Rethinking the Membrane Dynamics and Optimization Objectives of Spiking Neural Networks

Authors: hangchi  shen
qian  zheng
huamin  wang
gang  pan
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-14 16:08:07

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.

Main paper: 
 introduction: 
 In recent years, deep learning technology based on artificial neural networks (ANNs) has made significant breakthroughs in many fields [1, 2, 3, 4, 5] . However, as we all known, its high training and inference costs have become a major obstacle to restrict its further widespread applications. To overcome these challenges, a new generation of neural network architectures named Spiking Neural 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] as biological neurons, maintaining linearly increasing computational complexity. Therefore, the advantages of energy efficiency and biologically plausible dynamical mechanisms [7, 9, 10] 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, it is worth mentioning that SNNs can cleverly avoid multiplication operations on neuromorphic chips [11, 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 a formidable challenge at present. The conversion method of ANNs to SNNs (ANN2SNN) [14, 15, 16, 17, 18] has proved to be an effective approach for obtaining 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 to leverage surrogate gradient [19, 20, 21] and backpropagation [22] through time to train high-performing SNNs. This method only requires four time steps to achieve an accuracy surpassing that of conversion methods requiring hundreds of time steps, making it the most promising training approach for currently available 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 processing [30, 31] , etc, and have demonstrated significant energy efficiency advantages in these fields. It is a 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] . 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 1 ). Then, we discover that the novel spike patterns can be 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 we 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 a label-smoothed TET loss for neuromorphic tasks, which can 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 to 87.8% and 86.32% on CIFAR10DVS [35] and NCaltech101 [36] , respectively. Furthermore, our LTS method improves the accuracy of SEW-ResNet50 [37] on the ImageNet1k [38] dataset to 71.83%, surpassing the vanilla SEW-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, we 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 a label-smoothed TET loss to further enhance the performances of SNNs on the neuromorphic tasks.3) Compared with the baselines on the neuromorphic datasets and the large-scale static dataset ImageNet1k, our methods can achieve significant improvements. Moreover, there is almost no difference in the computational overhead and inference speed compared to the original models.This paper focuses on the fundamental research of spiking neural networks, with the goal of revealing the impact of membrane dynamics on the network and optimizing its performance. Generally, there are no negative societal impacts in this work. 
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 of decreased performance in SNNs. The parametric leaky integrate-and-fire spiking neuron [40] was introduced to design a learnable dynamic model, enabling each neuron to learn optimal membrane time constants, thus increasing neuronal diversity. The gated leaky integrate-and-fire neuron [41] was employed for a channel-wise 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 [43] were discussed to remove the membrane potential reset process and redefine the dynamic mechanism in a non-iterative manner, addressing the difficulty of ordinary spiking neurons in learning long-term dependencies.The binary spikes emitted by spiking neurons during the forward phase are generated by a step function, which is a 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) as a special type of recurrent neural network (RNN). In this approach, gradients are propagated backward along the temporal dimension, which requires more computational resources and memory compared to their corresponding ANNs [44] . tdBN [21] 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, a 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) to 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.Question: Does the paper discuss the limitations of the work performed by the authors? Answer: [Yes] Justification: We discussed the limitations of the proposed method in the appendix, which is enlightening for future work. Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
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 performance. 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.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 are related to membrane potential and input current. The leaky integrate-and-fire (LIF) [7] model is one of the commonly used spiking neuron models, and its iterative form of the dynamical equations can be represented as follows:EQUATIONEQUATIONwhere I[t] represents the neural input current at time t, τ represents the membrane potential decay coefficient. When τ = 0, it reduces to the Integrate-and-Fire (IF) [7] The most commonly used loss functions in direct training SNNs are SDT [20] and TET [34] . The SDT loss function L SDT is defined as:EQUATIONhere, T represents the total number of time steps, y[t] represents the raw output of the model at each time step, y gt represents the ground truth label, and L CE 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:EQUATIONthe L TET 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.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. specific pattern to all patterns. Figure 3b illustrates that through adjusting the IMP value from 0 to 0.25 can generate additional pattern mappings. Furthermore, Figure 3c demonstrates that when IMP is learnable, it exhibits a greater potential for establishing mappings among spike patterns. Therefore, we believe that the learnable IMP can effectively improve the expression capacity of spiking neurons.We further explore the effect of membrane potential variations on static tasks through a image classification task. We define SNN as follows to focus on its performance at each time step,EQUATIONwhere f (•) represents the network computation, θ represents the network weights, s[t] represents the set of membrane potentials of all neurons in SNN with time step t, x[t] represents the input at time step t, and y[t] is the corresponding output. Assuming x = x(t) is a constant input intensity for t = 1, 2, ..., T , then we can simplify Eq. 6 as:EQUATIONOn the static tasks, the temporal variations are determined solely by the state of the membrane potential s[t], 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 to the current MP. Figure 4 demonstrates the test accuracy of SNNs at each time step on cifar10 dataset [48] , which shows that the accuracy is extremely low at T=1, only 10.76%. However, as the time step T increases, the model accuracy exhibits an upward trend, exceeding 90%. It is worth noting that on the static tasks, since the input x and weight θ are fixed at each time step, the model's output at each time step is entirely determined by the current state of the membrane potential s[t]. For instance, when the membrane potential evolves to a "sufficiently good" state, such as at t = 4, the SNNs only requires the current membrane potential s [4] and input x to achieve an accuracy of 92.05%, which is close to the model's final performance of 92.36%. Therefore, these findings prompt us to reconsider how to accelerate the evolution of the membrane potential to enhance the SNNs performances within a limited number of time steps.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 on the static datasets and the neuromorphic datasets, and find that TET loss has a significant advantage on the neuromorphic datasets, but it is not superior to SDT loss on the static datasets, as shown in Table 1 . We believe that this phenomenon arises from the constant intensity input on the static datasets. By applying the TET loss Eq. 5 to the SNNs with the static input Eq. 7, we have:EQUATIONIt can be observed that on static tasks, the membrane potential s[t], as the only time-varying term in the dynamic system, evolves gradually as the time step progresses. However, according to Observation 3, we know SNNs are sensitive to s[t], which means that it is difficult to output the same result for different s[t]. The optimization goal of the TET loss is to make the network output the correct results for every time step, i.e. y[t] = y gt . In this case, TET requires more iterations to build a flat "landscape", slowing down the convergence, as shown in Figure 5 . 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.y[1] = y[2] = ... = y[T ] = 1 T T t y[t],then the output of the first time step is sufficient to represent the results of all T time steps. In this case, the computations for the subsequent time steps become redundant and meaningless.Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?Answer: [Yes] Justification: The dataset used in this article is publicly available, and the code will be made public to ensure that others can reproduce the experimental results.Guidelines:• The answer NA means that paper does not include experiments requiring code. • Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted. 
learnable imp: 
 The membrane potential in the current dynamic model of SNNs is typically initialized to a uniform constant value (usually 0). Based on Observation 1 and Observation 2, we find that the learnable IMP can enhance the expressive power of SNNs. Based on Observation 3, the learnable IMP can allow the membrane potential to start from a non-zero value, which may help improve the performances of SNNs on the static tasks. We can assign an independent learnable IMP for each spiking neuron. According to Eq. 1, the membrane potential accumulation can be represented as follows,EQUATIONwhere ŝ[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 0, in the initialization process, we set IMP to a uniform distribution with an expected value of 0,EQUATION)where λ is a hyper-parameter 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 0 with a trained IMP during the inference process will not incur additional computational overhead.We propose a new post-processing 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 SNNs 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 LTS T ,EQUATION)where y[T ] represents the LTS's output of the SNNs. When using only the LTS as the output, both SDT and TET losses yield the same representation,EQUATION)Based on the results in Table 1 , 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 error (MSE) regularization term was added to control the firing level of the last layer of the model, given byL REG = 1 T T t=1 L MSE (y[t], ϕ), where ϕ denotes the target firing level. The coefficient λ controls the proportion of the two losses, and the complete loss is defined as L Total = (1 -λ)L TET + λL REG . We think that this setup will prevent the training loss of the model from converging to zero, because when L REG = 0, the model will output a constant value 1 at every time steps, rendering the model unable to perform the classification task. On the other hand, when L TET = 0, L MSE > 0. Considering that L MSE plays a role similar to a smoothing process in the loss function, we propose removing L REG and replacing the cross-entropy loss with a label smooth cross-entropy loss, as shown by the following equation:EQUATIONhere, y gt represents the ground truth, ŷgt represents the smoothed label, ϵ represents the smoothing factor, and K represents the number of classes. It can be observed that L TET-S 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. We have conducted a validation of the convergence speed of SDT, TET, and LTS on the commonly used time steps (1, 2, 4, and 6), as shown in Figure 7 . The application of LTS post-processing has resulted in an improvement in the convergence speed of SNNs. We have applied our methods to a simple spiking VGG model and compare them with the SOTA SNNs on the neuromorphic datasets. Since the CIFAR10DVS and NCaltech101 datasets are not pre-divided into training and testing sets, we split these datasets in a 9:1 ratio. To ensure a fair comparison with other existed methods, we adopt the two configurations with resolutions of 48 and 128, respectively. The data preprocessing and training settings refer to the appendix A.8.Table 2 reports the experimental results on the CIFAR10DVS and NCaltech101 datasets. On the CIFAR10DVS 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 to 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] . In addition, we further explore the impact of using smoothed TET loss on 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 8. 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 87.86%. We apply our proposed IMP and LTS post-processing methods to the standard SEW-ResNet [52] architecture and compare them with the SOTA spiking neurons and the directly training SNN methods on the large-scale static dataset ImageNet1k [38] .Table 3 presents the detailed experimental results on the large-scale static dataset ImageNet1k. Specifically, by applying the LTS post-processing method to the SEW-ResNet18/34/50 models, we can obtain the accuracy improvements of 1.15%, 1.06%, and 3.46% compared to the baselines, respectively. These results demonstrate the effectiveness of LTS on the large-scale datasets. Furthermore, with the introduction of the learnable IMP, the accuracy can be further increased by 2.2%/1.86%/4.05%. With the LTS post-processing and learnable IMP, our SEW-ResNet50 achieves an accuracy of 71.83%, surpassing the accuracy of the vanilla SEW-ResNet152, 69.26%. Table 4 presents the results of a series of ablation studies conducted on the CIFAR10-DVS and ImageNet100 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 CIFAR10-DVS dataset, we explored methods including SDT, TET, and their variants TET-S and versions combined with IMP. VGG was used as the spiking neural network structure. The results show that for different ϵ values, the TET-S+IMP method achieved the best accuracy, with IMP+TET-S (λ = 0.2) reaching 87.10%, the highest among all methods on the CIFAR10-DVS dataset. For the ImageNet100 dataset, we tried TET, SDT, LTS, and their versions combined with IMP, using SEW-ResNet18 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. 
conclusions: 
 We have proposed a 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 neuromorphic 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 no additional computational cost is required. Since our 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.A Appendix / supplemental material A.Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?Answer: [Yes] Justification: The appendix of the paper provides detailed experimental settings.Guidelines:• The answer NA means that the paper does not include experiments.• The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them. • The full details can be provided either with the code, in appendix, or as supplemental material. 
experiment statistical significance: 
 Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?Answer: [Yes]Justification: The paper accurately presents error bars for the execution speed benchmark. Notably, our experiments involved comparing our method's optimal performance with other approaches.Guidelines:• The answer NA means that the paper does not include experiments.• The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.• The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions). • The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.) • The assumptions made should be given (e.g., Normally distributed errors). • It should be clear whether the error bar is the standard deviation or the standard error of the mean. Justification: The article provides the resource cost required for conducting experiments, as well as the execution time of our proposed method. Further detailed information is provided in the code.Guidelines:• The answer NA means that the paper does not include experiments.• The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage. • The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute. • The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper). 
code of ethics: 
 Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines? 
broader impacts: 
 Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?Answer: [NA] Justification: This paper focuses on the fundamental research of spiking neural networks, with the goal of revealing the impact of membrane dynamics on the network and optimizing its performance. Generally, there are no negative societal impacts in this work.Guidelines:• The answer NA means that there is no societal impact of the work performed.• If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact. • Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations. • The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. • The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. • If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). 
safeguards: 
 Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?Answer: [NA] Justification: This paper focuses on the fundamental research of spiking neural networks, which does not involve the development or release of data or models that have a high risk for misuse.Guidelines:• The answer NA means that the paper poses no such risks.• Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters. • Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images. • We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.12. Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?Answer: [Yes] Justification: The creators or original owners of the assets (such as code, data, and models) used in this paper have been properly credited. Their contributions have been explicitly mentioned in an appropriate manner. Additionally, the license and terms of use for each asset have been explicitly stated and adhered to, including obtaining any necessary permissions or authorizations.Guidelines:• The answer NA means that the paper does not use existing assets.• The authors should cite the original paper that produced the code package or dataset.• The authors should state which version of the asset is used and, if possible, include a URL. • The name of the license (e.g., CC-BY 4.0) should be included for each asset.• For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided. • If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset. • For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. • If this information is not available online, the authors are encouraged to reach out to the asset's creators. 13. New Assets Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets? Answer: [Yes] Justification: The experimental code will be made openly accessible, along with the necessary documents to facilitate reproducibility of the experimental results and utilization of the code for future work. Guidelines:• The answer NA means that the paper does not release new assets.• Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc. • The paper should discuss whether and how consent was obtained from people whose asset is used.  
 
 Appendix: IMP has a small gradient during training, which makes it sensitive to initialization (Figure 4 ). In addition, learnable IMP may lead to an excessive number of parameters, as it assigns initial states to each neuron, although this has the same computational cost as setting the IMP to 0. The advantage of LTS may reduce when the time step is set too large, due to the supervision is 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 to 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 a unified loss function that can achieve superior performance on both static tasks and neuromorphic tasks, which remains a challenge in the current research.We compared the convergence speed of TET and SDT at different time steps (T=1, 2, 4, 6, 8, 12, 16, 24, 32) . For static tasks, TET's convergence speed was lower than SDT's, and the difference in convergence speed diminished as the time step increased. The performance of SEW-ResNet-LTS can be close to some Transformer-based SNNs (Table 5 ). 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 use of LTS only in static tasks, as the effectiveness of LTS relies on the assumption of having the same input at each time step. The learnable IMP can significantly improve the accuracy of the first time step and lead to better overall performance (Figure 9 ). The following approach can be useful for implementing on-chip learning IMP: (1) Use an auxiliary neuron to distribute IMP (by firing a spike) to the other neurons at the initial time step. (2) Optimize the synaptic weights of this auxiliary neuron to adjust IMP.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 in the paper. • The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.Justification: The research in this paper adheres to the NeurIPS Code of Ethics.Guidelines:• The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.• If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics. • The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction). 


Decision: 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.

Reviews: review: paper_summary: paper_summary: presents a novel approach to understanding and modeling the dynamics of spiking neural networks
strength_weakness: strength_weakness: Some of the assumptions in the theoretical framework could be more explicitly stated and justified.
Additional experiments, particularly in real-world scenarios, could further validate the proposed methods.
The introduction and related work sections could provide more context to better situate the contributions within the broader literature.
questions: 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: 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.
paper_summary: paper_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.
strength_weakness: strength_weakness: Although this paper is well-analyzed, it still has some weaknesses.

It 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?

[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.

[2] Zhou Z, Zhu Y, He C, et al. Spikformer: When Spiking Neural Network Meets Transformer[C]//The Eleventh International Conference on Learning Representations.

[3] Yao M, Hu J, Zhou Z, et al. Spike-driven transformer[J]. Advances in neural information processing systems, 2023, 36.
questions: 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?
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.
3. 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: limitations: Please see the weaknesses and questions.
paper_summary: paper_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.
strength_weakness: strength_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.
questions: 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?
2. 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: limitations: Yes.
paper_summary: paper_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.
strength_weakness: strength_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).

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".

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.

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".
questions: questions: - Can learnable IMP can be implemented in neuromorphic hardwares such as Intel Loihi?
- Can the authors estimate the theoretical energy consumption like in other SNN papers?
- How is the performance on other datasets such as time series or NLP?
limitations: limitations: The main limitation is about hardware implement, which the authors did not discuss.

Comments: title: Discussion
Discussion
comment: Thank you for your response. Author's response addressed all my concerns. I will raise my score to weak accept.
I appreciate the authors' response, which makes sense. I think hardware implementation is an important matter that worth deeper investigations. I raise my score to 6 accordingly.
Thank you for your response. The primary focus of this paper is on enhancing the performance of SNNs by learnable IMP, and ensuring that the trained networks can be deployed on neuromorphic chips for low-power inference. Currently,  since neuromorphic chips [1] typically struggle to run standard surrogate gradient backpropagation [2,3], and synaptic plasticity-based approaches [4,5] often leads to lower performance，the performance of on-chip learning training SNNs still lags behind that of gradient-based methods [6,7]. Although some approaches have attempted to achieve on-chip approximate backpropagation [7-10], their training speed [11], network scale [12,13], and performance are still lower than standard surrogate backpropagation [2]. Therefore, in order to pursuit the SOTA performance and ensure energy efficiency, the related researches mainly focus on the approach of training high-performance SNNs [2,3,14,15] on GPUs and then deploying them on neuromorphic hardware [16].

At present, although we are unable to provide a new concrete on-chip learning method for the learnable IMP within such a short time, we hope the following approach can be useful for realizing on-chip learning IMP：(1) Use an auxiliary neuron to distribute IMP (by firing a spike) to the other neurons at the initial time step. (2) Optimize the synaptic weights of this auxiliary neuron to adjust IMP. In addition, we will further discuss on-chip learning in the limitations section of this paper and explore it in our future work. Thanks again for your questions of this work, and we hope our response can address your concerns.

[1] Davies M, Srinivasa N, Lin T H, et al. Loihi: A neuromorphic manycore processor with on-chip learning[J]. Ieee Micro, 2018, 38(1): 82-99.

[2] Neftci E O, Mostafa H, Zenke F. Surrogate gradient learning in spiking neural networks: Bringing the power of gradient-based optimization to spiking neural networks[J]. IEEE Signal Processing Magazine, 2019, 36(6): 51-63.

[3] Davies M, Wild A, Orchard G, et al. Advancing neuromorphic computing with loihi: A survey of results and outlook[J]. Proceedings of the IEEE, 2021, 109(5): 911-934.

[4] Kheradpisheh S R, Ganjtabesh M, Thorpe S J, et al. STDP-based spiking deep convolutional neural networks for object recognition[J]. Neural Networks, 2018, 99: 56-67.

[5] Zenke F, Ganguli S. Superspike: Supervised learning in multilayer spiking neural networks[J]. Neural computation, 2018, 30(6): 1514-1541.

[6] Bal M, Sengupta A. Spikingbert: Distilling bert to train spiking language models using implicit differentiation[C]//Proceedings of the AAAI conference on artificial intelligence. 2024, 38(10): 10998-11006.

[7] Yao M, Hu J, Hu T, et al. Spike-driven transformer v2: Meta spiking neural network architecture inspiring the design of next-generation neuromorphic chips[J]. arXiv preprint arXiv:2404.03663, 2024.

[8] Kaiser J, Mostafa H, Neftci E. Synaptic plasticity dynamics for deep continuous local learning (DECOLLE)[J]. Frontiers in Neuroscience, 2020, 14: 424.

[9] Lillicrap T P, Cownden D, Tweed D B, et al. Random synaptic feedback weights support error backpropagation for deep learning[J]. Nature communications, 2016, 7(1): 13276.

[10] Bellec G, Scherr F, Subramoney A, et al. A solution to the learning dilemma for recurrent networks of spiking neurons[J]. Nature communications, 2020, 11(1): 3625.

[11] Shrestha A, Fang H, Rider D P, et al. In-hardware learning of multilayer spiking neural networks on a neuromorphic processor[C]//2021 58th ACM/IEEE Design Automation Conference (DAC). IEEE, 2021: 367-372.

[12] Renner A, Sheldon F, Zlotnik A, et al. The backpropagation algorithm implemented on spiking neuromorphic hardware[J]. arXiv preprint arXiv:2106.07030, 2021.

[13] Shrestha A, Fang H, Wu Q, et al. Approximating back-propagation for a biologically plausible local learning rule in spiking neural networks[C]//Proceedings of the International Conference on Neuromorphic Systems. 2019: 1-8.

[14] Fang W, Yu Z, Chen Y, et al. Deep residual learning in spiking neural networks[J]. Advances in Neural Information Processing Systems, 2021, 34: 21056-21069.

[15] Zhou Z, Zhu Y, He C, et al. Spikformer: When spiking neural network meets transformer[J]. arXiv preprint arXiv:2209.15425, 2022.

[16] Ziegler A, Vetter K, Gossard T, et al. Spiking Neural Networks for Fast-Moving Object Detection on Neuromorphic Hardware Devices Using an Event-Based Camera[J]. arXiv preprint arXiv:2403.10677, 2024.
Dear authors,

This is a kind reminder that I asked a followed-up question and the due of author-reviewer discussion is near. I am still a bit confused about the detailed implementations of learnable IMP (since I have never considered adjusting IMP on neuromorphic hardwares), and more importantly I am curious about this. If there are any detailed instructions in the paper or appendix that I have missed, please just point them out.

Given that you have well addressed my other comments and the other reviewers' comments, I am wiling to raise my score if this question can be resolved.
Thank you for the rebuttal. I'd like to stick to my original score.
Thanks for the responses! I see how you can set the IMP of neurons to different values in Loihi by "imp = np.xxxxx". However, my question is whether IMP can be learnable via e.g., surrogate gradient back-prop in neuromorphic chips (as the paper proposed "learnable IMP).