Adaptive least mean square algorithm for pulse neural network deep learning

Abstract

The invention provides a self-adaptive least mean square algorithm for pulse neural network deep learning. The method is a self-adaptive least mean square (LMS) algorithm based on error gradient descent (also known as a Delta rule). Different from a traditional error gradient back propagation learning algorithm, a back propagation matrix adopts a symbol matrix of a forward propagation matrix, weight increment adopts online adjustment and is determined according to a Delta rule, and a value of the weight increment is a product of a back propagation error, a presynaptic potential and a postsynaptic potential.

Description

Technical Field

[0001] The present application relates to a spiking neural network, and in particular to an adaptive least mean square algorithm for deep learning of a spiking neural network. Background Art

[0002] Neurons are the computing units of neural networks. The neural networks formed by connecting them can acquire complex intelligent computing capabilities through training. Their mathematical modeling is the core of the neural network learning algorithm.

[0003] Neuron models have roughly gone through three generations. The first generation is digital neurons and their networks, such as the simplest McCulloch & Pitts (MP) model, which characterizes neurons into two states of inhibition and excitation represented by 0 and 1 by comparing the input value with the threshold. The second generation is analog neurons and their networks, which use monotonic excitation functions to express the relationship between input values ​​and spike discharge rates, and use this to characterize the degree of neuron inhibition and excitation. In recent years, researchers have used the simplified Hodgkin & Huxley (HH) model of neuron spike discharge as the computing unit of neural networks, such as the Leaky Integrate-and-Fire (LIF) model, which is the third generation of spiking neurons and their networks. This type of neuron and its network better maintains the morphology and dynamic characteristics of biological neurons, has great potential in brain-like modeling and computing, and has become the key to basic research on brain-like intelligence.

[0004] Since the middle of the last century, researchers have made considerable progress in the study of neurons, neural networks and their algorithms. Deep learning algorithms for the synaptic connection strength of neural networks with intelligent computing capabilities have been widely studied and have achieved great success, becoming a key core technology for machine learning. The earliest and most far-reaching learning algorithm with biological significance that does not require an identified data set is the Hebb rule, which requires the construction of a network energy function and then uses the Hebb rule learning algorithm to minimize the network energy function. This type of algorithm has achieved great success. However, if the labels corresponding to the data set used for learning or training are identified by experts, then the wise approach is obviously to minimize the difference between the actual output results generated by the network and the identified results. This method has spawned effective error-driven learning rules, such as the Widrow-Hoff algorithm of the Delta rule, also known as the adaptive LMS algorithm. Later, this method was extended to the training of multilayer perceptrons, which is the famous error gradient back-propagation (BP) algorithm that is still widely used in various deep neural network training. Recently, the spike timing-dependent plasticity (STDP) learning rule derived from the Hebb rule and applied to spiking neural networks has obtained biological evidence and is receiving widespread attention. However, the academic community generally believes that error-driven learning algorithms are superior to Hebb rule learning algorithms. Therefore, the extension of the BP algorithm to supervised learning of deep spiking neural networks has received more and more attention, especially the use of spike sequence identification data, which is more important and closer to brain-like intelligence.

[0005] Most of the existing deep learning algorithms for spiking neural networks use error-replacing gradient back propagation, and the back propagation matrices are all nonlinear functions of the forward propagation matrix. For example, the back propagation matrix of the spatiotemporal back propagation (STBP) algorithm is a nonlinear combination of the membrane potential error gradient, the output pulse error gradient, and the forward propagation matrix; the back propagation matrix of the time spike sequence learning back propagation (TSSL-BP) algorithm is a nonlinear combination of the postsynaptic-presynaptic derivative and the forward propagation matrix. These learning algorithms all require the back propagation matrix to be determined based on the forward propagation matrix, that is, the back propagation matrix is ​​a function of the forward propagation matrix, that is, the error gradient back propagation changes as the forward propagation matrix changes. The latest research has found that in the back propagation learning algorithm of simulated neural networks, randomly selecting a fixed back propagation matrix can still achieve good learning results. Compared with the stochastic gradient descent method, the use of the symbol matrix of the forward propagation matrix as the error back propagation matrix while normalizing batch processing and / or Manhattan batch processing still maintains robust performance. Summary of the invention

[0006] In view of the above problems, this application aims to propose an adaptive least mean square algorithm for deep learning of spiking neural networks.

[0007] The adaptive least mean square algorithm for deep learning of pulse neural network of the present application includes: First, by using the substituted gradient method, the three-factor delta learning rule of the output layer based on the nonlinear membrane voltage is obtained: , superscript represents the layer number of the neuron, the subscript i represents the position of the neuron in the layer, and t represents the discharge time of the neuron and is within the time window [0, T]. Indicates The i-th neuron and the The weight adjustment increment of the j-th neuron; is the resizing constant; , represents the error signal of the output layer neuron, where For the The jth neuron in the layer outputs a pulse time series, is the expected time series, is a constant; ,in is a replacement function, is the membrane potential, ,in for The integral of is the pulse sequence; Secondly, the back propagation network credit allocation strategy is used to achieve the output layer The error signal of the jth neuron in the layer Back propagation to the hidden layer The error signal of the i-th neuron in the layer ;but ,in , for The i-th neuron and the The connection weight of the jth neuron is such that , as the output layer The i-th neuron in the layer learns the rule, where For the The hth neuron in the layer and the The connection weight of the ith neuron; Finally, the output layer The learning rule of the i-th neuron in the layer is extended to the i-th neuron in the hidden layer. The hth neuron in the layer; The error signal of the hth neuron in the layer ,in , For the -hth neuron in layer 1 and The connection weight of the ith neuron of ,in For the The xth neuron in the layer and the The connection weight of the h-th neuron is calculated; this process is repeated to realize the back propagation of the pulse neural network.

[0008] In this application, the symbol matrix of the forward propagation matrix weights is used as the error gradient back propagation matrix, which helps to improve the performance and adaptability of the network. Combined with the normalized batch processing technology, the training stability and generalization ability of the network can be further improved, and the risk of overfitting can be reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 This is a diagram of the pulse neuron model and its multi-layer feedforward pulse neural network structure.

[0010] Figure 2 Schematic diagram of the error gradient back propagation strategy.

[0011] Figure 3 This is a new learning algorithm for the three-factor delta rule - the structure diagram of the adaptive LMS algorithm. DETAILED DESCRIPTION

[0012] The adaptive least mean square algorithm for deep learning of pulse neural networks in this application is an adaptive least mean square (LMS) algorithm based on error gradient descent (also known as Delta law). Different from the traditional error gradient back propagation learning algorithm, its back propagation matrix uses the sign matrix of the forward propagation matrix, and the weight increment is adjusted online, which is determined by the Delta law, and its value is the product of the back propagation error, presynaptic potential and postsynaptic potential. The specific algorithm derivation process is introduced below.

[0013] 1). Spiking neuron model Select the leak-integrated-discharge (LIF) spiking neuron model, whose membrane potential is: here is the membrane time constant, R is the membrane resistance, I(t) is the stimulation current and the action time window is T. , Consider the postsynaptic potential (PSP) and set it to Function, that is others are zero; yes The integral of Others are zero, is the time constant of the postsynaptic potential response. Considering that the neuron spike discharge, refractory period and reset are continuous processes, the above pulse neuron model is:

[0014] here is the connection weight of another neuron connecting to this neuron, is the 01 time series input from another neuron to this neuron, is the neuron's resting potential, is the neuron threshold potential. is the zero-crossing detection reset operator, whose differential It is a singular function , usually with a non-singular function Alternative , such as the bilateral exponential function, which is an alternative to the gradient descent method.

[0015] 2). Multi-layer spiking neural network model Without loss of generality, a multi-layer pulse neural network structure is selected, such as Figure 1 As shown. The output pulse time series of neuron i in the network is , where the superscript It indicates the layer number, the subscript i indicates its position in the layer, and t indicates its discharge time within the time window [0, T]. Indicates The i-th neuron in the layer is connected to the The connection weights between the jth neurons in the layer, Indicates The hth neuron in the layer is connected to the The connection weights between the i-th neurons in the layer. , and The number of neurons in each layer is , and . No. The hth neuron in the layer outputs a spike time series , No. The output pulse time series of the i-th neuron in the layer is , then The neurons in layer i and The membrane potential of neuron j in layer and They are:

[0016] in , remember The output pulse time series of the jth neuron in the layer is ,Right now Note the expected time series .

[0017] 3). Derivation of adaptive LMS algorithm Let at time t The square error function of the postsynaptic membrane potential of the jth neuron in the layer is: Then the integral of the neuron error square function is: use The output layer The sum of the squared errors between the actual and expected pulse time series of the postsynaptic potential of each neuron is used as the loss function, that is, Considering the connection weight of L(t) The gradient calculation is only related to Related, then For simplicity, the postsynaptic potential signal is , , , the error signal of the postsynaptic potential output layer neuron is , then the weight adjustment increment is: From (2) we get Calculate the membrane potential in the above formula Regarding the connection strength, that is, the weight The partial differential of Substituting the result into the above formula, we get: here is the iteration step size. Definition , , then the adaptive LMS algorithm for real-time online weight adjustment is:

[0018] The LMS algorithm for online real-time supervised learning of the above-mentioned time-coded multi-layer spike neural network ensures the instant adjustment of network parameters through a real-time update mechanism, thereby adapting to dynamically changing input data, which is particularly important for application scenarios that require real-time response.

[0019] First, by using the substituted gradient method, a three-factor delta learning rule for the output layer based on the nonlinear membrane voltage (the product of error, presynaptic and postsynaptic signals) is obtained, which is capable of training multilayer networks of integral-discharge neurons for nonlinear computation of spatiotemporal spike patterns.

[0020] Secondly, the back propagation network credit allocation strategy is used to achieve the output layer The error signal of the jth neuron in the layer Back propagation to the hidden layer The error signal of the i-th neuron in the layer ,in .

[0021] Finally, by adding the output layer The learning rule of the i-th neuron in the layer is extended to the i-th neuron in the hidden layer. The hth neuron in the layer ,in or , is the connection weight of the input layer. Back propagation is repeated in this way, such as Figure 2 As shown. An adaptive LMS algorithm for online real-time supervised learning is formed, as shown Figure 3 shown.

[0022] The invention provides a new tool for the research and practical application of deep spiking neural networks, and is expected to achieve better application results in related fields.

Claims

1. An adaptive least mean square algorithm for deep learning of spiking neural networks, comprising: First, by using the substituted gradient method, the three-factor delta learning rule of the output layer based on the nonlinear membrane voltage is obtained: , superscript represents the layer number of the neuron, the subscript i represents the position of the neuron in the layer, and t represents the discharge time of the neuron and is within the time window [0, T]. Indicates The i-th neuron and the The weight adjustment increment of the j-th neuron; is the resizing constant; , represents the error signal of the output layer neuron, where For the The jth neuron in the layer outputs a pulse time series, is the expected time series, is a constant; ,in is a replacement function, is the membrane potential, ,in for The integral of is a pulse sequence; Secondly, the back propagation network credit allocation strategy is used to achieve the output layer The error signal of the jth neuron in the layer Back propagation to the hidden layer The error signal of the i-th neuron in the layer ;but ,in , for The i-th neuron and the The connection weight of the jth neuron is such that , as the output layer The i-th neuron in the layer learns the rule, where For the The hth neuron in the layer and the The connection weight of the ith neuron; Finally, the output layer The learning rule of the i-th neuron in the layer is extended to the i-th neuron in the hidden layer. The hth neuron in the layer; The error signal of the hth neuron in the layer ,in , For the -hth neuron in layer 1 and The connection weight of the ith neuron of ,in For the The xth neuron in the layer and the The connection weight of the h-th neuron is calculated; this process is repeated to realize the back propagation of the pulse neural network.

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