that a state of the post- synaptic neuron has changed; and receive (S105), from the first node, a second pre-synaptic stimuli in response to the transmitted indication.

29. The apparatus (600) according to claim 28, wherein the indication that astate of the post-synaptic neuron has changed comprises an indication that the state of the post-synaptic neuron has decayed.

30. The apparatus (600) according to any one of claims 24-29, wherein thefirst node and the second node are geographically distinct nodes of a telecommunication network and the request response message is a hybrid automatic repeat request, HARQ, message.

31. The apparatus (600) according to any one of claims 24-29, wherein thefirst node is a network function or an application function and the second node is a network function or an application function or any other external application function.

32. The apparatus (600) according to any one of claims 24-29, wherein thefirst node and the second node are part of an open radio access network, O-RAN, and the request response message is one of: a response request message between near real-time radio interface and core, RIC, and non-real time RIC via the A1 interface; a response request message between non-real time RIC and an evolved nodeB, eNB, via the O1 interface; or a response request message between near real-time RIC and a radio access node via the E2 interface.

33. A computer program (602) comprising machine readable instructionswhich, on execution by a processor (604) of an apparatus (600), cause theapparatus to perform a method according to any one of claims 1-7.

34. A computer program product (603) comprising a non-transient storagemedium, on which a computer program (602) according to claim 33 is stored.

35. A computer program (602) comprising machine readable instructionswhich, on execution by a processor (604) of an apparatus, cause the apparatus toperform a method according to any one of claims 8-16.

36. A computer program product (603) comprising a non-transient storagemedium, on which a computer program (602) according to claim 35 is stored.

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