EICIL: Joint Excitatory Inhibitory Cycle Iteration Learning for Deep Spiking Neural Networks
Authors: Zihang Shao
Xuanye Fang
Yaxin Li
Chaoran Feng
Jiangrong Shen
Qi Xu
Venue: NeurIPS 2023 poster (2023)
Keywords: spiking neural networks cycle learning  spike encoding

Abstract: Spiking neural networks (SNNs) have undergone continuous development and extensive study for decades, leading to increased biological plausibility and optimal energy efficiency. However, traditional training methods for deep SNNs have some limitations, as they rely on strategies such as pre-training and fine-tuning, indirect coding and reconstruction, and approximate gradients. These strategies lack a complete training model and require gradient approximation. To overcome these limitations, we propose a novel learning method named Joint Excitatory Inhibitory Cycle Iteration learning for Deep Spiking Neural Networks (EICIL) that integrates both excitatory and inhibitory behaviors inspired by the signal transmission of biological neurons.By organically embedding these two behavior patterns into one framework, the proposed EICIL significantly improves the bio-mimicry and adaptability of spiking neuron models, as well as expands the representation space of spiking neurons. Extensive experiments based on EICIL and traditional learning methods demonstrate that EICIL outperforms traditional methods on various datasets, such as CIFAR10 and CIFAR100, revealing the crucial role of the learning approach that integrates both behaviors during training.

EICIL: Joint Excitatory Inhibitory Cycle Iteration Learning for Deep Spiking Neural Networks
Zihang Shao'
Xuanye Fang'
Yaxin Li'
Chaoran Feng'
Jiangrong Shen?
Qi Xu
SScoool of Artificial Intelligence, Dalian University of Technology "College of Computer Science and Technology. Zhejiang University
Abstract
Spiking neural networks (SNNs) have undergone continuous development and ex- tensive research over the decades to improve biological plausibility while opti- mizing energy efficiency. However, traditional deep SNN training methods have some limitations, and they rely strategies such pre-training and fine-tuning, indirect encoding and reconstruction, and approximate gradients. These strate- gies lack complete training models and lack biocompatibility. To overcome these limitations, we propose novel learning method named Deep Spiking Neural Net- works with Joint Excitatory Inhibition Loop Iterative Learning (EICIL). Inspired by biological neuron signal transmission, this method integrates excitatory and in- hibitory behaviors in neurons, organically combining these two behavioral modes into one framework. EICIL significantly improves the biomimicry and adaptabil- ity of spiking neuron models and expands the representation space of spiking neurons. Extensive experiments based on EICIL and traditional learning meth- ods show that EICIL outperforms traditional methods various datasets such CIFARIO and CIFAR100, demonstrating the key role of learning methods that integrate both behaviors during training.
Introduction
In recent years, the spiking neural network (SNN) has garnered significant attention and research in the fields of neuroscience and artificial intelligence (AI) [33, 26, M.. As computational model that simulates the functioning principles of biological neural systems, SNN exhibits high biological plausibility and energy efficiency, making crucial approach for neural information processing[IIA 20, [4]. However, traditional deep SNN training methods face certain limitations, such as reliance on pre-training and fine-tuning strategies, indirect encoding, and approximate gra- dients. These limitations lead to the training of SNNs leaning more towards deep learning-bases methods [12 20. 5 and away from the principles of brain heuristics.
In order to enhance the biological plausibility and adaptability of SNN, and overcome these limi- tations, we propose novel learning and training method called Dicitatory-Inhibitor Cooperative Iterative Learning (EICIL). The core idea of EICIL is to simulate the excitatory and inhibitory be- haviors of biological neurons and seamlessly integrate them into the training process of SNN. In this way, EICIL can better emulate the characteristics of neural signal transmission and expand the representation space of SNN.
Cooresponning author: xuqi @ dlut.cdu.cn
37th Conference on Neural Information Processing Systems (NcurIPS 2023).

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In particular, EICIL uses an iterative training framework that emphasizes and optimizes the interac- tion between excitatory and inhibitory mechanisms. During the training process, EICIL combines excitatory and inhibitory mechanisms in both temporal and spatial dimensions, and enables collab- orative training of the same network model structure. Additionally, we gradually adjust the ratio between excitatory and inhibitory mechanisms, aiming to approximate the ideal ratio of approxi- mately 8:2[[8]. This allows us to achieve better performance and effectiveness in SNN learning.
To validate the effectiveness of the EICIL method, we conducted extensive experiments and com- pared with traditional deep SNN training methods. The experimental results demonstrate signif- icant performance improvements of EICIL across multiple datasets, such as MNIST[5], CIFARIO [09]]] and CIFAR 100[20]] This further confirms the potential and advantages of the EICIL method in enhancing SNN learning capabilities. The main contributions in this paper are summarized as follows:
This paper introduces joint learning method based on excitatory and inhibitory mecha- nisms, namely the EICIL method. ELCII. provides a comprehensive and effective learning framework for deep SNN training and overcomes the limitations of traditional approaches. By integrating excitatory and inhibitory mechanisms in a cohesive manner, EICIL can bet- ter mimic the functional principles of the neural system, thereby enhancing the biological plausibility of SNN.
The proposed method combines excitatory and inhibitory mechanisms for training. In addition, this paper introduces a multi-layer STDP Buike-Timing-Depennae method as the inhibitory mechanism. At the same time, considering the poor training effect of the multi-layer STDP, we also modify and adjust the multi-layer STDP method. And keep it biologically interpretable and optimize its training results.
Plasticity)
EICIL has shown the ability to enhance the biological interpretability and adaptability of SNN, and expand its representation space. And it has achieved significant experimental results. This research is of great significance for further advancing the development of spiking neural networks in both theoretical and practical aspects.
2 Related Work
2.1 Learning of Spiking Neural Networks
In recent years, a number of learning methods have been developed to train deep SNNs with excel- lent performance, which can be categorized as ANN-to-SNN conversion (ANN2SNN) and end-to- end backpropagation methods. ANN2SNN pre-trains source ANN and then converts it to an SNN by replacing the artificial neurons with spiking neurons. The main idea is to use the firing rate of the spiking neuron or average postsynaptic potential to approximate the ReLU activation of the artifi- cial neuron. Although some advanced transformation methods achieve high accuracy on large-scale datasets in trained artíficial neural networks with ResNet and VGG structures(fL. H. If. 12], they ignore the rich temporal dynamics and require many time steps to achieve precoding precision. In contrast, backpropagation methods train SNNs directly by unfolding the network over time steps and then computing surrogate gradients in the spatial and temporal domains, which draws the idea of training recurrent neural networks (RNNs) via temporal backpropagation [26,, BIJ. Since the gra- dient of the spikes with respect to the membrane potential is not differentiable. surrogate gradients are proposed by approximating the gradient with a smoothing function [25]]. The backpropagation method with gradient surrogate can be applied to both static and neuromorphic datasets and re- quires much fewer time steps than the ANN2SNN method. Another backpropagation method is the based [32], which directly calculates the gradient from the spike firing time to the membrane potential without expanding the network over the time step. Inspired by the residual connections of Resnet and VGG network models, our EICIL improves the connection structure of residual networks to increase the representation space of SNN network models and improve the performance of SNNs.
2.2 Biological interpretabilityy of Spiking Neural Networks
The Surrogate Gradient Method [LL 27 and Deiee-TTmiin-DDDeenddd Plasticity(STDP))L 29] are two concepts commonly used in neuroscience to describe the synchronization behavior between neurons and synaptic plasticity, which can be used for weight learning in convolutional and fully

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connected layers in SNNs. However, GS is too simplified for the synchronization relationship be- tween neurons, but synchronization in the brain is relatively complex, and there exist different forms such partial synchronization and phase synchronization, so there are limitations in explaining and modeling the real synchronization phenomenon in the brain [24, 28. GO. 23). Although STDP has great significance in describing synaptic plasticity, STDP ignores other forms of synaptic plasticity [2). such as long-range synaptic enhancement (LTP) and long-range synaptic inhibition (LTD), In order to make up for the shortcomings of the above methods, based on the idea of spike/no-spike Classification(II. I33, [S] and combining the characteristics of STDP and GS, we developed an iter- ative training method of STDP and GS, aiming to improve the expression ability of spiking neurons and SNN.
Preliminary
3.1 Traditional IF
Integrate (ire(IF)( based on the principle of integration and firing of neurons for information transfer. Neurons receive input spike sequences from Presynaptic neurons and integrate the input signals by weighting and summing the input spike sequences. The weights used in the integration process can be adjusted according to the specific task and network structure. When the integrated potential reaches the threshold of the neuron, the neuron fires spike, At this point, the integrating potential resets to the baseline level, and the neuron undergoes a period of absolute underdrive. It does not respond to any input spikes during this time. The IF model is calculated as Eq. (9)
V(t) = Σ w. S(t (t)
(I)
where (t) denotes the integrated potential the neuron at time t, w; denotes the weight of the ith input spike, and S(t t4) is the firing function that represents the effect of the input spike at the moment of time 44-
The condition for determining whether a neuron issues an output spike is
V(t) V Vihreshold
(2)
If the integrated potential (t) exceeds the threshold Vihreshold. the neuron will fire spike.
3.2 Excitatory and inhibitory in neural systems
In the biological nervous system, signal transmission models mainly include two aspects: synaptic transmission and intra-neuronal electrical signal transmission. In terms of synaptic transmission, there are mainly two types: excitatory transmission and inhibitory transmission. Excitatory and in- hibitory neurons are usually combined to produce complex hehaviors and functions. For example, in the cerebral cortex, there is a widespread neural network between excitatory and inhibitory neu- rons, which can support higher functions such as perception, cognition, and decision decision-making In this type network, excitatory and inhibitory neurons are usually mixed in certain proportion. For example, in the visual cortex, about 80 percent of neurons are excitatory neurons, and 20 percent are inhibitory neurons. This proportion may vary in different brain regions and different biological species. In this combination, excitatory neurons can activate adjacent neurons by generating spiking signals, while inhibitory neurons can suppress adjacent neurons by generating opposite spiking sig- nals. This interaction between excitatory and inhibitory can generate complex dynamic behaviors and support information processing and control functions nervous system.
Method
4.1 Surrogate Gradient Method
The Surrogate Gradient Method is commonly used technique in training spiking neural networks (SNNs) that replaces continuous functions in gradient descent with surrogate gradient functions to generate neural spiking output. the backpropagation algorithm of SNNs, the gradient of each neuron is discrete in time, but traditional gradient descent algorithms require continuous gradient
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values to update weights, which necessitates converting discrete gradient values into continuous functions. GS achieves the use of discrete gradients by replacing these continuous functions with spike functions[[]] In this study, we select GS as the excitatory signal transmission method and choose sigmoid function as the gradient surrogate function. At the same time, we use the most basic neuron model to generate spikes. Below is the description of the sigmoid gradient approximation function: sigmoid function itself is defined as:
sigmoid(a) I+e
(3)
sigmoid_grade sigmoid(a)) (=ssmmmii(()))
(4)
4.2 Multi-STDP
STDP is a synaptic plasticity rule based on spiking neurons, which simulates the process of synapses continuously strengthening or weakening with the interaction between neurons. When neuronal synapse receives a series of spikes, there will be plastic changes due the difference in the timing of the firing of the spikes between the pre- and post-synaptic neurons. Specifically, if the pre-synaptic neuron spikes before the post-synaptic neuron, the strength of the synapse increases, while the pre-synaptic neuron spikes after the post-synaptic neuron, the strength of the synapse decreases. Let (t) be the weight of the synapse from neuron to neuron j at time t, and Át = ij t, be the time difference between the spikes of neurons i and j. The STDP rule can be expressed as Eq. (N)
Awyy (1) 114 (+(A)) (1 ())(
A > 0
Awyy(1) (t) -n-- -n (t)(t),
At <0
(5)
Amn =1)=0,
=
Where, 77 and 77- represent the learning rates for synaptic potentiation and depression, respectively, and f+ and f- denote the weight update functions for positive and negative spike timing differences. The commonly used weight change function exponential.
( (+(t) -A//++ (At) -
Where, 74 and T_ are the time constants for synaptic potentiation and depression, respectively.
Although for many years, due to factors such as the dynamic nature of neurons, complex inter- neuronal connections, and training time and computational costs, multi-layer STDP models have been rarely used by researchers[[I]], However, in terms of lateral inhibition, the STDP rule can make the lateral inhibition effect of a neuron more significant. Therefore, we adopt multi-layer STDP model as the inhibitory mechanism of the EICIL structure.
In multi-layer STDP model, the STDP method is utilized perform temporal logic processing of spike neuron propagation. In this model, the STDP rule is employed for weight adjustments in the linear layer, and convolutional layer.
The STDP rule adjusts connection weights based on timing differences in firing spikes between neurons. When the timing of the spikes between neurons is consistent, the connection weight is strengthened. When the timing difference is large, the connection weight weakened. So the strength of connections between neurons is adjusted according to their activity patterns. In this way, the connection weights between neurons in the multi-layer STDP model will be adjusted according to their temporal relationship, thereby achieving multi-layer propagation. This timing- deeendd plasticity mechanism allows the neural network to adaptively adjust the connection strength during the learning process to suit the statistical characteristics of the input data and task requirements.
In the initial experiments, we found that the original multi-layer STDP method performed extremely poorly in training across three network structures. It even failed to reach an accuracy of 50 percent on the CIFARIO dataset. Upon analyzing the multi-layer STDP model and its code, we discovered that the activation of neurons and synaptic weight updates only occurred during the forward propa- gation process. This limitation meant that the gradient information from backpropagation could not directly propagate to earlier layers, thereby restricting the model's learning capability and training effectiveness. Additionally, the inability to effectively transmit gradient information to earlier layers resulted in either diminishing gradients (gradient vanishing) or exponentially increasing gradients

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(gradient explosion). This instability during the training process made it challenging to achieve good convergence. Furthermore, the model lacked the ability to simultaneously adjust weights across the entire network to minimize the overall loss function. Therefore, after careful consideration, we introduced the STDP-BW method by incorporating the backpropagation technique into the STDP model. The integration of the STDP model with backpropagation presents comprehensive and enhanced framework for training multi-layer networks. This approach combines the biological prin- ciples of synaptic plasticity with the optimization capabilities of backpropagation. It not only takes into account the biological principles of synaptic plasticity but also leverages the optimization power of backpropagation. This integration provides more comprehensive and advanced framework for training multi-layer networks.
4.3
The combination of excitability and inhibition
4.3.1 Approach I: Heterogeneous Learning
We combine excitatory and inhibitory mechanisms by using them to compute different types of network layers within the same network structure. The excitatory mechanism is represented by the gradient replacement method, and the inhibitory mechanism is represented by the STDP method. The neural models for the gradient replacement method and the STDP method are denoted by F(-) and G(.), respectively. For neuron j. its membrane potential (t) at time t changes according to:
(t) dt
N
wig F(y(t - f,)+ +
Way G(s, - A) - s,(t - A) - -e5)
(7)
where Why represents the connection weight between neurons i and 9, represents the threshold of neuron j. 8, (t) represents the signal indicating whether neuron j has fired at time t, and A represents the time delay of spiking propagation. This equation expresses the rate of change in the membrane potential of neuron in response to input from other neurons, representing its excitatory or inhibitory nature.
In this study, we propose a novel approach combining STDP models, backpropagation, etc. to train different layers of a neural network. We utilize the STDP model to train the last linear layer in the network to dynamically update the weights according to the spiking neural network. For the convolutional layer and other layers. we employ gradient-based method to optimize the weights. This framework facilitates the integration of excitatory and inhibitory training by applying STDP based weight adjustments across the network after each training round.
Furthermore, we conducted additional experiments to explore various training configurations. First, we exclusively trained the convolutional layer using the STDP model while utilizing the gradient- based method to train the remaining layers. This allowed us to evaluate the individual impact of investigated hybrid approach where
STDP training on the convolutional layer. Additionally, the convolutional layer was trained using both STDP and backpropagation, while the other layers were trained using the gradient-based method. This multiple-STDP based inhibitory training regime enabled iterative fine-tuning of the neural network's weight parameters, creating a dynamic interplay between excitatory and inhibitory processes. We refer to this method as STDP-BW-GS.
4.3.2 Approach II: Cycle Iteration Learning
The second method involves training different epochs of the same network using both excitatory and inhibitory mechanisms within the network's 's structural framework. This approach entails training the complete network with different methods at distinct time steps, effectively encompassing a single training session within each time interval.
In terms of biological interpretability, excitatory and inhibitory mechanisms exhibit alternating and interacting patterns within neurons, employing diverse mechanisms to influence signal propagation. In the biological neural system, signal transmission between neurons subject to temporal dynam- ics, including time delays and other temporal information. The integration and analysis of these temporally modulated signals contribute to processing the input information before transmitting for further analysis in the brain. Motivated by this, we adopt distinct methods to train neurons dur- ing different epochs. Each epoch represents a training cycle within the network model, utilizing different time steps as intervals to train the network using excitatory and inhibitory mechanisms. We
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leverage the current optimal results obtained from the excitatory mechanism to train the inhibitory mechanism, and reciprocally, use the current optimal results from the inhibitory mechanism train the excitatory mechanism. This iterative process facilitates the network model's 's adaptation to both excitatory and inhibitory mechanisms, culminating in the attainment of optimal model parameters through synergistic training.
In this case, the network's connection weights each time step can be represented as W', where denotes the time step. At each time step i, the following update rules using gradient replacement and STDP can be employed as Eq. (8) and Eq. (9)
OW.
W41 W. aL
(8)
AW = E S+(t- tk))
E f-t- RES
(9)
REST
Where, L represents the network's loss function, 17 denotes the learning rate, and and j represent the indices of the neurons. S and S correspond to the excitatory and inhibitory spiking sequences received by neuron j from neuron i, respectively, and f- and f- represent the spatiotemporal weight functions for excitatory and inhibitory spiking. The updated connection weights can be obtained as Eq. (III)
W++ = W2 + nAW,
(10)
This approach can preserve the biological realism of SNN models certain extent while harness- ing the powerful capabilities of deep learning.
Simultaneously, considering that the excitatory and inhibitory mechanisms in the visual neural net- work of the human brain do not exhibit a 1:1 ratio, we introduce proportional adjustment of training durations for these mechanisms by controlling the ratio of time steps. Specifically, introduce pa- rameter K to modulate the relative durations training for the excitatory and inhibitory mechanisms. When K is a positive value, it indicates that the inhibitory mechanism accounts for proportion of 1/K. Conversely, when is a negative value, it indicates that the excitatory mechanism accounts for proportion of -1/K.B) By tuning the value of K, we seek to determine the optimal ratio. Here, refer to the iteration using the GS method and STDP-BW method as GSI, and the iteration using the GS method and STDP-BW-GS method as GSGI.
4.4 Network model based on excitatory inhibition
Combined with the fusion method in ! I. the proportion of excitatory mechanism and inhibitory mechanisms in the biological neural network is adjusted at the same time. We propose an idea: build a network model, set some layers as inhibitory mechanisms and some layers as excitatory mechanisms, and train the two mechanisms in this network model. At the same time, the ratio of excitatory and inhibitory mechanisms in this network model is also 4:1 [I8], that is, the excitatory mechanism accounts for about 80%, and the inhibitory mechanism accounts for about 20%. The method of the inhibitory mechanism we choose in this paper is the STDP method, and the STDP method has some limitations: it can only perform temporal logic training and the linear layer. Since the STDP method is used to train the last linear layer of the network structure separately, the structure of the network model ensures that the ratio of excitatory and in- hibitory mechanisms reaches an ideal ratio is small. So it is not necessarily possible to train to produce the best results. We use the STDP method to train the convolutional layer and combine the framework of the Resnet network model to build our own network model. The model consists of basic convolutional layers, BN layers, pooling layers, residual blocks, and linear layers. Each resid- ual block contains two sets of convolutional layers, maximum pooling layers, BN layers, and spike neurons. We train the convolutional layers with an inhibitory mechanism, and the linear, pooling, and BN layers with excitatory mechanism. Finally, the constructed model reached 77% of the excitatory mechanism and 23% of the inhibitory mechanism, which is close to the ratio of excitation and inhibition in the human neural network.
the convolutional layer

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Unear Layer
Noural If NNdoe
Normal
Pooling
Comvdd
Neura #Node
Downsample
Bitch Nermatzation
MauPooliing
Convod
The figure above presents the framework of the excitatory inhibition network. On the left side, we can observe the residual blocks of the network, while on the right side, the overall network architecture is depicted. The design of the network framework ensures ratio of 8:2 between excita- tory and inhibitory mechanisms.
Figure 1:
5 Experiment
In this section, we demonstrate the effectiveness of our proposed EICIL model. We first compare results with other existing state-of-the-art, then carry out ablation studies evaluate different aspects of our proposed method.
5.1 Experimental Settings
We conduct experiments on server equipped with 16-core Intel(R) Xeon(R) Xeon(R) Gold 6330 2.80GHz CPU and 20 NVidia GeForce RTX 3090 Ti GPUs. The training of SNN is based on the spikingjelly framework [E]. Our experiments mainly use three network frameworks of Resnet, VGG, and the network we built, and conduct experiments on three image data sets of MNIST(D), CIFAR [19] and CIFAR 00 this experiment, we adopt different training methods for the same experimental framework better verify the training advantages of iterative learning.
MNIST.MNIST picture dataset of handwritten digits. counts pictures of handwritten digits from 250 different people. The dataset is relatively simple and can initially demonstrate the perfor- mance of our model. When training, we use Resnet and VGG11 for training to get the results of different training methods.
CIFAR 10 & CIFAR 100. The CIFAR dataset collected from 80 million RGB miniature image datasets. The CIFAR dataset can be divided into CIFAR-10 and CIFAR-10 according to the number of classified objects involved. The dataset is relatively complex and can more realistically verify the performance of our proposed framework. When training, we need to first encode the static images into spike sequences, and then input them into the SNN, here the first spike neuron layer in the network is used as the encoding layer.
5.2 Evaluation on STDP-BW Method
Experimental results have demonstrated that the incorporation of backpropagation into the STDP model (STDP-BW) achieves an accuracy of 90.39 percent the CIFAR10 dataset, which is a percent
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Table 1: Test accuracies of EICIL CIFAR 10, CIFAR 100, and MNIST.
STDP-BW (Acc.
SIDP-BW-GS (Acc. %)
GSI (Acc. %)
GSGI (Acc. %)
Improvment (Ace. %)
SNN Model
Database
(Acc. %)
CIFARIO
89.39
90.39
89.16
90.05
90.34
0.95
Spiking Resnet 18
CIFARIO0
MNIST
99.17
99.35
99.26
99.36
99.44
0.27
CIFARIO
85.31
Spiking VGG 11
CIFARI00 100
54.01
54.63
52.44
55.44
55.71
1.70
MNIST
98.2
99.09
95.85
98.55
98.77
0.55
CIFARIO
89.14
89.43
Excitatory inhibition Ne
CIFARIOD
53.61
53.92
54.03
54.61
53.86
0.25
MNIST
99.33
99.34
99.30
99.33
99.35
0.02
improvement compared to the GS method. Comparable accuracy was observed on the CIFAR and MNIST datasets when compared the GS method. Furthermore, comparison with other network models such as Spiking Resnet18, 18, Spiking VGGI and Excitatory Inhibition Net reveals that the Spiking Resnet18 model outperforms the other two in terms of performance.
5.3 Evaluation on Iteration-based Methods
In the experiment, we continue to use Spiking Resnet18, Spiking VGG11 and the spiking form of our proposed Excitatory inhibitor Net to test the two training methods of GSI and GSGI, and then analyze the model.
For the MNIST data set, as shown in Table M. when using Spiking Resnet18, GSI is improved by 0.19% compared to the original GS method, GSGI is improved by 0.28%, when using Spiking VGG 11, GSI is compared to the original The GS method has been improved by 0.35%, and the GSGI has been improved by 0.57%, which shows that the iterative method can improve the expression ability of the enhanced neuron model. To better compare the effectiveness of using an iterative training approach, we visualize line graph of test accuracy.
For the CIFAR 10 data set, when Table uses Spiking Resnet18, 18, GSI improves by 0.66% compared to the original GS method, and GSGI further improves by 0.95%, while the model performance of VGGI1 is similar. The improvement is 0.15% and 1.35%, respectively, compared with the MNIST dataset, the algorithm based on iteration performs better on larger datasets.
For the CIFAR100 dataset, as shown in Table III when using Spiking Resnet18, GSI has improved by 6.75% compared the original GS method, and GSGI has further improved by 7.19%, but due to the model structure and complexity The reason for this is that the performance of the VGG11 model is relatively poor, with only increase of 1.43% and 1.70% respectively. The algorithm based on iteration performs better on larger data sets, which to a certain extent shows that the method based on iteration can improve the network's Biological interpretability. which more effectively use the excitatory and inhibitory information of neurons for collaborative training.
For our Excitatory inhibition Network, as shown in Table II the performance of the GSI and GSGI iterative models is slightly better than that of Spiking VGG but slightly lower than that of Spiking Resnet 18. This shows that the iterative method has stronger matching ability with the Resnet network structure and can greatly improve its expression. Ability, and model accuracy in the MNIST, CIFAR10, CIFAR100 data sets all show positive improvement effect.
At the same time, comparing the GSGI and GSI results of the three data sets in the three networks, the accuracy of GSGI is higher than that of GSI, which also proves that the STDP-BW-GE method is slightly better than the STDP-BW method. shows that the combination of excitatory mechanism and inhibitory mechanism proposed by us will lead to the improvement of training accuracy.
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(a) Spiking Resnet18 18 in CIFAR 10
(b) Spiking Resnet18 in CIFAR 100
Excitatory inhibition Net in CIFAR Excitatory inhibition Net in CIFAR
10
100
Figure 2: Performance of test accuracy of Spiking Resnet 18 and Excitatory inhibition Net in CIFAR 10 and CIFAR 100
Table 2: Test accuracies of EICIL on CIFAR 10, CIFAR 100, and MNIST.
MNIST (Acc.%)
CIFAR 10 Acc. (%)
CIFAR 100 Acc. (%)
SNN Vodel
Parameter
Learning Method
GSI
99.39
89.97
57.74
3
GSGI
GSI
99.33
90.16
62.59
4
GSGI
99.43
90.21
62.64
GSI
99.30
90.46
56.15
5
GSGI
99.34
90,58
66.36
Spiking Resnet 18
GSI
99.36
89.97
57.11
-3
GSGI
99.37
89.56
64.28
99.34
90.38
58.53
4
CSGI
GSI
99.32
90.34
56.62
-5
GSGI
99.34
90.01
62.86
5.4
Ablation Study
The effect of the hyperparameter on the expressiveness of the model.
Considering that different k values have different effects on the model, we conducted ablation ex- periments and tested the iterative training models GSI and GSGI based on Spiking Resnet 18. The experimental results are shown in T in the MNIST dataset On the above, the accuracy differ- ence between GSI and GSGI ranges from 0.03% 0.10%. On the CIFARIO data set, the accuracy difference between GSI and GSGI ranges from -0.33% to 0.29%. On the CIFAR100 data On the set, the accuracy difference between GSI and GSGI ranges from 0.05% 8.62%. We found that, limited by the size of the data set, the accuracy improvement on the MNIST and CIFAR10 10 data sets small, while under the CIFAR100 large data set, the expressive ability of the model is significantly improved. At the same time, we found that the larger the K value, the higher the accuracy rate and the better the excitation-inhibition trade-off ability. When the K value reaches the ideal 8:2 ratio of excitation and inhibition of the visual nervous system in the biological brain has been reached, which happens to be the highest accuracy rate of GST and GSGI at this time. Therefore, it is also proved that our model method is more biologically interpretable while improving accuracy.

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Conclusion
Inspired by the idea of neuron excitation-inhibiie this paper proposes a joint learning method based on excitation and inhibition mechanisms. The main idea is to better simulate the functional principles of the nervous system by integrating excitation and inhibition mechanisms in cohesive manner. Thereby enhancing the biological rationality of SNN and improving the expressive ability and accuracy of spiking neural networks.
Considering the limited expressive power of the model structure, the experimental results show that we can extend the work to more situations and improve the accuracy of the model under specific tasks through iterative training. It also shows that the proposed model and training method exhibit good performance both small and relatively large datasets.
In our future work, we will extend the joint learning method to exploit the biological properties of excitability and inhibition, continue to explore how the two are combined and paired, and evaluate them on more datasets.
Acknowledgement
This work supported in part by National Natural Science Foundation of China (NSFC No. No.62206037,663 62200777,,,2306274), National Key Research and Development Program of China (2021ZD0109803), the China Postdoctoral Science Foundation under Grant No. 2023M733067 and No. 2023T160567, and the Fundamental Research Funds for the Central Universities (DUT2IRC(3)091)
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Intelligence, volume 35, pages 11062 1070, 2021.
12


Reviews:
[{"review_id": "ohH8FBj4MQ", "reviewer": "Reviewer_imxR", "summary": "The paper presents the EICIL approach, an iterative excitatory/inhibitory learning mechanism to train task-specific spiking neural networks which still maintain a level of biological realism. The approach utilizes spike-timing dependent plasticity (STDP) as part of the inhibitory mechanism, showing that it can be scaled to multiple layers. The authors show promising results on the MNIST, CIFAR-10, and CIFAR-100 datasets, with slightly favorable results compared to a standard surrogate gradients approach. The authors also perform a simple ablation study by varying the number of excitatory/inhibitory iterations and show that this can influence final model performance.", "questions": "1. Could you explain the design rationale for separating out the surrogate gradient and STDP excitatory/inhibitory learning mechanisms?\n\n2. Could you please add a figure or diagram that shows the different model configurations (e.g. STDP-BW, STDP-BW-GS, GSI, GSGI)? It was sometimes hard to keep track of these purely based on descriptions in the text, and I believe such a figure would help the reader better understand the overall concept.\n\n3. How would this approach scale to more complex datasets beyond MNIST and CIFAR? I am not very familiar with the current literature on spiking neural networks and associated benchmarks, but a discussion at least of how the proposed approach might scale to larger datasets would be useful.", "limitations": "I don't think there are many potential negative societal impacts of the current work, given its current framing and context. The authors do briefly address some particular limitations of their approach.", "rating": 3, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The paper tackles an interesting problem, specifically biologically plausible neural networks based on spikes as the fundamental unit of computation. The authors propose an extension of existing spiking neural network methods by combining a tunable iterative excitatory/inhibitory learning mechanism. They show that their approach can be used with relatively standard convolutional neural network architectures, such as ResNet and VGG. The authors also performed detailed experiments across models and datasets, showing that their approach performs slightly favorably compared with other baselines.", "weaknesses": "Overall, the writing in the paper could be improved and the motivation/justification for certain design decisions made more clear. There were a couple of typos and incomplete sentences (e.g. line 314, \"but due to the model structure and complexity\" and line 330, \"On the CIFAR100 data\"). The motivation for using surrogate gradients for convolutional layers as the excitatory mechanism and STDP for the final linear layer as the inhibitory mechanism was somewhat unclear and seemed ad-hoc. Some of the connections to biological constraints were pretty forced (e.g. the 4:1 excitatory to inhibitory ratio and relating that to training ratio of excitatory/inhibitory mechanisms).\n\nIn general, I also found it hard to keep track of the different model configurations and their acronyms- I believe a figure showing the model architecture(s) would help the reader better understand the overall concept and map the different configurations to rows in the results tables. The experimental results were also somewhat weak, showing performance improvements that may not be statistically significant and could be purely due to randomness (e.g. <1%). The paper also claims that the EICIL approach \"enhances biological interpretability\" and \"expands its representation space\", but I do not really see this quantified anywhere in the paper. Are the representations learned by EICIL actually more biologically realistic or interpretable and how could this be demonstrated?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for your careful review and constructive comments, which have much contributed to improving the paper. We will address all the comments in the paper and provide responses to the comments below.\n\nWe have made revisions for writing problems\n\nFor Weakness1:\nFor the motivation of using GS for convolutional layers as the excitatory mechanism and STDP for the linear layer as the inhibitory mechanism we have the following explanations:the method of combining the excitatory and inhibitory mechanism acts on the overall network layer. That is, in the same epoch, we train the excitatory and inhibitory mechanisms on different layers. It can be understood that different layers in the same epoch training have different methods of updating weights. And the final linear layer is not mandatory to use STDP to train, but expresses a process of exploring the combination of excitatory and inhibitory mechanisms. The purpose is to observe whether this result is more in line with the expression of excitation and inhibition in biological neural networks. Facts have also proved that the effect is not ideal.The idea of using the convolutional layer to train the inhibitory mechanism and using other layers to train the excitatory mechanism is that the two are interleaved and promote each other, which is more in line with the expression of biological neural networks.And the experiment also proves that the result is indeed slightly better than GS.Similarly, these connections with biological constraints are not mandatory.It has been proved by experiments that the combination of excitatory and inhibitory mechanism is higher than other values when the ratio of excitatory and inhibitory mechanism reaches 4:1. And the 4:1 ratio is indeed a peak. This also proves that the setting of our model is consistent with the proportional distribution of excitatory and inhibitory mechanisms in biological neural networks.To explain with reference to biological science:There is a major interplay between excitation and inhibition. We considered a model of the primary visual cortex as a network consisting of excitatory and inhibitory cell populations, with both short and long range interactions[1] .So it shows that our proposed method enhances the biological interpretability of SNNs.\n\nFor Weakness2:\nIn view of whether there is randomness in the experimental results, we added a set of experiments: use GSI to train the CIFAR10 dataset under the SpikingResnet network model (Table 1). It proves that this method will improve every time, not a random improvement.And the main purpose of this paper is to illustrate this new training method that iteratively combines excitatory and inhibitory mechanisms in SNNs, not focusing on achieving a significant improvement effect. Of course, in the future, we will explore how other different and more advanced methods can improve SNNs.\nThe biological interpretability problem stated in weakness1\nThe expanding the representation space question, stated in Question3\n\nFor Question1:\nThe current GS or STDP methods use their own training features to update the weights independently. Although both have excitatory or inhibitory effects, there is no training method combining the two. In biological sciences, the excitatory and inhibitory mechanism are often interrelated and work together with neurons to transmit information. Therefore, this paper combines the excitatory and inhibitory mechanism in SNNs to make it more biologically interpretable. Since GS is widely used in SNNs, GS was used as the excitatory mechanism.  STDP is to update the weight parameters according to the spike generation time difference between two adjacent neurons. When multiple synapses are connected to the same neuron, if the strength of one synapse is enhanced, it may increase the activity threshold of subsequent synapses, causing the strength of these subsequent synapses to be suppressed.So it is also known as the side-suppression method. So we use STDP as an inhibitory mechanism. The idea of the combination of excitation and inhibition also broadens new ideas for the subsequent development of SNNs. \n\nFor Question2:\nWe have added an explanation of the different model in the Table2 . STDP-BW is the abbreviation of the method combining STDP with backpropagation in method4.2. STDP-BW-GS is the abbreviation of the method in the method4.3.1 that trains the STDP-BW method and GS separately on different network layers in the same network model. GSI and GSGI are the abbreviations of GS in method 4.3.2 to iteratively train the same network model with STDP-BW and STDP-BW-GS respectively. Display of some hyperparameters: the learning rate is selected as lr=0.002, the time step is selected as T=8, and the number of training rounds is epoch=320.\n\nFor Question3:\nAs for whether our method can be applied to other more complex data sets, we have added a set of experiments. The experimental data set is the DVSGesture dynamic dataset.  Please refer to Table 3 for the experimental results. The experimental results show that the STDP-BW-GS reaches 95.14%, which is higher than the 94.79% of the STDP-BW, which confirms the idea of method4.3.1. The results of GSGI and GSI are both higher than the accuracy of GS by at least 2%, which proves the effectiveness of the idea in method4.3.2. And the experimental results also show that the result of GSGI is higher than that of GSI, which also proves the idea of method4.3.1.Therefore, experiments have proved that our method is also applicable to more complex data sets, and the robustness and generalization of the method have been verified. At the same time, it shows that this method not only has an improvement in static data sets, but also has an excellent improvement effect when extended to dynamic data sets. The expansion effect on the representation space is proved.\n\n[1]Yael Adini, Dov Sagi, and Misha Tsodyks .Excitatory–inhibitory network in the visual cortex: Psychophysical evidence.September 16, 1997 "}, {"review_id": "cLrH15LAxs", "reviewer": "Reviewer_4jP2", "summary": "The article introduces a training method of spiking neural network, which combines the excitatory mechanism with the inhibitory mechanism. Through iterative training, the same network model is jointly trained at different time steps. The article fully combines the excitatory and inhibitory properties of the neural network structure in the biological brain with the artificial neural network.", "questions": "1. The data sets used in the experimental part are relatively traditional image data. I don’t know whether this method will also be applicable to pulse-form data sets, and there will be a significant improvement.\n2. The article only introduces a combination of excitation and inhibition. If another combination of excitation and inhibition methods can be added, it will further prove the feasibility of the method.\n3. The K value proposed in the article adjusts the ratio of the excitatory mechanism over the inhibitory mechanism. The experiments only showed a ratio of 8:2. It is not known whether the result is the best ratio. If an excitatory mechanism is increased with a ratio greater than 8:2, it will be better for the proof of the method.", "limitations": "The authors have not explicitly discussed limitations of their approach. Since this work is theoretical, it is unlikely it will have potential negative societal impacts.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The article combines the excitatory mechanism with the inhibitory mechanism, imitating the neural network mechanism in the biological brain, and enhancing the biological interpretability of the artificial neural network.\n2. The article makes full use of the unique hyperparameters of the spiking neural network: the time step to combine the excitatory mechanism with the inhibitory mechanism, allowing the two to jointly train the same network structure, and using each other for local optimal iterative training. This is an innovative breakthrough.\n3. Combining the excitatory-inhibitory ratio of the biological visual nervous system, the article sets the excitatory mechanism and the inhibitory mechanism in the spiking neural network to an ideal ratio of 8:2. It is verified by experiments that the accuracy rate obtained by this ratio is higher than the original 1:1. As a result, the effectiveness of the method is proved.", "weaknesses": "1. The expression of the article is not clear enough, and the authors’ idea is not expressed with the most concise sentence.\n2. The article introduces just one combination of an excitatory mechanism and an inhibitory mechanism. If there are more combinations to prove the idea proposed by the authors, it will be more convincing\n3. The methods used in the article are all the most basic methods, which have not yet reached the current highest accuracy rate. Although the comparison experiment has improved to a certain extent, it is still unknown whether it can improve the current highest accuracy rate.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for your careful review and constructive comments, which have much contributed to improving the paper. We will address all the comments in the paper and provide responses to the comments below.\n\nWe have made revisions for writing problems\n\nFor Question1:\n\nAs for whether our method proposed by you can be applied to other more complex data sets, we have added a set of experiments. The experimental data set is the DVSGesture data set. The \"DVSGesture\" data set is a gesture recognition data captured based on dynamic visual sensors. set. The main feature of the DVSGesture dataset is that it contains impulsive event sequences of gesture motions captured on dynamic vision sensors. Each pulse event records a change in pixel value within the region of interest, usually expressed as a timestamp, pixel coordinate, and polarity (increase or decrease).Please refer to Table 3(See the attachment or the table below for details)  for the experimental results. The experimental results show that the STDP-BW-GS method reaches 95.14\\%, which is higher than the 94.79\\% of the STDP-BW method, which confirms the idea of method 4.3.1. At the same time, the results of GSGI and GSI are both higher than the accuracy of the GS method baseline by at least 2\\%, which proves the effectiveness of the idea in method4.3.2. And the experimental results also show that the result of GSGI is higher than that of GSI, which also proves that the STDP-BW-GS method is better than STDP-BW. Therefore, experiments have proved that our method is also applicable to more complex data sets, and the robustness and generalization of the method have been verified.The table is shown below：\n                                              Table3:Test accuracies of EICIL on DVS Gesture.\n_____________________________________________________________________________________________________________\n| SNN Model &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; |  Dataset   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;   | GS&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| STDP-BW &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| STDP-BW-GS &nbsp; |    GSI  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;     |   GSGI  &nbsp;&nbsp;&nbsp;&nbsp;  |    Improvement |\n_____________________________________________________________________________________________________________\n| Spiking Resnet 18       |  DVS Gesture   | 93.14%  |     94.79%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;    |     95.14%&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;        |   95.47 %&nbsp;&nbsp;&nbsp;&nbsp; |  95.83%&nbsp;&nbsp;&nbsp; |       2.69%        | \n_____________________________________________________________________________________________________________\n\nFor Question2:\n\nFor the applicability of another combination, the iterative training method that we propose combines excitation and inhibition is aimed at training the same network with the excitatory mechanism and the inhibitory mechanism. In theory, as long as the two methods can be used in the same network If the training is carried out in the middle, then no matter which training method is selected as the excitatory mechanism or the inhibitory mechanism, as long as one method is the excitatory mechanism and the other is the inhibitory mechanism, then the method is effective. At the same time, we consider that the two existing methods are sufficiently representative in the training methods of spiking neural networks, and due to equipment limitations, there is not enough time for experiments. But in the future, we will explore what method is more suitable for our method, and continue to explore how to optimize the method and improve the efficiency and accuracy of the combination of the two.\n\nFor Question3:\n\nThe experiment you proposed only shows that the adjustment of the K value achieves an 8:2 ratio of excitatory and inhibitory mechanisms, which does not fully prove the effectiveness of the method. To this end, we added two sets of experiments to adjust the K value to 6 in the CIFAR10 and CIFAR100 data sets, that is, the ratio of excitation and inhibition mechanisms reached 10:2. The experimental results are shown in Table 4. From the experimental results, it can be seen that when K=6, the accuracy of GSI and GSGI training in the two data sets is lower than that of K=5. This also shows that the 8:2 ratio of excitation and inhibition mechanisms at K=5 is indeed the best ratio, which proves the correctness of our proposed ideas and improves biological interpretability.The table is shown below：\n\nTable4:Supplementary experiment: K=6(The ratio of excitatory mechanism to inhibitory mechanism is 10:2) on CIFAR10 and CIFAR100.\n________________________________________________________________________________________\nSNN Model  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                 Parameter K  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;         Learning Method &nbsp;&nbsp;&nbsp;&nbsp;     CIFAR10&nbsp;&nbsp;        CIFAR100\n________________________________________________________________________________________\n  Spiking Resnet 18      &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;        6        &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; GSI  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;            89.65%. &nbsp;&nbsp;  &nbsp;&nbsp;&nbsp;&nbsp; &nbsp;      54.27%\n\n Spiking Resnet 18     &nbsp;&nbsp;  &nbsp;&nbsp;&nbsp;         6    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;       &nbsp;&nbsp;&nbsp;&nbsp;             GSGI  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;                 90.34%&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;      63.47%\n________________________________________________________________________________________\n\n\n"}, {"review_id": "NzCxrsOADp", "reviewer": "Reviewer_a2bZ", "summary": "The paper is about a new learning method for spiking neural networks (SNNs). The authors introduce a method called EICIL that integrates both excitatory and inhibitory behaviors into one network, which improves plausibility and adaptability. They show that EICIL performs better than traditional methods on various datasets, such as CIFAR10 and CIFAR100.", "questions": "From Lines 210–222, I get the knowledge that the cycle iteration learning is to let excitatory and inhibitory circuits take turns to learn. However, I can only see one formula (equation 9) that generates updates. Can you further explain this to me?\n\n\n\nWhat is \"BN\" in the paper? I can only see the abbreviation in the paper.", "limitations": "The presentation of this paper can be improved.", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "The paper has several strengths: \n1. The number of people paying attention to the STDP algorithm is dwindling at NeurIPS conferences. This article provides a good idea to merge STDP with the common backpropagation methods of deep spiking neural networks, so that STDP can help the network learn.\n\n2. The process of integrating STDP is actually not complicated. The method first classifies the neurons (excitatory neurons or inhibitory neurons) and adjusts the synaptic connections according to the classes of neurons.\n\n3. This method works especially well on the CIFAR100 dataset.", "weaknesses": "The presentation of the paper needs improvement:\n1. Why can \"Surrogate Gradient Method\" be abbreviated as \"GS\", not \"SG\"? It is confusing.\n2. There should be a period or comma after each equation.\n3. In the term \"Excitatory inhibition Net\", the rule of capitalization is too causal. I think the authors should also capitalize the word \"inhibition\". Also \"Resnet\" should be \"ResNet\".\n4. There are places missing blanks, e.g., lines 42, 103, 147, and 173.\n5. In Section 5.4, k should be \"$k$\".\n6. There are multiple expressions of the CIFAR-10 dataset: \"CIFAR10\", \"CIFAR-10\" , \"CIFAR 10\". Please make them consistent. \n7. Figure (a) is too small to read.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for your careful review and constructive comments, which have much contributed to improving the paper. We will address all the comments in the paper and provide responses to the comments below.\n\nWe have made revisions for writing problems\n\nFor Weakness1:\n\nThe reason why the gradient substitution method is abbreviated as GS here is to make it easier to distinguish the naming after combining the gradient substitution method with the STDP method in method4.3.2. G in GSI stands for gradient substitution, S stands for STDP, and I stands for iteration. It would be confusing if it was abbreviated as SG.\n\nFor Question1:\n\nFor the update question you raised:Equation 5 describes that in the STDP method, the weights are updated according to the time difference between the spike excitations between adjacent neurons\n\n\\begin{equation}\\label{Eq:method1}\n\\frac{dV_j(t)}{dt} = \\sum_{i=1}^N w_{ij} F(s_j(t-\\Delta)-\\theta_j) + \\sum_{i=1}^N w_{ij} G(s_j(t-\\Delta)-s_i(t-\\Delta)-\\theta_{ij})\n\\end{equation}\nwhere $w_{ij}$ represents the connection weight between neurons $i$ and $j$, $\\theta_j$ represents the threshold of neuron $j$, $s_j(t)$ represents the signal indicating whether neuron $j$ has fired at time $t$, and $\\Delta$ represents the time delay of spiking propagation. And this equation expresses the rate of change in the membrane potential of a neuron in response to input from other neurons, representing its excitatory or inhibitory nature.\n\n\\begin{equation}\nW_{t+1} = W_t - \\eta \\frac{\\partial W_t}{\\partial L}\n\\end{equation}\n\\begin{equation}\n\\Delta W_{ij}(t) = \\sum_{k \\in S^+} f_+(t-t_k) - \\sum_{k \\in S^-} f_-(t-t_k)\n\\end{equation}\n\\begin{equation}\nW_{t+1} = W_t + \\eta \\Delta W_t\n\\end{equation}\n\nEquation 8 and Equation 9 indicate that the two combine their own weight update characteristics to jointly update the weight parameters, especially in Equation 9, which reflects the excitatory and inhibitory spike sequences, as well as the spike spatiotemporal sequence. The combined update weights in Equation 10 combine the joint update of excitation and inhibition with separate updates of excitation and inhibition. From the perspective of biological science, the excitatory mechanism and the inhibitory mechanism have their own system structure to maintain their independent activities. But when the two act on neurons together, they use the mechanism that jointly acts on neurons to affect neurons to generate spike.\n\n\n\nFor Question2:\n\nThe BN layer here refers to the Batch Normalization layer. It is also a layer of the network like the convolutional layer, pooling layer, and fully connected layer."}, {"review_id": "y39nanhtHV", "reviewer": "Reviewer_5jTx", "summary": "The authors introduce a novel training method for spiking neural networks which combines both excitatory and inhibitory mechanisms for iterative training. This method uses the time step of spiking neural networks to train the same network with two training methods in the overall training process.At the same time ,the authors design the training time ratio of the two, reaching the ideal ratio of 8:2 of excitatory and inhibitory mechanisms in the nervous system of biological brains. It enhances the biological interpretability of spiking neural networks.", "questions": "1. The paper only introduces one combination of excitatory and inhibitory mechanisms. Can you add another combination of excitatory and inhibitory mechanisms to fully demonstrate the feasibility of this training method?\n2. The datasets used in the paper are some more traditional datasets. I wonder if they can have the same effect on new datasets.\n3. Compared with 1:1 training, the positive and negative training results of K value have improved. Is this the effect of excitatory and inhibitory methods, or the result of 8:2 or 2:8 ratio of excitatory and inhibitory in spiking neural networks from the biological perspective of 8:2 ratio?", "limitations": "As I mentioned in weaknesses,the methods and neurons used in the paper are the most basic, using more advanced methods or neurons may be a limitation that can be solved in the future.Overall I see no negative societal impact to discuss.", "rating": 7, "confidence": 5, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1:The training method that combines excitatory and inhibitory mechanisms is an innovative breakthrough for spiking neural networks, making spiking neural networks more biologically interpretable.\n2:The new training idea proposed in this paper expands the training thought of spiking neural networks. The excitatory and inhibitory mechanisms use different time to train the same network structure in one overall training process, making full use of the time characteristics of spiking neural networks.\n3:The paper also designs the ideal ratio of 8:2 of excitatory and inhibitory mechanisms to the neural network model in biological brains, making the above method more persuasive.", "weaknesses": "1:The author’s writing is immature and the expression is not clear enough.\n2:The paper only introduces the combination of one excitatory mechanism and one inhibitory mechanism, and does not fully express the effectiveness and feasibility of the method.\n3:The methods and neurons used are basic and do not fully reflect the improvement of the current highest accuracy.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for your careful review and constructive comments, which have much contributed to improving the paper. We will address all the comments in the paper and provide responses to the comments below.\n\nWe have made revisions for writing problems\n\nFor Question1:\n\nFor the applicability of another combination, the iterative training method that we propose combines excitation and inhibition is aimed at training the same network with the excitatory mechanism and the inhibitory mechanism. In theory, as long as the two methods can be used in the same network If the training is carried out in the middle, then no matter which training method is selected as the excitatory mechanism or the inhibitory mechanism, as long as one method is the excitatory mechanism and the other is the inhibitory mechanism, then the method is effective. At the same time, we consider that the two existing methods are sufficiently representative in the training methods of spiking neural networks, and due to equipment limitations, there is not enough time for experiments. But in the future, we will explore what method is more suitable for our method, and continue to explore how to optimize the method and improve the efficiency and accuracy of the combination of the two.\n\nFor Question2:\n\nAs for whether our method proposed by you can be applied to other more complex data sets, we have added a set of experiments. The experimental data set is the DVSGesture data set. The \"DVSGesture\" data set is a gesture recognition data captured based on dynamic visual sensors set. The main feature of the DVSGesture dataset is that it contains impulsive event sequences of gesture motions captured on dynamic vision sensors. Each pulse event records a change in pixel value within the region of interest, usually expressed as a timestamp, pixel coordinate, and polarity (increase or decrease).Please refer to Table 3(See the attachment or the table below for details) for the experimental results. The experimental results show that the STDP-BW-GS method reaches 95.14\\%, which is higher than the 94.79\\% of the STDP-BW method, which confirms the idea of method 4.3.1. At the same time, the results of GSGI and GSI are both higher than the accuracy of the GS method baseline by at least 2\\%, which proves the effectiveness of the idea in method4.3.2. And the experimental results also show that the result of GSGI is higher than that of GSI, which also proves that the STDP-BW-GS method is better than STDP-BW. Therefore, experiments have proved that our method is also applicable to more complex data sets, and the robustness and generalization of the method have been verified.The table is shown below：\n                                              Table3:Test accuracies of EICIL on DVS Gesture.\n_____________________________________________________________________________________________________________\n| SNN Model &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; |  Dataset   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;   | GS&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| STDP-BW &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| STDP-BW-GS &nbsp; |    GSI  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;     |   GSGI  &nbsp;&nbsp;&nbsp;&nbsp;  |    Improvement |\n_____________________________________________________________________________________________________________\n| Spiking Resnet 18       |  DVS Gesture   | 93.14%  |     94.79%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;    |     95.14%&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;        |   95.47 %&nbsp;&nbsp;&nbsp;&nbsp; |  95.83%&nbsp;&nbsp;&nbsp; |       2.69%        | \n_____________________________________________________________________________________________________________\nFor Question3:\n\nThe experiment you proposed only shows that the adjustment of the K value achieves an 8:2 ratio of excitatory and inhibitory mechanisms, which does not fully prove the effectiveness of the method. To this end, we added two sets of experiments to adjust the K value to 6 in the CIFAR10 and CIFAR100 data sets, that is, the ratio of excitation and inhibition mechanisms reached 10:2. The experimental results are shown in Table 4. From the experimental results, it can be seen that when K=6, the accuracy of GSI and GSGI training in the two data sets is lower than that of K=5. This also shows that the 8:2 ratio of excitation and inhibition mechanisms at K=5 is indeed the best ratio, which proves the correctness of our proposed ideas and improves biological interpretability.The table is shown below：\n\nTable4:Supplementary experiment: K=6(The ratio of excitatory mechanism to inhibitory mechanism is 10:2) on CIFAR10 and CIFAR100.\n________________________________________________________________________________________\nSNN Model  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;                 Parameter K  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;         Learning Method &nbsp;&nbsp;&nbsp;&nbsp;     CIFAR10&nbsp;&nbsp;        CIFAR100\n________________________________________________________________________________________\n  Spiking Resnet 18      &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;        6        &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; GSI  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;            89.65%. &nbsp;&nbsp;  &nbsp;&nbsp;&nbsp;&nbsp; &nbsp;      54.27%\n\n Spiking Resnet 18     &nbsp;&nbsp;  &nbsp;&nbsp;&nbsp;         6    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;       &nbsp;&nbsp;&nbsp;&nbsp;             GSGI  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;                 90.34%&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;      63.47%\n________________________________________________________________________________________\n\n"}]

Author rebuttal:
We will revise the final version. For better presentation, Reviewer imxR, Reviewer 4jP2, Reviewer a2bZ and Reviewer 5jTx were noted as R1, R2, R3 and R4.

We sincerely thank all reviewers for their time and thoughtful feedback. In particular, we are grateful for the largely positive reception of our work:

The reviewers seem to agree with our proposal for an innovative training method for spiking neural networks[R1,R2,R3,R4]“The authors propose an extension of existing spiking neural network methods by combining a tunable iterative excitatory/inhibitory learning mechanism.” [R1] “a good idea”[R3]“an innovative breakthrough ”[R2，R4].We will incorporate all feedback and correct all typos and incorporate suggestions.

Contributions:

This paper combines the excitatory mechanism with the inhibitory mechanism, imitating the neural network mechanism in the biological brain, and enhancing the biological interpretability of the artificial neural network.

This paper makes full use of the unique hyperparameters of the spiking neural network: the time step to combine the excitatory mechanism with the inhibitory mechanism, allowing the two to jointly train the same network structure, and using each other for local optimal iterative training. 

This paper also designs the ideal ratio of 8:2 of excitatory and inhibitory mechanisms to the neural network model in biological brains, making the above method more persuasive.

This paper improves the training mode of STDP, so that STDP can help the network to learn. And it improves the accuracy of STDP training multi-layer neural network.

The reviewers raised individual points of criticism, which we address in detail in our direct responses to each reviewer. The main comment is to add a more complex dataset to test our ideas. Here we have added a set of experiments on the DVS Gesture dataset, successfully verifying that our method is also adaptable to more complex datasets.We also fully illustrate and explain how the method improves biological interpretability.In addition, we also proposed to explain and verify the idea that the combination ratio of excitatory mechanism and inhibitory mechanism here reaches 8:2.In response to these questions you raised, we will fully explain and respond below, and supplemented several sets of related experiments (see Table 1-4) to fully verify the feasibility of this idea.

We believe that the remarks of the reviewers and the additional results further improved the paper, and will happily respond to any additional questions or comments during the discussion phase.

Meta-review: The reviewers mentioned several positive aspects of the paper, e.g.:
- The paper proposes an extension of existing spiking neural network methods by combining a tunable iterative excitatory/inhibitory learning mechanism.
- The article combines the excitatory mechanism with the inhibitory mechanism, imitating the neural network mechanism in the biological brain, and enhancing the biological interpretability of the artificial neural network.
-  This article provides a good idea to merge STDP with the common backpropagation methods of deep spiking neural networks so that STDP can help the network learn.
- This method works especially well on the CIFAR100 dataset.

However, they also raised multiple doubts about it, such as:
- The writing in the paper could be improved and the motivation/justification for certain design decisions made more clear.
- It is hard to keep track of the different model configurations and their acronyms.
- The paper only introduces the combination of one excitatory mechanism and one inhibitory mechanism and does not fully express the effectiveness and feasibility of the method.

Three out of four reviewers agree (8-7-6 vs. 3) that the paper should be accepted. I tend to agree with them, thus, I vote to accept the paper.
Decision: Accept (poster)