Pulse neural network error back propagation training method based on local synaptic plasticity

Abstract

The invention discloses a pulse neural network error back propagation training method based on local synaptic plasticity, and the method comprises the steps: 1, building a pulse response model, taking a pulse sequence before and after synaptic neurons discharge as input, calculating a post-synaptic potential through a synaptic kernel function and weighted summation, and enabling the post-synaptic neurons to generate a new pulse as output; 2, simplifying the post-synaptic potential into two independent components by refining the pulse discharge time and approximately calculating the post-synaptic potential boundary value; 3, approximating a derivative between the post-synaptic potential and pulse counting by using pulse time dependent plasticity through a simplified post-synaptic potential calculation formula; and 4, combining local synaptic plasticity with a global optimization mechanism through a pulse time dependent plasticity approximate unknown derivative. According to the method, the advantages of local synaptic plasticity and a global optimization mechanism are fully utilized, the learning and adaptive capacity of the spiking neural network is enhanced, the method is closer to a biological nervous system, and the classification precision on training static and neuromorphic data sets is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of computer vision applications, and in particular relates to a pulse neural network error back propagation training method based on local synaptic plasticity. Background Art

[0002] Spiking neural networks are becoming increasingly popular due to their biological plausibility, hardware compatibility, and energy efficiency. They mimic the biological brain by examining the transmission of signals at the circuit level and consist of spiking neuron models that encode information using spike trains, thereby increasing computational power and the ability to effectively utilize spatiotemporal features.

[0003] Since multi-layer spiking neural networks have non-differentiable spiking activities and complex temporal dynamics, there are still significant challenges in discovering effective training rules. Existing spiking neural network learning methods can be divided into two categories: one is unsupervised learning, such as spike-timing dependent plasticity (STDP), and the other is supervised learning based on proxy gradient backpropagation (BP) and artificial neural network to spiking neural network conversion.

[0004] Nevertheless, there is no conclusive evidence that unsupervised learning or supervised learning is more suitable for training spiking neural networks. On the one hand, spike timing-dependent plasticity (STDP) takes into account the firing times of presynaptic and postsynaptic neurons, facilitating the adjustment of synaptic weights in response to their temporal dynamics. However, due to the lack of a global optimization strategy, it is susceptible to neural signal noise and encounters difficulties in scaling to larger networks and more complex tasks. On the other hand, backpropagation uses gradient descent to adjust network weights, which can speed up the convergence process and improve network performance. However, these backpropagation methods are limited in the weight calculation process and require appropriate gradient values, which is different from unsupervised methods in biological neural systems.

[0005] Recently, efforts have been made to integrate backpropagation (BP) and spike timing-dependent plasticity (STDP) methods, aiming to exploit the global optimization capability of backpropagation while maintaining the inherent biological plausibility of spike timing-dependent plasticity (STDP). However, these methods cannot exploit the inherent temporal features to handle event-based neuromorphic tasks in deep networks, which achieve better generalization by focusing on the spike rate and the last few firing times. Summary of the invention

[0006] In view of the fact that most existing spiking neural network training methods ignore the plasticity of local synapses and limit the ability to characterize time and connect neuronal dynamics, the purpose of the present invention is to propose a spiking neural network error back propagation training method based on local synaptic plasticity, which is used to capture the rate and time effects of discrete discharge times. The present invention can integrate local synaptic plasticity into the error back propagation training process, enhance the learning and adaptability of spiking neural networks, and improve the classification accuracy of spiking neural networks in static and neuromorphic data sets through a method that is closer to the biological nervous system.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] A pulse neural network error back propagation training method based on local synaptic plasticity comprises the following steps:

[0009] Step A: Establish an impulse response model, take the pulse sequence before the discharge of the presynaptic neuron and the postsynaptic neuron as input, calculate the postsynaptic potential through the synaptic kernel function and weighted summation, and when the cumulative postsynaptic potential exceeds the discharge threshold, the postsynaptic neuron generates a new pulse as output;

[0010] Step B: By refining the pulse discharge time of the pre- and post-synaptic neurons and approximating the boundary value of the post-synaptic potential, a simplified calculation formula for the post-synaptic potential is obtained, which is only related to the pulse discharge count of the pre- and post-synaptic neurons and the time difference of the last discharge of the pulse train;

[0011] Step C: Using the simplified calculation formula of postsynaptic potential in step B, the derivative between postsynaptic potential and pulse count is approximated by pulse time-dependent plasticity based on pulse count to untangle the rate and time effects of postsynaptic potential;

[0012] Step D: For the impulse response model established in step A, the unknown derivative between the postsynaptic potential and the impulse count is approximated by the impulse time-dependent plasticity in step C, and the overall gradient can be fully calculated for training. This effectively utilizes the superior performance of the error backpropagation method in achieving global error optimization, and also integrates the local update strategy provided by the impulse time-dependent plasticity.

[0013] The specific steps of step A are as follows:

[0014] Step A01: When calculating the postsynaptic potential, the spike neuron takes the spike sequence before the discharge of the presynaptic neuron and the postsynaptic neuron as input, and calculates the unweighted postsynaptic potential of the presynaptic neuron through the synaptic kernel function. in, represents the pulse discharge time of postsynaptic neuron i, represents the pulse discharge time of presynaptic neuron j, represents the last discharge time before the discharge time of the postsynaptic neuron, ∈(·) represents the synaptic kernel function, and the calculation formula is Among them, τ m and τ s denote membrane potential constant and time constant, respectively, and H(-·) denotes a step function;

[0015] Step A02: Substitute the unweighted postsynaptic potentials e of all presynaptic neurons i|j The weighted summation gives the total postsynaptic neuron cumulative potential u i (t) = ∑ j w ij e i|j , where w ij represents the weight connection between presynaptic and postsynaptic neurons;

[0016] Step A03: When the postsynaptic neuron accumulates potential u i Accumulate to the predetermined discharge threshold V th When the postsynaptic neuron outputs a pulse count o i And release voltage, the output pulse count calculation formula of postsynaptic neuron i is Among them, g(u i ) represents the floor function; during this period, the neuron does not respond to any additional input and enters the absolute refractory period.

[0017] The specific steps of step B are as follows:

[0018] Step B01: Calculate the synaptic kernel function calculation formula in step A01 in different cases. When ts≥0, let τ m =8τ s and but and The synaptic kernel function is approximated as Similarly, when ts<0, the synaptic kernel function is approximately Step B02: Calculate the effect of all presynaptic and postsynaptic spike train discharge times on the postsynaptic potential e i|j The total contribution of the presynaptic neuron j to the spike discharge time Assume that the first n discharge times are less than The postsynaptic potential can be expressed as: Under the same approximate conditions, e i|j It can be further expressed as:

[0019] For ease of observation, it is further simplified to Among them, j represents the output pulse count of postsynaptic neuron j;

[0020] Step B03: Simplify the postsynaptic potential of step B02 into a function It can be seen that the potential of the postsynaptic neuron is linearly related to the pulse count, and exponentially related to the last discharge time difference between the pre- and post-synaptic pulse trains.

[0021] The details of step C are as follows:

[0022] According to the simplification of the postsynaptic potential in step B04, the derivative between the postsynaptic potential and the pulse count is calculated using the pulse time-dependent plasticity based on the pulse count

[0023]

[0024] Among them, A + and A - represents the weight of synaptic change, τ represents the time decay constant, is the difference between the last firing times of presynaptic neuron j and postsynaptic neuron i.

[0025] The specific steps of step D are as follows:

[0026] Step D01: The present invention uses the mean square error loss function Where L represents the total loss function, o and y represent the actual discharge count and expected discharge count of the output neuron, respectively; the gradient derivative of each layer of the spiking neural network is Need to be calculated and then update the weight;

[0027] Step D02: For the i-th neuron in the output layer K, the chain rule is as follows in, represents the back-propagated firing rate error of neuron i, represents the time-dependent differential of spike activity, the back-propagated firing rate error of neuron i Calculation formula The calculation formula of the time effect differential of pulse activity

[0028] Step D03: In each hidden layer k, the back-propagated firing rate error of neuron i is: The calculation formula of the time effect differential of pulse activity

[0029] Step D04: For unknown and The derivative of the format uses spike-timing-dependent plasticity to approximate the derivative between the postsynaptic potential and the spike count, making the training process complete.

[0030] Compared with the prior art, the present invention has the following advantages:

[0031] First, the present invention calculates the contribution of the pulse discharge time series to the postsynaptic potential before the membrane potential of each postsynaptic neuron reaches the discharge threshold in the pulse response model, so that the construction of the pulse neuron is closer to that of the biological neuron;

[0032] Second, the present invention simplifies and approximates the postsynaptic potential, decomposing it into two independent variables, including the pulse discharge count of the pre- and post-synaptic neurons and the last discharge time difference of the pre- and post-synaptic neurons, thus solving the rate and time dependence of strong coupling;

[0033] Third, the present invention uses local spike time-dependent plasticity to approximate the derivative of spike time dependence during back-propagation, thereby enhancing the learning and adaptability of spike neural networks, and improves the classification accuracy of spike neural networks in static and neuromorphic data sets through an approach that is closer to biological nervous systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a forward calculation diagram of the pulse neural network of the method of the present invention.

[0035] Figure 2 Schematic diagram of postsynaptic potential calculation in the method of the present invention.

[0036] Figure 3 It is the overall forward transmission and backward training flow chart of the method of the present invention. DETAILED DESCRIPTION

[0037] The specific details of each step of the present invention are described in detail below with reference to the accompanying drawings.

[0038] The present invention proposes a pulse neural network error back propagation training method based on local synaptic plasticity.

[0039] The method mainly includes the following steps:

[0040] Step A: Establish a new impulse response model such as Figure 1As shown in FIG. 1 , it is a forward calculation flow chart of the spiking neural network of the present invention. For the i-th neuron in the l-th layer, the short gray thick solid arrow represents the existing pre- and post-synaptic neuron pulse sequence, the short black thick solid arrow represents the pulse signal generated by the post-synaptic neuron, the thin black solid arrow represents the existing spiking neural network calculation process, and the thick long black solid arrow represents the contribution of the pulse sequence before the post-synaptic neuron discharges to the post-synaptic potential. Specifically, the pulse sequence of the pre-synaptic neuron The spike train preceding the postsynaptic neuron's discharge As input, the postsynaptic potential u is calculated by the synaptic kernel function ∈(·) of the spiking neuron and the weight matrix W. i (t), when the cumulative postsynaptic potential u i (t) Exceeding the discharge threshold V th When , the postsynaptic neuron generates a new pulse as output;

[0041] The specific steps are as follows:

[0042] Step A01: When calculating the postsynaptic potential, the spiking neuron converts the presynaptic neuron pulse train The spike train preceding the postsynaptic neuron's discharge As input, the unweighted postsynaptic potential is calculated by the synaptic kernel function ∈(·) in, represents the pulse discharge time of postsynaptic neuron i, represents the pulse discharge time of presynaptic neuron j, represents the last discharge time before the discharge time of the postsynaptic neuron, ∈(·) represents the synaptic kernel function, and the calculation formula is Among them, τ m and τ s denote membrane potential constant and time constant, respectively, and H(·) denotes a step function;

[0043] Step A02: Substitute the unweighted postsynaptic potentials e of all presynaptic neurons i|j The total postsynaptic neuron potential is obtained by weighting and summing the weighted matrix W. Among them, w ij represents the weight connection between presynaptic and postsynaptic neurons;

[0044] Step A03: When the postsynaptic neuron accumulates potential u i Accumulate to the predetermined discharge threshold V th When , the postsynaptic neuron i outputs a pulse count o i And release voltage, the output pulse count calculation formula of postsynaptic neuron i is Among them, g(u i) represents the floor function; during this period, the neuron does not respond to any additional input and enters the absolute refractory period.

[0045] Step B: By refining the pulse discharge time of the pre- and post-synaptic neurons and approximating the boundary value of the post-synaptic potential, a simplified calculation formula for the post-synaptic potential is obtained. This formula is only related to the pulse discharge count of the pre- and post-synaptic neurons and the time difference of the last discharge of the pulse train.

[0046] The specific steps are as follows:

[0047] Step B01: Calculate the synaptic kernel function calculation formula in step A01 in different cases. When ts≥0, let τ m =8,τ s and but and The synaptic kernel function is approximated as Similarly, when ts<0, the synaptic kernel function is approximately

[0048] Step B02: Calculate the effect of all presynaptic and postsynaptic spike train discharge times on the postsynaptic potential e i|j The total contribution of the presynaptic neuron j is Assume that the first n discharge times are less than The postsynaptic potential can be expressed as: Under the same approximate conditions, e i|j It can be further expressed as:

[0049] For ease of observation, it is further simplified to

[0050] Step B03: Simplify the postsynaptic potential of step B02 into a function like Figure 2 The unweighted postsynaptic potential e is shown in i|j Schematic diagram of calculation, the gray short solid arrows represent the pulse discharge sequence of the pre- and post-synaptic neurons, the black short solid arrows represent the last discharge time of the pulse sequence of the pre- and post-synaptic neurons, and the gray dotted arrows represent e i|j Calculation process. Postsynaptic neuron potential e i|j Only the pre- and post-synaptic neuron spike counts i and j It is linearly related to the final discharge time difference of the pre- and post-synaptic spike train. An exponential relationship.

[0051] Step C: Using the simplified calculation formula of postsynaptic potential in step B, the derivative between postsynaptic potential and pulse count is approximated by pulse time-dependent plasticity based on pulse discharge to untangle the rate and time effects of postsynaptic potential;

[0052] The details are as follows:

[0053] According to the simplification of the postsynaptic potential in step B04, the derivative between the postsynaptic potential and the pulse count is calculated using the pulse time-dependent plasticity based on the pulse count

[0054]

[0055] Among them, A + and A - represents the weight of synaptic change, τ represents the time decay constant, is the difference between the last firing times of presynaptic neuron j and postsynaptic neuron i.

[0056] Step D: For the impulse response model established in step A, the unknown derivative between the postsynaptic potential and the impulse count is approximated by the impulse time-dependent plasticity in step C, and the overall gradient can be fully calculated for training. This effectively utilizes the superior performance of the error backpropagation method in achieving global error optimization, and also integrates the local update strategy provided by the impulse time-dependent plasticity.

[0057] The specific steps are as follows:

[0058] Step D01: The present invention uses the mean square error loss function Where L represents the total loss function, o and y represent the actual firing count and expected firing count of the output neuron, respectively. Gradient derivative of each layer of the spiking neural network Need to be calculated and then update the weight;

[0059] Step D02: For the i-th neuron in the output layer K, the chain rule is as follows in, represents the back-propagated firing rate error of neuron i, represents the time-dependent differential of spike activity, the back-propagated firing rate error of neuron i Calculation formula The calculation formula of the time effect differential of pulse activity

[0060] Step D03: In each hidden layer k, the back-propagated firing rate error of neuron i is: The calculation formula of the time effect differential of pulse activity

[0061] Step D04: For unknown and The derivative of the format uses spike-time-dependent plasticity to approximate the derivative between the postsynaptic potential and the spike count, as Figure 3 The figure shows the complete error back-propagation training process based on local synaptic plasticity. The thin black solid arrow and the thin black dashed arrow represent the forward calculation and reverse gradient derivation process of the traditional spiking neuron, respectively. The thick black solid arrow represents the computational contribution of the spike sequence before the postsynaptic neuron discharges to the output of the spiking neuron. The thick black dashed arrow represents the corresponding back-propagation calculation using spike time-dependent plasticity.

[0062] The present invention fully utilizes the advantages of local synaptic plasticity and global optimization mechanism, enhances the learning and adaptation ability of spiking neural network, is closer to biological nervous system, and improves the classification accuracy on training static and neuromorphic data sets.

Claims

1. A method for training a spiking neural network error back propagation based on local synaptic plasticity, characterized by: The steps include: Step A: Establish an impulse response model, take the pulse sequence before the discharge of the presynaptic neuron and the postsynaptic neuron as input, calculate the postsynaptic potential through the synaptic kernel function and weighted summation, and when the cumulative postsynaptic potential exceeds the discharge threshold, the postsynaptic neuron generates a new pulse as output; Step B: By refining the pulse discharge time of the pre- and post-synaptic neurons and approximating the boundary value of the post-synaptic potential, a simplified calculation formula for the post-synaptic potential is obtained, which is only related to the pulse discharge count of the pre- and post-synaptic neurons and the time difference of the last discharge of the pulse train; Step C: Using the simplified calculation formula of postsynaptic potential in step B, the derivative between postsynaptic potential and pulse count is approximated by pulse time-dependent plasticity based on pulse count to untangle the rate and time effects of postsynaptic potential; Step D: For the impulse response model established in step A, the unknown derivative between the postsynaptic potential and the impulse count is approximated by the impulse time-dependent plasticity in step C, and the overall gradient is fully calculated for training. This effectively utilizes the superior performance of the error backpropagation method in achieving global error optimization, and also integrates the local update strategy provided by the impulse time-dependent plasticity.

2. The method for training a spiking neural network error back propagation based on local synaptic plasticity according to claim 1, characterized in that: The specific steps of step A are as follows: Step A01: When calculating the postsynaptic potential, the spike neuron takes the spike sequence before the discharge of the presynaptic neuron and the postsynaptic neuron as input, and calculates the unweighted postsynaptic potential of the presynaptic neuron through the synaptic kernel function. in, represents the pulse discharge time of postsynaptic neuron i, represents the pulse discharge time of presynaptic neuron j, represents the last discharge time before the discharge time of the postsynaptic neuron, v(·) represents the synaptic kernel function, and the calculation formula is Among them, τ m and τ s denote membrane potential constant and time constant, respectively, and H(·) denotes a step function; Step A02: Substitute the unweighted postsynaptic potentials e of all presynaptic neurons i|j The weighted summation gives the total postsynaptic neuron cumulative potential u i (t)=∑ j w ij e i|j , where w ij represents the weight connection between presynaptic and postsynaptic neurons; Step A03: When the postsynaptic neuron accumulates potential u i Accumulate to the predetermined discharge threshold V th When , the postsynaptic neuron i outputs a pulse count o i And release voltage, the output pulse count calculation formula of postsynaptic neuron i is Among them, g(u i ) represents the floor function; during this period, the neuron does not respond to any additional input and enters the absolute refractory period.

3. The method for training a spiking neural network error back propagation based on local synaptic plasticity according to claim 2, characterized in that: The specific steps of step B are as follows: Step B01: Calculate the synaptic kernel function calculation formula in step A01 in different cases. When ts≥0, let τ m =8,τ s and but and The synaptic kernel function is approximated as Similarly, when ts<0, the synaptic kernel function is approximately Step B02: Calculate the effect of all presynaptic and postsynaptic spike train discharge times on the postsynaptic potential e i|j The total contribution of the presynaptic neuron j to the spike discharge time Assume that the first n discharge times are less than The postsynaptic potential is then expressed as: Under the same approximate conditions, e i|j Further expressed as: For ease of observation, it is further simplified to Among them, j represents the output pulse count of postsynaptic neuron j; Step B03: Simplify the postsynaptic potential of step B02 into a function It can be seen that the potential of the postsynaptic neuron is linearly related to the pulse count, and exponentially related to the last discharge time difference between the pre- and post-synaptic pulse trains.

4. The method for training a spiking neural network error back propagation based on local synaptic plasticity according to claim 3, characterized in that: The specific steps of step C are as follows: According to the simplification of the postsynaptic potential in step B04, the derivative between the postsynaptic potential and the pulse count is calculated using the pulse time-dependent plasticity based on the pulse count Among them, A + and A - represents the weight of synaptic change, τ represents the time decay constant, is the difference between the last firing times of presynaptic neuron j and postsynaptic neuron i.

5. The method for training a spiking neural network error back propagation based on local synaptic plasticity according to claim 1, characterized in that: The specific steps of step D are as follows: Step D01: Use the mean square error loss function, Where o and y represent the actual discharge count and expected discharge count of the output neuron, respectively; the gradient derivative of each layer of the spiking neural network Need to be calculated and then update the weight; Step D02: For the i-th neuron in the output layer K, the chain rule is as follows in, represents the back-propagated firing rate error of neuron i, represents the time-dependent differential of spike activity, the back-propagated firing rate error of neuron i Calculation formula The calculation formula of the time effect differential of pulse activity Step D03: In each hidden layer k, the back-propagated firing rate error of neuron i is: The calculation formula of the time effect differential of pulse activity Step D04: For unknown and The derivative of the format uses spike-timing-dependent plasticity to approximate the derivative between the postsynaptic potential and the spike count, making the training process complete.

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