Rethinking the Membrane Dynamics and Optimization Objectives of Spiking Neural Networks
Authors: Hangchi Shen
Qian Zheng
Huamin Wang
Gang Pan
Venue: NeurIPS 2024 poster (2024)
Keywords: Spiking neural networks
Neural dynamics
Neuromorphic Computing
Spike patterns
Spiking neuron
Primary area: neuroscience_and_cognitive_science

Abstract: Despite spiking neural networks (SNNs) have demonstrated notable energy efficiency across various fields, the limited firing patterns of spiking neurons within fixed time steps restrict the expression of information, which impedes further improvement of SNN performance. In addition, current implementations of SNNs typically consider the firing rate or average membrane potential of the last layer as the output, lacking exploration of other possibilities. In this paper, we identify that the limited spike patterns of spiking neurons stem from the initial membrane potential (IMP), which is set to 0. By adjusting the IMP, the spiking neurons can generate additional firing patterns and pattern mappings. Furthermore, we find that in static tasks, the accuracy of SNNs at each time step increases as the membrane potential evolves from zero. This observation inspires us to propose a learnable IMP, which can accelerate the evolution of membrane potential and enables higher performance within a limited number of time steps. Additionally, we introduce the last time step (LTS) approach to accelerate convergence in static tasks, and we propose a label smooth temporal efficient training (TET) loss to mitigate the conflicts between optimization objective and regularization term in the vanilla TET. Our methods improve the accuracy by 4.05\% on ImageNet compared to baseline and achieve state-of-the-art performance of 87.80\% on CIFAR10-DVS and 87.86\% on N-Caltech101.

Rethinking the Membrane Dynamies and Optimization Objectives of Spiking Neural Networks
Hangchi S.2 Qian Zheng Huamin Wang 1.2,, Gang Pan
College of Artificial Intelligence, Southwest University
2 Chongqing Key Laboratory of Brain Inspired Computing and Intelligent Chips The State Key Lab of Brain-Machine Intelligence, Zhejiang University College of Computer Science and Technology. Zhejiang University stephen Sraphhen99@@@mail... swu. edu. en, hmwang@swu. edu. cn, {qi Cgianzheng, gpan) @zju. edu.
Abstract
Despite spiking neural networks (SNNs) have demonstrated notable energy effi- ciency across various fields, the limited firing patterns of spiking neurons within fixed time steps restrict the expression of information, which impedes further im- provement of SNN performance. In addition, current implementations of SNNs typically consider the firing rate average membrane potential of the last layer the output, lacking exploration of other possibilities. In this paper, we identify that the limited spike patterss of spiking neurons stem from the initial membrane poten- tial (IMP), which is set to 0. By adjusting the IMP, the spiking neurons can generate additional firing patterns and pattern mappings. Furthermore, we find that in static tasks, the accuracy of SNNs at each time step increases as the membrane potential evolves from zero. This observation inspires us propose a learnable IMP, which can accelerate the evolution of membrane potential and enables higher performance within limited number time steps. Additionally, we introduce the last time step (LTS) approach to accelerate convergence in static tasks, and we propose a label smooth temporal efficient training (TET) loss to mitigate the conflicts between opti- mization objective and regularization term in the vanilla TET. Our methods improve the accuracy by 4.05% on ImageNet compared to baseline and achieve state-of the- art performance of 87.80% on CIFAR 10-DVS and 87. 37.86% on N-Caltech The code is available at wittts::/// // // thub. com www.//tppeeeaaall111988//11111 IMC0//MPPSSNN
Introduction
In recent years, deep learning technology based on artificial neural networks (ANNs) has made significant breakthroughs in many fields 2 4 5) However,
all known, its high training and inference costs have become major obstacle to restrict its further widespread applications. To overcome these challenges, networks (SNNs) [6] have been developed, which may be a feasible path to refer to the efficient dynamics mechanism of biological nervous systems [7]. SNNs leverage the dynamic mechanisms of membrane potential integration and fire from biological neural networks, which can process time-varying input data by using a single model (8) biological neurons, maintaining linearly increasing computational complexity. Therefore, the advantages of energy efficiency and biologically plausible dynamical mechanisms 77 I0] make them a bridge between the fields of brain science and artificial intelligence, which is widely regarded as the next generation of ANNs (6) In addition, is worth mentioning that SNNs can cleverly avoid multiplication operations on neuromorphic chips
generation of neural network architectures named spiking neural
Coorrepondingg author.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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12 13 by spike-based computing, achieving synaptic computation and membrane potential accumulation solely through addition operations, which can significantly enhance their computational efficiency.
It should be noted that training SNNs to achieve the comparable performance with the same ANN architecture remains formidable challenge at present. The conversion method of ANNs to SNNs (ANN2SNN) [4, high-performance SNNs. However, these methods mainly incorporate knowledge from the ANN's learning of static inputs into the converted SNNs, which motivates us to concern about the biological plausibility of these SNNs as they do not require the acquisition of spatiotemporal information. Another alternative is leverage surrogate gradient [19 20 [2]] and backpropagation [22] through time to train high-performing SNNs. This method only requires four time steps to achieve an ac- curacy surpassing that of conversion methods requiring hundreds of time steps, making the most promising training approach for currently available energy energy-efficient SNNs. Therefore, due to the development of direct training methods, SNNs have been extended to various tasks, including image classification 23 24 25 image reconstruction 26 27 28) object detection [29], natural language
I5
16 [8] has proved to be an effective approach for obtaining
17
processing 30 31, etc, and have demonstrated significant energy efficiency advantages in these fields. It is pity that these training methods and architecture designs typically consider the firing rate or average membrane potential of the last layer as the output, instead of fully exploring the impacts of the membrane potential on the model performance and the training process [32 33
mambrara
(a) Adjusting IMP.
(b) Adjusting input intensity.
Figure 1: Membrane potentials and spikes (yellow) generated by adjusting IMP and input intensity.
In this paper, we find that the initial membrane potential (IMP) has different effects on the membrane potential integration and spike firing compared to input intensity(Figure]] Then, we discover that the novel spike patterns can generated by adjusting the IMP of spiking neurons and additional mappings between firing patterns can be established, which motivates us to propose a learnable IMP. Furthermore, we find that in static tasks, the variation of the output accuracy at each time step for SNNs is directly related to the membrane potential, as it is the only time- varying term. Then can explain why the convergence speed of temporal efficient training (TET) [34] in static tasks is significantly lower than standard direct training (SDT) 20). To address this problem, we propose a method called last time steps (LTS) to achieve faster convergence in static tasks. And then, we propose label-smoothed TET loss for neuromorphic tasks, which outperform vanilla TET on neuromorphic datasets [35 36]. It is worth noting that the proposed novel IMP method can obtain significant performance without any additional adjustments for the network structure and training method. By simply setting the IMP of the original LIF neurons to a learnable version, we achieve SOTA accuracies of up 87.8% and 86.32% CIFAR 1ODVS (35) and NCaltech (36), respectively. Furthermore, our LTS method improves the accuracy of SEW-ResNet50 [37 on the ImageNetlk (88) dataset 71.83% surpassing the vanilla 2EW-ResNet152, 69.26%. The main contributions are as follows:
1) We discover that SNNs can generate new spike patterns by adjusting the IMP values, and prove that on the static tasks, the variation of SNN accuracy at each time step is only caused by the change of membrane potential. In addition, innovatively introduce the learnable IMP in SNNs to accelerate the evolution of membrane potential.
2) To alleviate the slow convergence of TET on the static tasks, we propose the LTS method, which can accelerate the rate of convergence on the static tasks. Additionally, we construct label-smoothed TET loss to further enhance the performances of SNNs on the neuromorphic tasks.

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3) Compared with the baselines on the neuromorphic datasets and the large-scale static dataset ImageNetIk, our methods can achieve significant improvements. Moreover, there is almost no difference in the computational overhead and inference speed compared to the original models.
2 Related Works
2.1 Neuron Dynamics Modeling
The leaky integrate and analog fire spiking neuron [39 was proposed to replace binary spike with analog values for transmission, alleviating the issue decreased performance SNNs. The paramet- ric leaky integrate-and- enabling each neuron to learn optimal membrane time constants, thus increasing neuronal diversity. The gated leaky integrate-and-fin neuron [4] was employed for channel- parameterization approach to fully parameterize the spiking neuron, including learnable decay mechanisms, potential thresholds, reset voltages, input conductance, and gating factors. The multi-level firing method 42 was used to enhance the expressive ability and achieve more efficient gradient propagation by integrating neurons with different thresholds to realize multi-level firing. Parallel spiking neurons [4 were discussed to remove the membrane potential reset process and redefine the dynamic mechanism in non-iterative manner, addressing the difficulty of ordinary spiking neurons in learning long-tern term dependencies.
spiking neuron [40] was introduced to design learnable dynamic model,
2.2 Direct Training Methods
The binary spikes emitted by spiking neurons during the forward phase are generated by step func- tion, which is non-differentiable activation. In the backward propagation phase, this step function can be replaced with a surrogate gradient [19] to achieve direct training. The most common direct training method currently is backpropagation through time (BPTT) [22]. which treats spiking neural networks (SNNs) special type of recurrent neural network (RNN). In this approach, gradients propagated backward along the temporal dimension, which requires more computational resources and memory compared to their corresponding ANNs [4]. tdBN [1] explored normalization methods for spiking neural networks (SNNs) and achieved direct training of large-scale SNNs on the ImageNet dataset for the first time. Based on this, more effective normalization method called TEBN [45 was proposed, which rescales the presynaptic inputs at each time step using distinct weights. TET [34 enabling spiking neural networks (SNNs) converge to flatter minima compared to SDT (20) which enhances generalization capabilities. OTTT (46) and SLTT [47) simplified the gradient calculations along the temporal dimension in BPTT, significantly reducing memory and computational costs.
3 Analysis of Membrane Dynamics
In this section, we first investigate how the initial membrane potential affects neuronal spike patterns, and then analyze how the dynamic evolution of membrane potential drives improved SNN perfor- mance. These analyses underscore the critical role of membrane dynamics in SNNs and provide new insights into its impact on the SNN's representational capacity and convergence.
3.1 Preliminary of Spiking Neurons and Loss Functions
Spiking neurons are the fundamental unit of SNNs, used to simulate the dynamic behavior of brain neurons. Their operation is described by dynamical equations that related to membrane potential and input current. The leaky integrate-and-fi (LIF) 77] model is one of the commonly used spiking neuron models, and its iterative form of the dynamical equations be represented follows:
A[t] (1 [ + [[],
I I TxN
o[t] = h[d > Van.
o E (0,1
VA ER
(2)
8|t + 1| [[4]
8 S TXN
s(0] (0)
where 7[4] represents the neural input current at time I, represents the membrane potential decay coefficient. When T 0, reduces the Integrate-and- (IF) 77] neuron. s|{ represents the state of the membrane potential at time step and s is the state of the IMP, which is typically set
3

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to constant 0. h[]] represents the change in membrane potential during time step f. oft] indicates whether the neuron fires a spike at time and V1A represents the firing threshold of the neuron.
The most commonly used loss functions in direct training SNNs are SDT 20 and TET 34 SDT loss function LSDr is defined as:
The
I LSDT LeEl T x Σ vlt). Bgt),
(4)
here, 7' represents the total number of time steps, y|t] represents the raw output of the model at each time step, Vg represents the ground truth label, and LCE denotes the cross-entropy loss. SDT aggregate the outputs of the SNN by taking the mean of the outputs from all time steps, then calculate the loss based on the voting result. In TET, the averaging step is placed after the calculation of cross entropy loss:
T
1 T Σ
LTE
Cce(vlt).
(5)
the LIET calculates the loss for each time step individually and then aggregates the losses from each time step to obtain the final loss. This approach can effectively improve the performance of SNN on neuromorphic datasets.
3.2 Membrane Dynamics Related to IMP
The membrane potential is commonly reset to zero before the next task in the current implementations of SNNs. However, through some experiments and the analysis of experimental results, we find that novel firing patterns and pattern mappings can be generated by adjusting IMP.
IMP=0.0
IMP-0.5
MMP=1.0
0000 .0.125)
(- .0.25)
0.0 0000 O
(0.125,0.166)
0001
-.00 ,0.333)
10000 0
(0.25,0.33)
0001
10.16...220)
00
(0.333.0.500)
(0.33,0.50)
(02250.05500
O O
[0.500.0.100
(0.50,0.75)
[0.500,1.000
O O
[1.000, to
[1.00, +
[10000. + 00)
Input Intensity
Firing Pattern
Input Intensity
Firing Pattemn
Input Intensity
Firing Pattern
Figure 2: All firing patterns that IF neurons can generate under constant intensity input and 4 time steps. The red box highlights the disappearing firing patterns, while the green and yellow boxes denote the additional firing patterns due to the IMP change.
Observation 1: Novel firing patterns under constant intensity input can be generated by adjusting IMP. Figure 2 displays the firing patterns (spike sequences) generated by an IF neuron under constant input intensity. The number of patterns varies depending on the IMP. When the value of IMP increases from 0.0 to 0.5, the pattern '0101" disappears, while the new patterns '0100' and '1010' emerge, resulting in increased pattern diversity. Conversely, setting the IMP to 1.0 leads to the emergence of new patterns 10000, 11011," and 1001', but reduces the overall number of patterns. These additional patterns that cannot be generated if IMP is set to O, can benefit static tasks by enabling SNNs to encode more information during the processing of static inputs.
New mappings of firing patterns can be generated by adjusting IMP. Apart from its impact on input encoding, our primary focus is whether the model's capabilities can be enhanced by modifying IMP. In ANNs, artificial neurons can map any single input variable to any value by adjusting the weights. Similarly, we hope that spiking neurons can also map input sequences to as many firing patterns possible, thereby enabling the network to have better representation capabilities. From figure 3 we observe that every output pattern has at least one available pattern mapping. However, we can notice that black areas present in the figure, which means that no matter how the synaptic weights are adjusted, mapping among these spike patterns still cannot be established. In other words, spiking neurons theoretically generate all firing patterns, but they cannot map any
Observation 2:

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(a) IMP=0.0
(b) IMP=0.25
(c) Learnable IMP
Figure 3: Pattern mapping IF neuron over 4 time steps. The horizontal and vertical axes in the figure represent all possible spike patterns (16 total) that IF neurons may receive and emit. The white squares indicate that neuron can receive the spike pattern from the horizontal axis and emit a spike pattern on the vertical axis, known as pattern mapping.
specific pattern to all patterns. Figure 3b il lusttrates that through adjusting the IMP value from O to 0.25 can generate additional pattern mappings. Furthermore, Figure dedoonsraatee that when IMP is learnable, it exhibits greater potential for establishing mappings among spike patterns. Therefore, we believe that the learnable IMP can effectively improve the expression capacity of spiking neurons.
3.3 Membrane Potential Evolution in Static Tasks
We further explore the effect of membrane potential variations static tasks through image classification task. We define SNN as follows to focus on its performance at each time step,
(slt + 1], v(t)) + [x]t) 0),
(6)
where f()) represents the network computation, represents the network weights, s[{] represents the set of membrane potentials of all neurons in SNN with time step t, x/(]] represents the input at time step l, and y|{] the corresponding output. Assuming æ = =x() is a constant input intensity for t 1,2, 1,2.... T, then we simplify Eq. aas
vit| f(z, s)t
On the static tasks, the temporal variations are determined solely by the state of the membrane potential s(4), resulting in corresponding changes for the output y|t].
Observation 3: In static tasks, the accuracy of SNNs at the each time step is sensitive the current MP. Figure demonstrates the test accuracy of SNNs each time step on cifar10 dataset [48]. which shows that the accuracy is extremely low at T=1, only 10.76%. However, the time step increases, the model accuracy exhibits an upward trend, exceeding 90%. It is worth not- ing that on the static tasks, since the input x and weight 0 are fixed at each time step, the model's output at each time step entirely determined by the current state the mem- brane potential s[]] For instance, when the membrane potential evolves to a "sufficiently good" state, such as at
Constani
92.04
92.05
92-
Accurcy
991
90.44
t == 4, the SNNs only requires the current membrane po- tential s [4] and input æ to achieve an accuracy 92.05%, which is close to the model's final performance of 92.36%.
60
40-
Therefore, these findings prompt us to reconsider how to accelerate the evolution of the membrane potential hance the SNNs performances within limited number of time steps.
Figure 4: The test accuracy at each time step on the CIFAR10 dataset.
Observation 4: TET performs well on the neuromorphic tasks but exhibits slow convergence on the static tasks. We compare the SDT loss and the TET loss the static datasets and the neuromorphic

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Table 1: Test accuracy TET and SDT on the static and neuromorphic datasets.
Loss Function
Static (Stase((SEW-RI8)
Neuromorphic Datasct(VGG11)
CIFARI0/100
ImageNet100
ImageNet1k
CIFARIODVS DVSG128
NCaltech101
SDT Loss
94.56/76.58 94.33/76.40
78.42 77.80
63.21 62.92
84.3
98.26
85.78
TET Loss
85.6
98.61
86.32
2.5
SDT
2.5
SDT
2.5-
SDT
2.5
SDT
2.0
TET
2.0
TET
3 1.5
1.5
3 [.55
1.5
1,0
1.0
0.5
0.5
0.5
0.0
0,0
0.0
500
1000
1000
500
1000
1000
Epoch
Epoch
Epoch
Epoch
(a) T=1
(b) T=2
(c) T=4
(d) T=6
Figure 5: The convergence speed of TET and SDT on the static data.
datasets, and find that TET loss has significant advantage on the neuromorphic datasets, but it is not superior to SDT loss on the static datasets, as shown in Table I We believe that this phenomenon arises from the constant intensity input on the static datasets. By applying the TET loss Eq. to the SNNs with the static input Eq.
M we have:
1 LTET - T
Σ ECn(y(l).ull (g))) where u(4 [
can be observed that on static tasks, the membrane potential s(1). as the only time-varying term in the dynamic system, evolves gradually the time step progresses. However, according to Observation 3, we know SNNs are sensitive to 8 (t). which means that is difficult to output the same result for different s[t]. The optimization goal of the TET loss to make the network output the correct results for every time step, i.e. y(t] Yot- In this case, TET requires more iterations build a flat "landscape", slowing down the convergence, as shown in Figure [ Additionally, if the SNNs are insensitive to the value of s(t] and even tends to the same value for all time steps, i.e.
v[1] y[ the results of all T time steps. In this case, the computations for the subsequent time steps become redundant and meaningless.
y| Σ/ y/t]. then the output of the first time step is sufficient to represent
4 Methods
4.1
Learnable IMP
The membrane potential in the current dynamic model of SNNs is typically initialized to uniform constant value (usually 0). Based on Observation I and Observation 2, we find that the learnable IMP enhance the expressive power of SNNs. Based Observation the learnable IMP can allow the membrane potential to start from a non-zero value, which may help improve the performances of SNNs the static tasks. We can assign independent learnable IMP for each spiking neuron. According to Eq. [ the membrane potential accumulation can be represented as follows,
[tt) š[t) + x(t),
I T h TXN å T $ $[0] R.N.
where 8[0] represents the state of the IMP that is extended from zero to the real number. As a counterpart to the method of setting IMP to O, in the initialization process, we set IMP to uniform distribution with an expected value of O,
8[0] Uniform(-A,
(10)
where À is a hyper-parametes used to control the boundaries of the uniform distribution, ensuring the IMP remains within an appropriate range. Since the current implementation of SNNs requires memory allocation to store membrane potential states, replacing with trained IMP during the inference process will not incur additional computational overhead.

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4.2 LTS Method for the Static Tasks
We propose a new post-pree pest-proesssing representation method called last time step (LTS) to alleviate the convergence difficulties of TET on the static tasks, based on Observation 3 and Observation 4. This approach masks all outputs of the SNNNs before the LTS and only retains the output of the LTS as the result of the entire model, which ensures that the SNNs can generate the most "high-quality" membrane potential without interference before the LTT T.
y fs 0).
(11)
where T represents the LTS's output of the SNNs. When using only the LTS the output, both SDT and TET losses yield the same representation,
LITS Lcr(v(T), (gt).
(12)
4.3 Label Smooth TET Loss for the Neuromorphic Tasks
Based on the results in Table [ we recommend using TET loss to achieve better performances when dealing with the neuromorphic tasks. In the original version of TET [34,, an additional mean squared eπror (MSE) regularization term was added to control the firing level of the last layer of the model, given by CRGG + Σt= CMSE (yse(y(t), ø). where e denotes the target firing level. The coefficient controls the proportion of the two losses, and the complete loss is defined as Greal (1 AET + >LREG- We think that this setup will prevent the training loss of the model from converging to zero, because when CREG = 0, the model will output a constant value at every time steps, rendering the model unable to perform the classification task. On the other hand, when LTET 0, LMSF > 0. Considering that LMSE plays a role similar to smoothing process in the loss function, propose removing CREG and replacing the cross-entropy loss with label smooth cross-entropy loss, as shown by the following equation:
1 = T
CIETS
CCE
CCE(f 2))) 0g, where Ogt = =(1 (1-c)yge K'
(13)
here, Vgt represents the ground truth, Ngt represents the smoothed label, represents the smoothing factor, and represents the number classes. can be observed that LTET. can effectively avoid the trade-off between firing level and classification accuracy for model training. and can theoretically allow the training loss to converge to zero.
Experiments
In this section, we demonstrate the effectiveness of our proposed method by extensive experiments. We compare the results of our method with other methods on both the neuromorphic dataset and the static dataset. Additional training procedures and other hyperparameter settings are provided in the appendix A
5.1 Execution Speed Benchmark of IMP
We compare the execution speed and the mem- ory consumption between the vanilla IF neurons and IF+IMP neurons in Figures 6 The number
20-
IF 2
IF+MMP 2
of neurons are
28, 212 216 and 220 with
212
1F+1MP 212
time steps of 2, 4, 8, 16, and 32. All neurons are implemented by using spikingjelly and Py- Torch, and the computations are performed on GPU. It can be observed that there is almost no difference (about +1. +1.03%) in the execution time between the IF neurons with IMP and the vanilla IF neurons, including forward and back- ward propagation. addition, since the compu- tational consumption of SNNs is mainly caused by synaptic computation, the additional over- head caused by adding IMP can be neglected.
15
IF 216
IF+IMP 216
22
IF+IMP 2.
5
T-2
T-4
T-8
T-16
T-32
Figure 6: Execution time (ms) for the forward and backward pass of IF neurons, w/wo IMP.
7

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5.2
Convergence Speed of LTS on the Static Data
2.5
SOT
2,5
SDT
2,5
S07
2,5
SDT
TET
2.0
TET
TET
2.0
TET
2 1.5
1.5
1.5
1.0-
1.0-
0.5
01.5
0.5
0.5
0.8
500 Epoch
1000
500 Epoch
500
1000
500
1000
Epoch
Epoch
(a)
(b) T=2
(c) T=4
(d) T=6
Figure 7: Convergence speed of LTS, TET, and SDT on the static data.
We have conducted a validation of the convergence speed of SDT, TET, and LTS the commonly used time steps (1, 2, 4, and 6), shown in Figure 7 The application of LTS post-pracessing has resulted an improvement in the convergence speed of SNNs.
5.3 Performances on the Neuromorphic Data Classification
Table 2: Comparison of our methods and other SOTA methods on the neuromorphic datasets. Size
refers to the input resolution of SNNs.
Dataset
Method
SNN Architecture
Size
Time Steps
Accuracy(%
GLIF
Wide 7B Net
48
16
78.10 10
NDA 49
VGG
48
10
79.60
TET134
VGG
48
10
83.17
TEBN 45
VGG
48
10
84.90
PSN[43]
VGG
48
10
85.90
IMP(ours)
VGG
10
85,90
IMP+TET-S(Ours)
VGG
48
10
87.10
IMP+TET-S(Our))
VGG
87.80
CIFARIO-DVS
PLIF140
PLIF Net
128
20
74.80
TDBN 21
ResNet-19
128
67.80
Dspike 50
ResNet-18
128
10
75.40
KLIF 51
PLIF Net
128
70.90
SEW [5sNer
Wide 7B Net
128
16
74.40
Spikformer 23
Spikformer
128
10
78.90
Spikformer 23
Spikformer
128
16
80.90
NDA (49
VGG
128
10
81.70
IMP(ours)
VGG
128
16
86.30
IMP+TET-S(ours)
VGG
128
16
87.00
NDA[49]
VGG
48
10
78.20
EventMix 53
ResNet18
48
10
79.47
ESP[54
SNN7-LIFB
48
10
81.74
TCIA
TCJA-SNN
48
10
82.50
[KS[56]
VGG-TKS
10
84.10
IMP(ours)
VGG
48
10
84.68
N-Caltech101
IMP+TET-S(our')
VGG
85.01
EventDrop(57]
VGG
128
10
74.04
NDA 49]
VGG
128
83,70
EventRPG 58
VGG
128
10
85.62
[TR[59] IMP(uurs) IMP+TET-S(our))
VGG
128
85.91
VGG
128
16
86.12
VGG
128
87.86
We have applied our methods simple spiking VGG model and compare them with the SOTA
SNNs on neuromorphic datasets. Since the CIFARIODY and NCaltech10" datasets are not
pre-divided into training and testing sets, split these datascts in 9:1 ratio. To ensure fair

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comparison with other existed methods, we adopt the two configurations with resolutions of 48 and 128, respectively. The data preprocessing and training settings refer the appendix A.8
Table 2 reports the experimental results on the CIFARIODVS and NCaltech10r datasets. On the CIFARTODVS dataset, when setting the resolution to 48, the IMP method achieves the SOTA accuracy of 85.9%, which is 2.73% higher than the baseline [34] and is on par with the current SOTA method PSN. It should be noted that the removal of the reset process in PSN means that the spiking activities in the previous time steps will not affect the membrane potential values in the subsequent time steps. When we set the resolution 128, the IMP method once again demonstrates its superiority, achieving the SOTA accuracy of 86.3%, which exceeds all other methods, including the current SOTA data augmentation method EventRPG(58). TET loss model performance. The experimental results show that the performance of the model has been significantly improved under both configurations, achieving accuracies of 87.00% and 87.10% respectively. In addition, the accuracy can be further improved to 87.8% by setting the time step to On the NCaltech101 dataset, our method can also demonstrate excellent performance. Specifically, when we set the resolution to 48, our method achieves the current SOTA accuracy of 85.01% %. When switching to resolution of 128, our method further demonstrates its advantages, achieving the SOTA accuracy of 87 87.86%.
addition, further explore the impact of using smoothed
5.4 Performances on the Static Data Classification
Table 3: Comparison of our methods and other methods on the ImageNetlk dataset.
Method
Network Architecture
Reset
Params
Time Steps
Accuracy(%)
SEW R8sNet-18
X
11.69
67.63
4S
SEW ResNet-34
X
21.79
4
70.54
ResNet-34
21.79
6
68.19
Dspike 50
VGG-16
138.42
5
71.24
TET 34
SEW ResNet-34
21.79
4
68.00
TDBN211
ResNet-34
21.79
6
67.05
TEBN 45
SEW ResNer-34
21.79
4
68.28
GLIF
ResNet-34
21.79
4
67.52
Spikformer-6-23
23.37
4
72.64
Spikformer
1elformer-885111
29.68
73.38 4
SEW ResNet-18
11.69
63.18
SEW ResNet-34
21.79
67.04 4
SEW ResNet 52
SEW ResNet-50
25.56
4
67.78
SEW ResNet-101
44.55
4
68.76
SEW ResNet-152
60.19
69.26
SEW ResNet-18
11.69
4
64.33(+1.15)
LTS
SEW ResNet-34
21.79
4
68. 68.10(+1.06)
SEW ResNet-50
25,56
4
71.24(+3.46)
SEW ResNet-18
14.17
65.38(+2.20)
IMP+LTS
SEW ResNet-34
25.54
4
68.90(+1.886
SEW Re
36.67
4
71.83(+4.05)
We apply our proposed IMP and LTS post-processing methods to the standard SEW-ResNet architecture and compare them with the SOTA spiking neurons and the directly training SNN methods on the large-scale static dataset ImageNetlk [38]
3 the detailed experimental results on the large-scale static dataset ImageNetlk. Specifi- cally, by applying the LTS post-processing method the accuracy improvements of 1. 1.15% 1.06%, and 3.46% compared to the baselines, respectively. These results demonstrate the effectiveness LTS on the large-scale datasets. Furthermore, with the introduction of the learnable IMP, the accuracy can be further increased by 1.2% With
NeW-ResNetl 88/4//50 models, we can obtain

---

the LTS post-processing and learnable IMP. our SEW-ResNet50 achieves an accuracy of 71.83%,
surpassing the accuracy of the vanilla JEW-ResNet152, 69.26%.
5.5 Further Ablation Studies
Table 4: Ablation Study on CIFARIODVS and Imagenet100.
Dataset
Method
Spiking Network
Time-steps
Accuracy (
SDT(E 0.0)
VGG
10
83.70
TET(E 0.0)
VGG
10
84.90
TET-S(E = 0.1)
VGG
10
85.60
TET-S(E 0.01)
VGG
10
86.10
TET-S( = 0.001)
VGG
10
85.40
CIFARIO-DVS
SMPA 0.0)
VGG
10
83.70
IMP+TET(A -0.0)
VGG
10
85.90
TET-SC -0.0)
VGG
10
86.20
IMP+TET-S = 0.2)
VGG
10
87.10
IMP TET-SAA 0.4)
VGG
86.40 10
TET
SEW-ResNet18
4
78.50
SDT
SEW-ResNet18
79.
LTS
SFW-ResNetl
4
80.20
ImageNet100
IMP+TET
SEW-ResNet18
78.70
IMP+DDT IMP+LTS
SEW-ResNet18
4
79.90
SEW-ResNe118
4
80.80
Table presents the results of series of ablation studies conducted the CIFARIO-DVS and ImageNet 100 datasets, aimed at analyzing the impact of various factors on model performance. This helps understand the role of different components and parameters in the overall model, and aids in optimizing the model design. For the DFFARIO-VSS dataset, we explored methods including SDT, TET, and their variants TET-S and versions combined with IMP. VGG was used the spiking neural network structure. The results show that for different values, the TET-S+IMP method achieved the best accuracy. with IMP+TET-S (A 0.2) reaching 87%10% the highest among all methods on CIFAR O-DVVS dataset. For the ImageNer100 00 dataset, we tried TET, SDT, LTS, and their versions combined with IMP, using SEW-ResNet1& 18 as the spiking neural network structure. On this dataset, the LTS method and its combined version with IMP, IMP+LTS, performed the best, reaching 80.80% accuracy.
6 Conclusions
We have proposed learnable IMP by rethinking the membrane dynamics of SNNs to enhance the dynamics mechanism of spiking neurons. Additionally, we have presented a LTS post-processing method for the static tasks and a label-smoothed TET loss for the neuromorphie tasks. It is worth mentioning that our methods only require very minor modifications to the settings and loss functions of spiking neurons to effectively improve the performance of SNNs on the static tasks and the neuromorphic tasks. At the same time, almost additional computational cost is required. Since proposed method has broad compatibility with existing model structures and training methods, it can be widely applied on the existed methods to further improve their network performances.
Acknowledgement
This work was supported by Fundamental Research Funds for the Central Universities (Grant No. SWU021002), Project of Science and Technology Research Program of Chongqing Education Commission (Grant No. KJZDD-K221002003 Key R&D Program of Zhejiang (2022C01048) and National Natural Science Foundation of China (Grant Nos. U1804158, 62376247, U20A20220, and 62334014).
10

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A Appendix supplemental material
A.1 Broader Impacts
This paper focuses on the fundamental research spiking neural networks, with the goal of revealing the impact of membrane dynamics the network and optimizing its performance. Generally, there are no negative societal impacts this work.
A.2 Limitations
IMP has a small gradient during training, which makes it sensitive to initialization (Figure 4 In addition, learnable IMP may lead an excessive number of parameters, as it assigns initial states to each neuron, although this has the same computational cost setting the IMP to O. The advantage of LTS may reduce when the time step is set large, due to the supervision only applied at the last time step. Therefore, we only recommend using LTS on static tasks with time steps less than 8 (Table 8). which should be able handle most situations. Additionally, the performance of the combination of LTS and the latest spike transformer technology is not yet clear. Furthermore, we have not found unified loss function that can achieve superior performance on both static tasks and neuromorphic tasks, which remains challenge in the current research.
A.3 Convergence Speed
We compared the convergence speed of TET and SDT at different time steps (1=1,2446..211,6222233 For static tasks, TET's convergence speed was lower than SDT's,, and the difference in convergence speed diminished as the time step increased.
SDT
SDT
2.5
SDT
SDT
2.0
TET
2.0
TET
2.0
TBT
TET
8 1.5
1.5
1.5
1.0
1.0
0.5
0.5
0.5
0.0
0.0
500
1000
500
1000
500
1000
500
1000
Epoch
Epoch
kpoch
Epoch
(a) T=1
(b) T=2
(c) T=4
(d) T=6
2.5
2.5
SDT
2.5
2.5
SDF
2.0
2.0
LTS
1.5
LTT
LTS
1.5
LITS
1.0
1.0
0.5
0.5
0.0
0,0
0.0
500
1000
1000
500
1000
1000
Epoch
Epoch
Epoch
Epoch
(e) T=8
(f) T=16
(g) T=24
(h) T=32
Figure The convergence speed of SDT, TET and LTS on static data.
A.4
Compared with Transformer-based SNNs
The performance of SEW-ResNet-LTTS can be close to some Transformer-based SNNs (Table 5).
Table 5: Accuracy and theoretical energy consumption compared with Transformer-based SNNs.
Model
Param (M)
SOPs (G)
Power (mJ)
Accuracy
Spikformer-8-38%
16.81
6.82
7.73
70.24
Spikformer-6-511
23.37
8.69
9.42
72.46
Spike-driven 8-384
16,81
3,90
72.28
Meta-SpikeFormer
15.10
16.70
74.10
SEW-R50-LTS (ours)
25.56
3.10
2.79
71.24
SEW-RSO-LTS+IMP (ours)
36.67
3.45
3.11
71.83
15

---

A.5 Energy Consumption
IMP does not incur significant additional theoretical power consumption, but can effectively improve the performance of SNNs 6).
Table 6: Accuracy and theoretical energy consumption on ImageNet dataset.
Model
Training Method
Aceuracy
SOPs(G)
Power(mJ)
SEW-ResNer18
TET
62.92
1.36055
1.22449
SEW-ResNet18
SDT
63.21
1.37418
1.23676
SEW-ResNet18
LTS
64.33
1,21427
1.09285
SEW-ResNet18
LTS+IMP
65.38
1.31371
1.18234
SEW-ResNet34
TET
67.98
3.59539
3,23585
SEW-ResNe134
SDT
68.10
3,52732
3.17459
SEW-ResNe134
LTS
68.10
3.11694
2.80525
SEW-ResNet34
LTS+IMP
68.90
3.12180
2.80962
SEW-ResNet50
TET
69.87
3,40181
3.06163
SEW-ResNe150
SDT
70.33
3.20071
2.88064
SEW-ResNet50
LTS
71.24
3,10432
2.79389
SEW-ResNet50
LTS+IMP
71.83
3,45325
3.10792
A.6 Performance of LTS on DVS Tasks
The LTS method can lead to information loss, especially on DVS tasks with a large number of time steps (Table 7). Therefore, we suggest considering the of LTS only in static tasks, as the effectiveness of LTS relies on the assumption of having the same input at each time step.
Table 7: Accuracy CIFARIODVS dataset with different time-steps.
Model
Training Method
T=4
T=8
T=10
T=16
VGG
TET
83.8
85.0
85.8
86.4
VGG SDT
83.4
84.3
84.4
85.1
VGG
LTS
83.7
83.0
82.9
82.3
A.7
Enhancing Performance by Learnable IMP
The learnable IMP significantly improve the accuracy of the first time step and lead to better overall performance (Figure 9).
94
Constant IMP
Leurnable IMP
93,19
93-
93
92.8
92.36
92.32
92.04
92.05
91.97
Aceuracy
91
90.44
Accuracy
72.35
60-
60-
40-
40
10.76
0
T=1
2
T
T
mean
T=1
T-2
T=3
T=4
mean
(a) ConstandIP
(b) LearnableIMP
Figure 9; The test accuracy each time step the CIFAR10 dataset.
16

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A.8 Experimental Configurations and Hyperparameter Settings
Table 8 lists the key parameters required for training on the static datasets ImageNetlk, ImageNet100.
CIFARIO, and CIFARI00. Table outlines the key parameters used for training on the neuromorphic Tutleeooutines
datasets CIFARIO-DVS- 128. CIFARIO-DVS-45
-alltcch111-1221 and N- N-Caltech101-48.
Table 8: Experimental configurations static task.
hyper-parameter architecture
ImageNerIK ImageNet100
CIFARTO
CIFARTOO
SEW-ResNet
SEW-ResNet
SEW-ResNet
SEW-ResNet
time steps enable TEBN
4
4
4
4
No
No
No
No
detach reset spiking neuron
Yes
Yes
Yes
Yes
IF+IMP
IF+IMP
IF+MMP
IF+IMP
function membranc decay
Atan
Atan
Atan
Atan
optimizer
Adam W
Adam W
Adam W
Adam W
learning rate
0.001
0.001
0.001
0.001
weight decay
5e-4
5e-4
5e-4
5e-4
momentum
epoch
320
200
200
200
warm
10
10
10
10
Ir schedule
cosine
cosine SDT/TET
cosine
cosine
loss function
SDT/TET
SDT/TET
SDT/TET
label smooth
0.1
0.1
0.1
data augment
standard
standard
standard
standard
enable cutmix
No
Yes
Yes
Yes
enable mixup
No
Yes
Yes
Yes
GPUs
Table 9: Experimental configurations on ncuromorphic task.
syper-paramees
C8
CIFARIODVS-128
NCTO1-48
NC101-128
architecture
VGG11
VGG11
VGG11
VGG11
time steps enable TEBN detach reset spiking neuron sg function membrane decay optimizer learning rate weight decay momentum
10
16
Yes
No
Yes
No
Yes
Yes
Yes
Yes
LIF+IMP
LIF+IMP
LIF+IMP
LIF+IMP
ZIF
sigmoid
ZIF
sigmoid
0.25
0.5
0.25
0.5
SGD
AdamW
SGD
Adam W
0.1
0.001
0.1
0.001
5e-4
0.06
5e-4
0.06
0.9
0.9
epoch warm up Ir schedule
200
200
150
150
30
cosine
cosine
cosine
cosine
loss function label smooth event augment enable cutmix
SDT/TET
SDT/TET
SDT/TET
SDT/TET
0.01
0.01
0.01
0.01
standard
NDA
standard
NDA
No
Yes
No
Yes
enable mixup
No
Yes
No
Yes
GPUs
A.9 On-chip Learning
The following approach can be useful for implementing on-chip learning IMP: (1) Use auxiliary neuron to distribute IMP (by firing a spike) the other neurons the initial time step. (2) Optimize the synaptic weights of this auxiliary neuron to adjust IMP.
17

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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification:
The abstract and introduction clearly state our contributions in the field of spiking neural networks, including the discovery of special phenomena caused by SNN dynamics and the inspired improvement methods.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
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Reviews:
[{"review_id": "eHQX9NEz6I", "reviewer": "Reviewer_AWRd", "summary": "presents a novel approach to understanding and modeling the dynamics of spiking neural networks", "questions": "Can the authors provide more details on the assumptions made in the theoretical framework? How do these assumptions impact the generalizability of the proposed methods?How does the proposed framework compare to other state-of-the-art models in terms of computational efficiency and scalability?", "limitations": "The authors have addressed the limitations of their work to a reasonable extent. They acknowledge the assumptions made in their theoretical framework and discuss potential areas for future research. However, the discussion on the broader societal impact of the work could be expanded, particularly in terms of ethical considerations and potential negative consequences.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "offering new insights into SNN modeling and potential applications in various domains.\ntheoretical framework for SNN dynamics is novel and addresses existing limitations in the field.", "weaknesses": "Some of the assumptions in the theoretical framework could be more explicitly stated and justified.\nAdditional experiments, particularly in real-world scenarios, could further validate the proposed methods.\nThe introduction and related work sections could provide more context to better situate the contributions within the broader literature.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your efforts in reviewing our article and providing constructive feedback. We’d like to reply to your concerns in detail.\n\n> Weakness 1: Some of the assumptions in the theoretical framework could be more explicitly stated and justified.\n\n**Answer:** We will provide a clearer explanation of our assumptions in the subsequent version and ensure that the proof process strictly follows the format specifications, in order to improve the accuracy and readability of the content.\n\n> Weakness 2: Additional experiments, particularly in real-world scenarios, could further validate the proposed methods.\n\n**Answer:** Thank you for the suggestion.  We can provide the performance of our IMP method on the DVS128Gesture dataset, which captures human gesture movement trajectories using event cameras, thus being closer to real-world scenarios. Due to the current limitations in time and computational resources, we hope to try applying our method on larger-scale real-world scenarios dataset in our future work.\n\n|   Model    | Training Method | Spike Neuron | Time-step | Accuracy  |\n|:----------:|:---------------:|:------------:|:---------:|:---------:|\n| Spikformer |       TET       |     LIF      |    64     |   97.57   |\n| Spikformer |       TET       |  LIF + IMP   |    64     | **98.26** |\n\n**Table R4: Accuracy on DVS128Gesture dataset.**\n\n> Weakness 3: The introduction and related work sections could provide more context to better situate the contributions within the broader literature.\n\n**Answer:** We agree with your suggestion. We will supplement the introduction and related work sections to ensure they can better highlight our contributions.\n\n> Question 1: Can the authors provide more details on the assumptions made in the theoretical framework?\n\n**Answer:** Sure. For static tasks, we define $f(\\cdot)$ as the network computation, $\\theta$ represents the network weights, $s[t]$ is the set of membrane potentials of all neurons in SNN with time step $t$, $x$ is the constant input intensity for time step $t=1,2,...,T$, and $y[t]$ is the corresponding output, the output of the SNN at each time step can be represented in the following form,\n$$\ny[t] = f(x, s[t], \\theta).\n$$\nIt can be found that the temporal variations of the output $y[t]$ is determined solely by the membrane potential set $s[t]$. Based on experimental observations, we have the following assumptions:\n\n**A1**: $s[t]$ is time-varying in SNNs.\n**A2**: The change in $s[t]$ can alter the output $y[t]$.\n**A3**: Applying the same supervised label to $y[t]$ across all time steps may lead to difficulties in SNN convergence.\n\n> Question 2: How do these assumptions impact the generalizability of the proposed methods?\n\n**Answer:** **A1** typically holds true, except in the absence of external input. For **A2**, these phenomena are commonly observed in experiments, although minor perturbations may not significantly alter the output of the SNN. For **A3**, it is important to note that for static image classification tasks, the correct results can be obtained without perfect fitting. Therefore, when the model has sufficient expressive power to output similar $y[t]$ for different $s[t]$, and the task is simple enough, the performance of TET can approach the level of LTS.\n\n> Question 3: How does the proposed framework compare to other state-of-the-art models in terms of computational efficiency and scalability?\n\n**Answer:** By combining our proposed method, the performance of SEW-ResNet can be close to the Transformer-based SNNs. However, compared to the current state-of-the-art Spiking Transformer models, there is still a certain gap (For more details, please refer to the PDF file we have submitted). Additionally, we hope to combine the proposed method with these advanced models, and explore its potential in a wider range of application scenarios.\n\n|      Architecture      | Param (M) | SOPs (G) | Power (mJ) | Accuracy |\n| :--------------------: | :-------: | :------: | :--------: | :------: |\n|    Spikformer-8-384    |   16.81   |   6.82   |    7.73    |  70.24   |\n|    Spikformer-6-512    |   23.37   |   8.69   |    9.42    |  72.46   |\n|   Spike-driven 8-384   |   16.81   |    -     |    3.90    |  72.28   |\n|    Meta-SpikeFormer    |   15.1    |    -     |   16.70    |  74.10   |\n|   SEW-R50-LTS (ours)   |   25.56   |   3.10   |    2.79    |  71.24   |\n| SEW-R50-LTS+IMP (ours) |   36.67   |   3.45   |    3.11    |  71.83   |\n\n**Table R5: Accuracy and theoretical energy consumption on ImageNet test set.**\n\n> Limitation 1: The discussion on the broader societal impact of the work could be expanded, particularly in terms of ethical considerations and potential negative consequences.\n\n**Answer:** In this work, we found that adjusting the initial membrane potential can alter the spiking patterns of SNNs. Furthermore, in static tasks, the variation in SNN membrane potentials can influence the output. This finding may lead to the development of novel adversarial attack methods targeting SNNs. Attackers could achieve this by manipulating the membrane potential at specific future time steps. Such attacks would only require perturbation of the first few input frames, and could control the timing of errors in the SNN at a future time step. Compared to adding adversarial noise at all input time steps, this approach could be more stealthy.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "sKRcSdYHMb", "reviewer": "Reviewer_jQZD", "summary": "This paper analyzes the dynamics of membrane potential and proposes to improve performance by correcting the initial membrane potential to learnable parameters. This article proposes to use only the output of the last timestep as the classification feature during inference. In general, this paper proposes a simple but effective method.", "questions": "1. In the DVS datasets, each timestep has its own unique information. Will LTS lose the information of the previous time step and cause unstable recognition accuracy?\n2. Why does PSN lose dynamics and biological rationality? Aren't soft-reset SNNs dynamic? Biological rationality seems to have nothing to do with the reset method, and biological rationality is not important in deep learning.\n3. Hard reset will cause the model to be unable to calculate in parallel. Is the method proposed in this article only applicable to Hard-reset SNNs? Can this method scale up to a larger timestep (for example, 64)? In language and autoregressive tasks, the timestep of SNN is aligned with the sequence length, which is extremely large. Using hard-reset SNNs may cause serious inefficiency. What do you think of this?", "limitations": "Please see the weaknesses and questions.", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper provides a comprehensive and detailed analysis of the dynamics of membrane potential, which can inspire others.\n2. The method proposed in this paper is simple but effective. Taking SEW-ResNet as the basic model, IMP and LTS both bring significant gains.", "weaknesses": "Although this paper is well-analyzed, it still has some weaknesses.\n\nIt is not enough to just experiment with SEW-ResNet on a static dataset. If the residual technique is altered, such as MS-ResNet [1], the residual connection is calculated using the membrane potential. In this instance, will a better initialization of the membrane potential result in considerable gains? If the network design is altered, such as the Spikformer [2] with SEW residual connections and the Spike-driven transformer [3] with MS residual connections. Are the proposed IMP and LTS still valid?\n\n[1] Hu Y, Deng L, Wu Y, et al. Advancing spiking neural networks toward deep residual learning[J]. IEEE Transactions on Neural Networks and Learning Systems, 2024.\n\n[2] Zhou Z, Zhu Y, He C, et al. Spikformer: When Spiking Neural Network Meets Transformer[C]//The Eleventh International Conference on Learning Representations.\n\n[3] Yao M, Hu J, Zhou Z, et al. Spike-driven transformer[J]. Advances in neural information processing systems, 2023, 36.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your insightful comments. We first list your advice and questions, then give our detailed answers.\n\n> Weakness 1: If the residual technique is altered, such as MS-ResNet, the residual connection is calculated using the membrane potential. In this instance, will a better initialization of the membrane potential result in considerable gains?\n\n**Answer:** Yes. The effectiveness of our proposed IMP and LTS methods in membrane potential residuals on the MS-ResNet architecture can be evaluated on the ImageNet100 dataset.\n\n|    Model    | Method  | Epoch |   Acc1    |   Acc5    |\n|:-----------:|:-------:|:-----:|:---------:|:---------:|\n| MS-ResNet18 |   TET   |  100  |   73.92   |   91.62   | \n| MS-ResNet18 |   SDT   |  100  |   74.78   |   91.98   | \n| MS-ResNet18 |   LTS   |  100  |   75.78   |   92.92   |\n| MS-ResNet18 | LTS+IMP |  100  | **76.12** | **93.36** |\n\n**Table R6: Accuracy on ImageNet100 dataset.**\n\n> Weakness 2: If the network design is altered, such as the Spikformer with SEW residual connections and the Spike-driven transformer with MS residual connections. Are the proposed IMP and LTS still valid?\n\n**Answer:** Yes, we have tried the SpikingResFormer[1] with self-attention mechanism and membrane potential residual connections. Due to the limitations of time and computational resources, we used fewer epochs compared to the original paper. Although LTS is slightly lower than SDT, it still outperforms TET, which is consistent with our analysis. Additionally, we have verified the effectiveness of the combination of self-attention mechanism and IMP on the CIFAR10DVS dataset (**Table R3** and **Table R8**). We hope these results can address your concerns.\n\n|        Model        | Method |  Accuracy  |   SOPs(G)   |  Power(mJ)  |\n|:-------------------:|:------:|:----------:|:-----------:|:-----------:|\n| SpikingResFormer-S  |  TET   |   73.500   |   3.77187   |   3.39468   |\n| SpikingResFormer-S  |  SDT   | **73.988** |   3.42255   |   3.08029   |\n| SpikingResFormer-S  |  LTS   |   73.974   | **3.31618** | **2.98456** |\n\n**Table R7: Accuracy and theoretical energy consumption on ImageNet1k dataset.**\n\n|   Model    | Training Method | Spike Neuron | Time-step | Accuracy |\n| :--------: | :-------------: | :----------: | :-------: | :------: |\n| Spikformer |       TET       |     LIF      |    16     |   82.8   |\n| Spikformer |       TET       |  LIF + IMP   |    16     | **83.4** |\n\n**Table R8: Accuracy on CIFAR10DVS dataset.**\n\n[1] Shi X, Hao Z, Yu Z. SpikingResformer: Bridging ResNet and Vision Transformer in Spiking Neural Networks[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024: 5610-5619.\n\n> Question 1: In the DVS datasets, each timestep has its own unique information. Will LTS lose the information of the previous time step and cause unstable recognition accuracy?\n\n**Answer:** Yes, the LTS method can lead to information loss, especially in DVS tasks with a large number of time steps. We only suggest considering the use of LTS in static tasks, as the effectiveness of LTS relies on the assumption of having the same input at each time step. \n\n|   Model    | Training Method | T=4 | T=8 | T=10 | T=16 |\n|:----------:|:---------------:|:---:|:---:|:----:|:----:|\n|VGG| TET | 83.8 | 85.0 | 85.8 |86.4|\n|VGG| SDT | 83.4 | 84.3 | 84.4 |85.1|\n|VGG| LTS | 83.7 | 83.0 | 82.9 |82.3|\n\n**Table R9: Accuracy on CIFAR10DVS dataset (resize to 48).**\n\n> Question 2: Why does PSN lose dynamics and biological rationality? Aren't soft-reset SNNs dynamic? Biological  rationality seems to have nothing to do with the reset method, and biological rationality is not important in deep  learning.\n\n**Answer:** PSN is not a soft-reset dynamics, but rather a no-reset mechanism. PSN removes the reset mechanism and achieves parallelization through linear mapping or convolution (scanning) across the time dimension. But we agree with your point that biological rationality is not important in deep learning. We will modify the statement to: \"It should be noted that the removal of the reset process in PSN means that the spiking activities in the previous time steps will not affect the membrane potential values in the subsequent time steps.\" and change the \"Dynamic\" item in the table to \"Reset\".\n\n> Question 3.1: Hard reset will cause the model to be unable to calculate in parallel. Is the method proposed in this  article only applicable to Hard-reset SNNs? \n\n**Answer:** Our proposed methods and theoretical analysis do not conflict with the reset mechanism. IMP can generate new spiking patterns and pattern mappings for both Hard and Soft reset SNNs. LTS is designed specifically for static tasks, and the reset mechanism used in SNNs does not affect our hypotheses and theoretical results.\n\n> Question 3.2: Can this method scale up to a larger timestep (for example, 64)? \n\n**Answer:** Yes,  IMP remains effective with larger numbers of time steps (T=64), as demonstrated by experiments on the CIFAR10DVS (**Table R3**)，and IMP is also effective on time series tasks, as shown in **Table R2**.\n\n> Question 3.3: In language and autoregressive tasks, the timestep of SNN is aligned with the sequence length, which is extremely large.  Using hard-reset SNNs may cause serious inefficiency. What do you think of this?\n\n**Answer:** We agree with your point that the hard-reset mechanism can lead to inefficiency and affect the performance of SNNs on time series tasks, as the information from previous time steps will be completely lost when hard-reset neurons fire.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "EIyJiuvJjh", "reviewer": "Reviewer_Cj2j", "summary": "This paper investigates how the initial membrane potential affects the neuronal spike pattern and the model performace. The evolve of initial membrane potential would generate novel firing pattern and furthermore change the SNN output. Thus, by making the initial membrane potential a trainable parameter, the SNN can achieve significant improvement.", "questions": "1. Since we only use the output of the last time step to give an inference, I wonder if there is any information missing in this process. Have you ever considered using the last few time steps output instead of just one?\n2. From another point of view, adjusting the initial membrane potential is just injecting a controlled noise into the membrane potential at first. Have the authors ever considered giving a controlled noise to each time step to improve the performance?", "limitations": "Yes.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper gives a detailed illustration that, by adjusting the initial membrane potential, additional pattern mapping can be generated, thus improving the expression capacity. So the proposed idea is natural.\n\n2. This paper designs a specific label smooth loss function to effectively control the firing level, which is delicate and efficient.\n\n3. Figure 4 shows that with a sufficient good membrane potential, one time step is enough for a good output, all these observations make the trainable initial membrane potential theoretical sound.\n\n4. Enough experiments are done, which makes the proposed method more convinced. We can see with a trainable initial membrane potential, the accuracy are more satisfactory.", "weaknesses": "1. In this paper, all experiments and illustrations are 4 time steps SNN. It remains non clear that in the long time steps task, how much could the initial membrane potential influence the output.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for acknowledging our research direction and the innovative approach we have employed. \n\n> Weakness 1: In this paper, all experiments and illustrations are 4 time steps SNN. It remains non-clear that in the  long time steps task, how much could the initial membrane potential influence the output.\n\n**Answer:** To enhance the clarity and readability of the chapter content, we set T=4 to simplify the analysis process. It is worth noting that in the experimental section, we cover the cases of T values of 8, 10, and 16 (on page 8 Table 2). The experimental results demonstrate that IMP can maintain its effectiveness even at longer time steps (**Table R3** and **Table R11**). IMP also exhibits significant improvements in time series tasks, which can be seen in **Table R2**.\n\n|   Model    | Training Method | Spike Neuron | Time-step | Accuracy  |\n|:----------:|:---------------:|:------------:|:---------:|:---------:|\n| Spikformer |       TET       |     LIF      |    64     |   97.57   |\n| Spikformer |       TET       |  LIF + IMP   |    64     | **98.26** |\n\n**Table R10: Accuracy on DVS128Gesture dataset.**\n\n> Question 1: Since we only use the output of the last time step to give an inference, I wonder if there is any\n> information missing in this process. Have you ever considered using the last few time steps output instead of just one?\n\n**Answer:** In static tasks, using only the last time step can indeed lead to information loss, but applying the same supervision label to multiple or all time steps may also make the model difficult to fit. There may be a tradeoff between information loss and fitting difficulty. LTS only uses the last time step for supervision and output representation, which can directly verify the hypothesis.\nAdditionally, we believe that using the mean value of a few time steps' outputs instead of just one could be a good alternative to LTS, especially when time steps is relatively large. As mentioned in the A.2 Limitations section, the advantages of LTS tend to weaken as T increases, particularly when $T > 8$, as shown in Figure 8.\n\n> Question 2: From another point of view, adjusting the initial membrane potential is just injecting a controlled noise\n> into the membrane potential at first. Have the authors ever considered giving a controlled noise to each time step to\n> improve the performance?\n\n**Answer:** We have not yet tried related methods, this is a direction that remains unexplored. Adding controlled noise at each time step can be seen as a new method of membrane potential reduction/increase, which may have the potential to improve the capacity of the model. Similar methods like GLIF have achieved beneficial improvements by learning key parameters in the membrane dynamics. In summary, we appreciate your suggestions for future research directions.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "CeNtvPyvdm", "reviewer": "Reviewer_UfLQ", "summary": "The paper discusses the role of initial membrane potential (IMP) of neurons in spiking neural networks (SNNs). The authors found that IMP has a significant impact on the firing patterns of LIF neurons. Then, they propose a learnable IMP mechanism to improve the performance of SNNs. Additionally, the paper introduces the last time step (LTS) approach to enhance convergence speed, and proposes a label smooth temporal efficient training (TET) loss to improve training. The empirical experiements on image classification tasks show the effeciveness of the propsoed methods.", "questions": "- Can learnable IMP can be implemented in neuromorphic hardwares such as Intel Loihi?\n- Can the authors estimate the theoretical energy consumption like in other SNN papers?\n- How is the performance on other datasets such as time series or NLP?", "limitations": "The main limitation is about hardware implement, which the authors did not discuss.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The idea of learnable IMP is simple and intuitive, and easy to be implemented in computer simulations.\n2. The paper is written in a very straightforward way, making it easy to follow.\n3. The simulated experiments are comprehensive on image classifications tasks, showing consistent performance gain by using learnable IMP and additional techniques compared to vanilla SNNs.", "weaknesses": "1. One major concern is about whether learnable IMP can be implemented in neuromorphic chips since the IMP is a float number. To my experience, I do not believe it can be effectively implemented in current hardwares such as Loihi (and the whole paper does not discuss hardware implementation issues). If I am wrong, the authors please corrected me by comprehensively addressing this issue. If hardware implementation is hard or energy-ineffecient (so the main advantage of SNN disappears), then the proposed models should be compared with ANN models with similar model size (and apparently it is behind ANNs).\n\n2. The title is info-less and not proper. The are a few problems. First, it should be the dynamics of neurons, not neuron networks, since the IMP is the property of individual neurons. Second, dynamics of neurons include various aspects, such as the model choice (LIF or Hudgekin-Hoxley model), noise term, etc. The readers obtain no information from \"rethinking the dynamics\", and other aspsects are not disucussed in the paper. A better title might be something like \"learnable initial membrane potental enhances spiking neural networks\".\n\n3. By improving the dynamics of spiking neurons, it is reasonable to expect the model to be enhance in time series or sequential processing (e.g. NLP) tasks rather than image classifications tasks (since \"dynamics\" is temporal property). The lack of experiments on corresponding datasets making it unclear whether the proposed methods are effective only on CV tasks or in general.\n\n4. When compared with baseline methods, the baseline methods should be shortly explained. Otherwise, it is unclear whether the comparisons are fair, and lack insights other than \"our methods are good\".", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your insightful feedback. We have carefully studied your comments and argue that your concerns can be addressed.\n\n> Weakness 1: One major concern is about whether learnable IMP can be implemented in neuromorphic chips since the IMP is  a float number. To my experience, I do not believe it can be effectively implemented in current hardwares such as  Loihi (and the whole paper does not discuss hardware implementation issues). If I am wrong, the authors please corrected  me by comprehensively addressing this issue. If hardware implementation is hard or energy-ineffecient (so the main  advantage of SNN disappears), then the proposed models should be compared with ANN models with similar model size (and  apparently it is behind ANNs).\n\n**Answer:** IMP can be implemented on neuromorphic chips. Loihi supports setting the membrane potential (a floating-point number) to a non-zero floating-point value, and the LAVA (Loihi's toolchain) also provides APIs for setting IMP.\n\n```python\nimport numpy as np\nfrom lava.proc.lif.process import LIF\n\n# Create LIF Neuron with constant Initial Membrane Potential (IMP)\nimp = 0.\nlif = LIF(\n    shape=(16,),   # Number and topological layout of units in the process\n    v=imp,         # Initial value of the neurons' voltage (membrane potential).\n    vth=1.0,       # Membrane threshold\n    dv=0.5,        # Inverse membrane time-constant\n    name=\"lif\"\n)\n\n# Create LIF Neuron with custom Initial Membrane Potential (IMP)\nimp = np.random.uniform(high=0.2, low=-0.2, size=(16,))\nlif_imp_version1 = LIF(\n    shape=(16,),   # Number and topological layout of units in the process\n    v=imp,         # Initial value of the neurons' voltage (membrane potential).\n    vth=1.0,       # Membrane threshold\n    dv=0.5,        # Inverse membrane time-constant\n    name=\"lif\"\n)\n```\nIt is worth noting that in previous research, IMP has always existed, but due to the lack of relevant research on more appropriate settings, researchers usually set it to a floating-point value of 0. Apart from that, according to our results on the ImageNet test set (**Table R1**), IMP does not incur significant additional  theoretical power consumption overhead, but can effectively improve the performance of SNNs.\n\n\n> Weakness 2: The title is info-less and not proper. The are a few problems. First, it should be the dynamics of  neurons, not neuron networks, since the IMP is the property of individual neurons. Second, dynamics of neurons include  various aspects, such as the model choice (LIF or Hudgekin-Hoxley model), noise term, etc. The readers obtain no  information from \"rethinking the dynamics\", and other aspsects are not disucussed in the paper. A better title might be  something like \"learnable initial membrane potental enhances spiking neural networks\".\n\n**Answer:**  We appreciate your suggestions. As you mentioned, in this paper, we have investigated the dynamics of spiking neurons and its impact on the supervised learning and output representations of SNNs. We have taken your suggestions into consideration and propose to change the title to \"Enhancing Spiking Neural Networks via Initial Membrane Potential and Optimized Objectives\".\n\n> Weakness 3: By improving the dynamics of spiking neurons, it is reasonable to expect the model to be enhance in time series or sequential processing (e.g. NLP) tasks rather than image classifications tasks (since \"dynamics\" is  temporal property). The lack of experiments on corresponding datasets making it unclear whether the proposed methods  are effective only on CV tasks or in general.\n\n**Answer:** Thank you for the suggestion to further validate the effectiveness of our method.  We have conducted additional experiments on time series tasks. By incorporating IMP in SNN-delay[1], we have achieved an effective improvement from 95.10% to 96.02% (**Table R2**). Nevertheless, it is important to note that the neuromorphic datasets we used in our experiments (page 8 **Table 2**), including CIFAR10DVS[1] and NCaltech101[2], contain temporal dynamics, rather than static images. \n\n[1] Li H, Liu H, Ji X, et al. Cifar10-dvs: an event-stream dataset for object classification[J]. Frontiers in neuroscience, 2017, 11: 309.\n\n[2] Orchard G, Jayawant A, Cohen G K, et al. Converting static image datasets to spiking neuromorphic datasets using saccades[J]. Frontiers in neuroscience, 2015, 9: 437.\n\n> Weakness 4: When compared with baseline methods, the baseline methods should be shortly explained. Otherwise, it is unclear whether the comparisons are fair, and lack insights other than \"our methods are good\".\n\n**Answer:**  Due to the length constraint of the main text, we have provided the ablation experiments in the appendix (page 15 **Table 4**). We kept the experimental setup and hardware equipment completely consistent in the ablation experiments, except the parameters that needed to be compared. We hope that the results of the ablation experiments can address your concerns, and we will pay more attention to the explanation of our experimental results, providing more insights.\n\n> Question 1: Can learnable IMP can be implemented in neuromorphic hardwares such as Intel Loihi?\n\n**Answer:** Yes. Please refer to the response to Weakness 1.\n\n> Question 2: Can the authors estimate the theoretical energy consumption like in other SNN papers?\n\n**Answer:** Please refer to the response to Weakness 1 and the PDF we submitted.\n\n> Question 3: How is the performance on other datasets such as time series or NLP?\n\n**Answer:** Please refer to the response to Weakness 3 and **Table R2**.\n\n> Limitation 1: The main limitation is about hardware implement, which the authors did not discuss.\n\n**Answer:** Please refer to the response to Weakness 1.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
Thanks for all reviewers' valuable comments. We are encouraged that reviewers recognize the effectiveness of setting learnable initial membrane potential states (IMP) for spiking neurons, and consider the idea of using the output of the last time step for supervised learning and output representation in static tasks to be interesting. Meanwhile, most of the reviewers concerned about the power consumption of the learnable IMP method, as well as the effectiveness of the IMP method in time series tasks. Our responses to these questions are as follows.

### Power Consumption
IMP does not incur significant additional theoretical power consumption, but can effectively improve the performance of SNNs. More information can be found in the PDF we have submitted.

|    Model     | Method  | Accuracy  |   SOPs(G)   |  Power(mJ)  |
| :----------: | :-----: | :-------: | :---------: | :---------: |
| SEW-ResNet18 |   TET   |   62.92   |   1.36055   |   1.22449   |
| SEW-ResNet18 |   SDT   |   63.21   |   1.37418   |   1.23676   |
| SEW-ResNet18 |   LTS   |   64.33   | **1.21427** | **1.09285** |
| SEW-ResNet18 | LTS+IMP | **65.38** |   1.31371   |   1.18234   |
| SEW-ResNet34 |   TET   |   67.98   |   3.59539   |   3.23585   |
| SEW-ResNet34 |   SDT   |   68.10   |   3.52732   |   3.17459   |
| SEW-ResNet34 |   LTS   |   68.10   | **3.11694** | **2.80525** |
| SEW-ResNet34 | LTS+IMP | **68.90** |   3.12180   |   2.80962   |
| SEW-ResNet50 |   TET   |   69.87   |   3.40181   |   3.06163   |
| SEW-ResNet50 |   SDT   |   70.33   |   3.20071   |   2.88064   |
| SEW-ResNet50 |   LTS   |   71.24   | **3.10432** | **2.79389** |
| SEW-ResNet50 | LTS+IMP | **71.83** |   3.45325   |   3.10792   |

**Table R1: Accuracy and theoretical energy consumption on ImageNet1k dataset.**


### Time Series Tasks
We have conducted additional experiments on time series dataset Spiking Heidelberg Digits [1]. By incorporating IMP in SNN-delay [2], we have achieved an improvement from 95.10% to 96.02%, surpassing the current state-of-the-art ANN model Event-SSM [3], to our best knowledge.


|    Model     | Network Architecture | Spike Neuron | Param  | Accuracy |
| :----------: | :------------------: | :----------: | :----: | :------: |
| Event-SSM[3] |       SSM(ANN)       |      -       | ~400k  |  95.50   |
| SNN-Delay[2] |       MLP+DCLS       |     LIF      | 214.0k |  95.11   |
| SNN-Delay[2] |       MLP+DCLS       |  LIF + IMP   | 214.5k |  96.02   |

**Table R2: Accuracy on Spiking Heidelberg Digits.**

The Spiking Heidelberg Digits (SHD) [1] dataset is an audio-based classification dataset of 1k spoken digits ranging from 0 to 9 in the English and German languages. The audio waveforms have been converted into spike trains using an artificial model of the inner ear and parts of the ascending auditory pathway.

[1] Cramer B, Stradmann Y, Schemmel J, et al. The heidelberg spiking data sets for the systematic evaluation of spiking neural networks[J]. IEEE Transactions on Neural Networks and Learning Systems, 2020, 33(7): 2744-2757.

[2] Hammouamri I, Khalfaoui-Hassani I, Masquelier T. Learning Delays in Spiking Neural Networks using Dilated Convolutions with Learnable Spacings[C]//The Twelfth International Conference on Learning Representations.

[3] Schöne M, Sushma N M, Zhuge J, et al. Scalable Event-by-event Processing of Neuromorphic Sensory Signals With Deep State-Space Models[J]. arXiv preprint arXiv:2404.18508, 2024.

### Long Time-Steps

We further validated the effectiveness of IMP over longer time steps.

|   Model    | Training Method | Spike Neuron | Time-step | Accuracy |
| :--------: | :-------------: | :----------: | :-------: | :------: |
| Spikformer |       SDT       |     LIF      |    32     |   82.6   |
| Spikformer |       SDT       |  LIF + IMP   |    32     | **83.1** |
| Spikformer |       SDT       |     LIF      |    48     |   81.5   |
| Spikformer |       SDT       |  LIF + IMP   |    48     | **82.5** |
| Spikformer |       SDT       |     LIF      |    64     |   81.1   |
| Spikformer |       SDT       |  LIF + IMP   |    64     | **81.4** |

**Table R3: Accuracy on CIFAR10DVS dataset.**

Meta-review: I have read all comments and responses. Reviews appear to be consentaneous, with four positive scores of 7, 6, 6, and 6. However, there are still some concerns that were not fixed, e.g., the hardware implementation presented by Reviewer UfLQ, which a significant point of spiking dynamics. Thus, I weakly recommend to accept this manuscript.
Decision: Accept (poster)