Efficient ANN-SNN Conversion with Error Compensation Learning
Authors: Chang Liu
Jiangrong Shen
Xuming Ran
Mingkun Xu
Qi Xu
Yi Xu
Gang Pan
Venue: ICML 2025 poster (2025)
Keywords: ANN-SNN Conversion
Deep Spiking Neural Network
brain-inspired computing
neuromorphic computing
Primary area: applications->neuroscience_cognitive_science

Abstract: Artificial neural networks (ANNs) have demonstrated outstanding performance in numerous tasks, but deployment in resource-constrained environments remains a challenge due to their high computational and memory requirements. Spiking neural networks (SNNs) operate through discrete spike events and offer superior energy efficiency, providing a bio-inspired alternative. However, current ANN-to-SNN conversion often results in significant accuracy loss and increased inference time due to conversion errors such as clipping, quantization, and uneven activation. This paper proposes a novel ANN-to-SNN conversion framework based on error compensation learning. We introduce a learnable threshold clipping function, dual-threshold neurons, and an optimized membrane potential initialization strategy to mitigate the conversion error. Together, these techniques address the clipping error through adaptive thresholds, dynamically reduce the quantization error through dual-threshold neurons, and minimize the non-uniformity error by effectively managing the membrane potential. Experimental results on CIFAR-10, CIFAR-100, ImageNet datasets show that our method achieves high-precision and ultra-low latency among existing conversion methods. Using only two time steps, our method significantly reduces the inference time while maintains competitive accuracy of 94.75% on CIFAR-10 dataset under ResNet-18 structure. This research promotes the practical application of SNNs on low-power hardware, making efficient real-time processing possible.

Efficient ANN-SNN Conversion with Error Compensation Learning
Chang Liu
Jiangrong Shen 23
Xuming Ran
Mingkun Xu
Qi Xu
Yi Gang Pan
Abstract
1. Introduction
Artificial neural networks (ANNs) have demon- strated outstanding performance in numerous tasks, but deployment in resource-constrained environments remains a challenge due to their high computational and memory requirements. Spiking neural networks (SNNs) operate through discrete spike events and offer superior energy efficiency, providing bio-inspired alternative. However, current ANN-to-SNN conversion of- ten results in significant accuracy loss and in- creased inference time due to conversion errors such as clipping, quantization, and uneven activa- tion. This paper proposes a novel ANN-to-Si conversion framework based on error compensa- tion learning. We introduce learnable threshold clipping function, dual-threshold neurons, and optimized membrane potential initialization strategy to mitigate the conversion error. To- gether, these techniques address the clipping error through adaptive thresholds, dynamically reduce the quantization error through dual-threshold neu- rons, and minimize the uniformity error by effectively managing the membrane potential. Ex- perimental results on CIFAR-10, CIFAR-100, Im- ageNet datasets show that our method achieves high-precision and ultra-low latency among ex- isting conversion methods. Using only two time steps, our method significantly reduces the infer- ence time while maintains competitive accuracy of 94.75% on CIFAR-I0 dataset under ResNet- 18 structure. This research promotes the practi- cal application of SNNs on low-power hardware, making efficient real-time processing possible.
In recent years, artificial neural networks (ANNs) have achieved remarkable success across range of domains, including computer vision, natural language processing, and speech recognition (Liu et al., 2024c). However, as model complexity increases, ANNs often demand substantial mem- ory and computational resources, which can be a significant challenge in essource-constraiigg environments, such as embedded systems or mobile devices (Hubara et al., 2016). In contrast, spiking neural networks (SNNs), inspired by the biological mechanisms of the brain, offer an alternative approach (Liu et al., 2025). SNNs employ an event-driven spike firing mechanism for information transmission (Stöckl & Maass, 2021), where neurons are only activated in re- sponse to incoming spikes, and only trigger spikes when their membrane potential surpasses a certain threshold (Liu et al., 2024b). Outside of these events, neurons remain dor- mant. This asynchronous operation results in significantly lower energy consumption compared to traditional deep ANNs (Xu et al., 2024b). Furthermore, SNNs primarily rely on accumulation operations, which are less computationally expensive than the muliipicaatonnacccuulliii operations commonly used in ANNs (Xu et al., 2023). These character- istics make SNNs particularly advantageous for hardware implementation, offering promising potential for the de- velopment of low-power, real-time information processing systems (Stöckl & Maass, 2021).
Despite the advantages of SNNs in terms of energy efficiency, their spike train output introduces a non- differentiable nature, which obstructs the application of backpropagation like ANNs (Xu et al., 2024a). To address this limitation, two main strategies have emerged for training deep SNNs. The first approach, direct training, uses surro- gate gradients to enable backpropagation during layer-to- layer training. However, significant performance gap still exists between ANNs and SNNs on complex tasks (Shen et al., 2025). To bridge this gap. efficient ANN-to-SNN conversion methods have been proposed to preserve the performance of ANNs during the conversion process, by adjusting network structures, optimizing the spike neuron fir- ing modes, and designing novel spike encoding techniques (Pfeiffer & Pfeil, 2018). However, current ANN-to-SNN conversion typically requires long inference times to match the accuracy of the original ANN (Sengupta et al., 2019).
'qqual contribution 'School of Computer Science and Technol- ogy, Dalian University of Technology, Dalian, China Faculty of Electronic and Information Engincering, Xi'an an Jiaotong University "State Key Lab of Brain-Machine Intelligence, Zhejiang Univer- sity "National University of Singapore Guangdong Institute of Intelligence Science and Technology. Zhuhai, China "College of Computer Seience and Technology, Zhejiang University. Corre- spondence to: Qi Xu <xuqiι @ diut.edu.en">.
Proceedings of the 42nd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Efficient ANN-SNN Conversion with Error Compensation Learning
This is primarily due the reliance on the equivalence between the ReL.U activation function in ANNs and the firing rate of the integrate-and-fire (IF) model in SNNs (Cao et al., 2015). Therefore, although extending inference time can reduce conversion errors, excessively long inference times hinder the practical deployment of SNNs on neu- romorphic hardware (Liu et al., 2024a). Another major challenge in ANN-to-SNN conversion lies in the remain- ing membrane potential in neurons, which is difficult to eliminate within a few time steps (Shen et al., 2024). Al- though various optimization techniques have been proposed, such as weight normalization (Dichl et al., 2015), threshold readjustment(
10 dataset in only 2 time steps under the ResNet- structure, which is significantly better than others.
2. RELATED WORK
The research on ANN-to-SNN conversion began with Cao et al. (2015), and then Diehl et al. (2015) successfully con- verted a three-layer convolutional neural network (CNN) to spiking neural network (SNN) through data- and model- based normalization methods. In order to improve the perfor- mance of SNNs on complex datasets and deeper networks, Rueckauer et al. (2016) and Sengupta et al. (2019) proposed more precise scaling strategies for normalizing network weights and adjusting thresholds, respectively, which were later shown to be equivalent (Ding et al., 2021). However, due to the conversion error discussed in Chapter 3.1, deep SNNs often require hundreds of time steps after conversion to achieve accurate results. To address the potential infor- mation loss problem. Rueckauer et 22.6601 and Han et al. (2020) proposed an alternative to "reset-by-subbractionn" neurons to replace the "reset-to-zero" neurons. In recent years, methods to eliminate conversion errors have emerged in an endless stream. Rueckauer al. (2016) suggested us- ing the 99.9% activation percentile as scaling factor, while Ho & Chang (2021) introduced trainable cropping layers. In addition, Han et al. (2020) prevented improper activation of spiking neurons by rescaling the SNN threshold.
et al., 2019), soft reset (Han & Roy, 2020), and threshold offset (Deng & Gu, 2021), these meth- ods often require tens to hundreds of time steps to achieve conversion accuracy comparable the original ANN.
In order to obtain high-peeformance SNNs with ultra-low latency (e.g.. 2 time steps), we construct an ANN-to-SNN equivalent mapping model, analyze the errors in the conver- sion process, and provide solutions to reduce the errors in the conversion process. Our main contributions are summa- rized as follows:
This paper first analyzes the three types of errors in the ANN-to-SNN conversion process and proposes a comprehensive training framework to address these issues. The framework includes: replacing the ReLU activation function with a clipping function to train the source ANNs, mapping the weights and threshold parameters to facilitate ANN-to-SNN conversion, and setting the optimal initial membrane potential for each layer of spiking neurons.
Our work has similarities with the work of Deng & Gu (2021) and Li al. (2021), which also revealed er- rors in the conversion process. Deng & Gu (2021) reduced the layer error by introducing additional biases after SNN conversion, while Li et al. (2021) further proposed method to calibrate weights and biases through quantization fine- tuning. They successfully achieved good results in the case of 16 and 32 time steps without using excessively long time steps. Bu et al. (2023) proposed to use of quantization clip-florr-hiff activation function train ANNs, which can only minimize some of the conversion errors. In contrast, our research goal is to eliminate these conversion errors by combining existing technologies and achieving an effec- tive transition from ANNs to SNNs. In addition, we also improve the overall performance by introducing quantized layers trained end-to-end, so that SNNs can perform well at ultra-low time steps and longer time steps. Even supervised learning methods such as backpropagation through time (BPTT) are challenging to maintain SNN performance in fewer time steps. Although BPTT methods can reduce the number of time steps required with sufficient training, they are computationally expensive, especially when training on GPUs (Neftci et al. (2019); Lee et al. (2020); Zeng and Vo- gels, (2021)). The timing- based backpropagation methods (Tavanaci al. (2019); Kim et al. (2020)) can train SNNs in shorter time windows, typically only 5-10 time steps,
We introduce a clipping function with a learnable threshold, a dual-threshold neuron design, and a mem- brane potential initialization strategy, to jointly address the three types of errors in the conversion. Specifi- cally, the clipping error is mitigated by mapping the threshold leamedd during ANN training. The dual- threshold mechanism addresses the imbalance in mem- brane potential activation, where excessive activation of the positive potential is often neglected, and the negative potential is underutilized. Finally, the quan- tization error is reduced by appropriately initializing the membrane potential, leading to a high- preeissci,i,nn, low-latency SNN.
We evaluate the proposed ANN-to-SNN conversion method on the CIFAR-10. 10, CIFAR- 100 and ImageNet datasets. Compared with other existing methods based on ANN-to-SNN conversion and methods that directly train through surrogate gradients, our method achieves higher accuracy in fewer time steps. For example, our method achieves 94.75% accuracy on the CIFAR-
2

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Efficient ANN-SNN Conversion with Error Compensation Learning
but these methods are generally limited to processing sim- pler datasets such as MNIST (Kheradpisheh & Masquelier, 2020) and CIFARIO (Zhang & Li, 2020). In addition, Rathi et al. (2020) proposed to initialize SNNs through conversion methods and further adjust them using STDP to shorten the simulation time step. In this paper, our proposed method achieves high-peeformmnce SNNs running in only time steps, showing the advantage of ultra-low latency.
The output o' (T) of the SNN is in the range [0, 0'). How- ever, the output at of the ANN is in the larger range [0, dmaac where a'ax represents the maximum value of a'. a' can be mapped to (T) by the following equation:
( T N 0, 0,
a'T
((TT) cllip clip
(I)
Here the clip function sets the upper limit 6' and the lower limit O. [-] indicates floor function. X' represents the ac- tual maximum value of the output a' mapped to the maxi- mum value 0' of d' (T)) Rueckauer et al.(2017) concluded that 99% of the activation values in ANN are in the range [o, Simgs= so the threshold A is set to 99% of the maximum activation value to avoid the influence of outliers and thus reduce the inference delay in the conversion. The activation between X' and d'max in the ANN is mapped to the same value 6' in the SNN, which will cause conversion error called clipping error. In Figure 1a, the blue line represents the ReLU activation function, the red line represents the IF neuron, and the dotted line position pointed to by the clipping error shows the part where the maximum activation value of the ANN greater than the maximum spike firing rate of the SNN. This part of the activation value cannot be accurately represented by the spike firing rate, so it can only be represented by the maximum spike firing rate, resulting in clipping error.
3. Efficient ANN-SNN Conversion with Error Compensation Learning
3.1. Conversion Error Analysis
In this section, the conversion error between the source ANN and the converted SNN in each layer is analyzed in detail. The conversion error will lead to performance degradation in the conversion process, especially in the case of low la- tency. Although the error can be significantly mitigated by increasing the number of discrete states (higher infer- ence latency), it will be detrimental to the computational efficiency and energy efficiency of real-time applications. The growing inference latency will proportionally increase the number of operations and actual running time of the de- ployed SNN, which offsets the advantages of deep spiking neural networks, so it is particularly important to deeply study the error in the ANN-to-SNN conversion process. The conversion error comes from the activation deviation, that is, the deviation between the ANN activation value and the SNN spike firing rate. As analyzed in the literature(Bu et al., 2023), the conversion error in the ANN-to-SNN conversion process can be specifically divided into three categories: clipping error, quantization error, and uneven error. Fig- ure Ia shows the clipping error and quantization error, and Figure 1b- 1d shows the unevenness error.
Quantization errors arise from emulating continuous ANN activation values with discrete SNN firing rates. The spike rate output value o' (T) of the SNN is discrete, resulting in a quantization resolution g¹ 7., As shown in Figure la, z' E Rx' (2k+1)A** T 21 (k 0, 1..,, T) is mapped to o' (T) and
AA! will be rounded down to 7 2' (2k-1)x' AA T: (k
In the conversion process from ANN to SNN, clipping error refers to the error that occurs when mapping continuous- valued weights (usually used in ANN) discrete weights in SNN. In ANN, weights are continuous and can take any real value. However, in SNN, since the activation of neurons is represented by spike transmission, weights are usually discretized into a series of integers or binary forms. Clip- ping error occurs when continuous weights are mapped to discrete weights in SNN. Since the weights in SNN are dis- crete, the continuous weights in ANN cannot be accurately represented, which will lead to some information loss and errors. Clipping errors will have a negative impact on the performance of SNN. Especially in tasks with high precision requirements, clipping errors will cause the performance of SNN to degrade. Therefore, when converting ANN to SNN, is necessary to consider how to minimize clipping error, and some adjustments and parameter optimization are required.
gf 0, ..., will be rounded up to T. causing quantization error. The black dashed line at the position pointed by the quantization error represents the quantization error. At this position, the activation values of the continuous ANN cannot be accurately simulated by the spike firing rate of the SNN, but are represented by the same spike firing rate value.
The unevenness error originates from the non non-uniform dis- tribution of the input spike arrival time in the total time step. The discussion of the previous two types of errors is based on the assumption that the input spike arrival time is uniformly distributed. However, the spikes received by the deep layer often non- non-uniform to some extent, which leads to differences in the output of the layer, and then to non-uniform errors. As shown in Figure 1b, Ic and 1d, the three cases show that non- non-uniform inputs can lead to more or fewer output spikes compared to the ideal case. Idcally, as shown in Figure 1b, assume that the two simulated neu-
3

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Efficient ANN-SNN Conversion with Error Compensation Learning
20
1F
IF
(a) Clipping error and Quantiza- tion error
(b) Equivalent spikes
(c) More spikes
(d) Fewer spikes
Figure Three types of errors ANN-SNN conversion
rons in the - layer are connected to a simulated neuron in the layer, whose weights w² [2, -2]. and the output layer is [0.6, 0.4],
of the model with extremely low latency.
vector a' of the neuron in the the threshold g'-1 1, 5, and the ANN activation value a' = _ is calculated. Then, the average postsynaptic membrane potential is calculated by the internal membrane potential of the IF neuron. As shown in the box in the fig- ure, the internal membrane potential change diagram shows that the spiking neuron emits spikes at = and and (T) Σi_ -i (000'' Th is calculated, which is the same as a.. Therefore, the activation value of the I layer of the ANN is correctly simulated. However, in the cases of Figure ic and 1d, the spike train output generated according to the membrane potential change in the box is calculated as (T) = and (T) = 5. respectively, which are not equal to a' terms of value. These three cases can intuitively demonstrate the unevenness error.
3.2. Clipping Function with Learnable Threshold
In ChapterA.2, we analyzed the principle of the ANN-SNN conversion method. We hope to directly train the appropri- ate threshold value of each layer through ANN to realize threshold mapping, and then directly map the ANN weight to SNN to realize the conversion from ANN to SNN. Specif- ically, first, in order to reduce the clipping error, we use clipping function with learnable threshold À to replace the ReLU activation function in the ANN, We use the quanti- zation clip- hhip-floor-shie activation function proposed by (Bu et al., 2023) to train the ANN, and the formula as follows:
3,
(7 d'L x + +l.00.1)
a' = dh=h(z=== = Xelip
(2)
There are some limitations in the existing ANN-SNN con- version methods. In previous studies, these three errors can be reduced by replacing the activation function in the neural network. Specifically, Opt (Bu et al., 2022) uses the settings learnable upper bounds and membrane potential initialization to eliminate the clipping error and reduce the quantization error certain extent. Quantized activation functions are proposed replace the ReLUU activation func- tion in ANN, thereby reducing the quantization eиror in the conversion process (Yan et al., 3021). SRP (Hao et al., 2023) proposed an optimal strategy based on residual membrane potential to eliminate uneven errors. However, how to solve these three types of conversions at the same time remains challenge. For image classification tasks, a pre-trained model is usually required to fine-tune the network. However, using pre-trained model with ReLU to fine-tune model with quantization function is not ideal. It is meaningless to use an ANN network with unsatisfactory results to convert into an SNN. Therefore, the purpose of this paper to solve the three conversion errors ANN-SNN conversion in image classification tasks and achieve high performance
The hyperparameter represents the quantization step size of the ANN, and the displacement term yp set to }. Note that 2' W W W Then, train the ANN with the clipping function. This learnable threshold À is obtained through training in the ANN and can be directly mapped to the corresponding layer of the SNN. Finally, the learned threshold À in the ANN is directly mapped to the spike emission threshold 0 in the SNN, and the weight parameters of the ANN are also mapped to the weight parameters of the SNN complete the conversion from ANN SNN. Since in the threshold mapping process, the learnable threshold À in the ANN is equal to the spike emission threshold 0 in the SNN, the numerical difference between the two thresholds disappears, so the clipping error can be avoided.
3.3. Dual Threshold Neuron
In response to the three types of errors analyzed in this chapter, this section proposes a dual-threshold neuron that effectively alleviates the quantization error and unevenness error in the conversion, while eliminating the clipping error

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Efficient ANN-SNN Conversion with Error Compensation Learning
caused by the scaling threshold. Specifically, due the observation of the changes in the membrane potential in- side the IF neuron, it was found that the positive membrane potential is always over-released, while the release of the negative membrane potential always ignored. This was ignored in previous work, according to Equation 3, because when the time step T long enough (that is, hundreds or thousands of time steps), has little effect on the perfor- mance.
d'=0
x-4
AN
N T
N +1 T
-
--11-21-314
where N is the number of output spikes. However, when reducing the delay T few time steps, the unevenness error will significantly affect the approximation between the ANN activations and the SNN firing rate. An example of the cause and effect of the unevenness error and the principle of the dual threshold neuron to solve the unevenness error is demonstrated in Figure 2.
Tee-dy
(0) 1+| ad
4
1-12 21 12
IF
In the negative spike it reaches the negative discharge threshold and has fired at least one positive spike. In order to restore the incorrectly subtracted membrane potential, our model changes the reset mechanism of negative spikes by adding positive threshold (i.e.,0) 0). The spike function ((t) is then rewritten as:
neuron model, a neuron can only fire a
1-1--213r=c
1-1+1-1
(0)
21-
1, (f >
(()) = 1, (t) < o' and (!(() 2 1, (4)
(d)
0, otherwise, no firing.
Figure 2. The principle of dual threshold neuron. (a) The ANN neuron receives two inputs: 4 and -4, and its output is 0; For SNN, assuming the threshold 0f = 1. (b) The IF neuron receives four spike charges (-2, 2,, 2) at = 1, 3, 4. Its output firing rate is equivalent to ANN activation. (c) The IF neuron receives four spike charges (2, -2, 2, 2)) at t = 1, 2, 4, However will immediately fire spike is greater than the excitation threshold. No spike is fired at t 2. When 3, another spike is fired because the membrane potential is greater than the excitation threshold. When t = 4, no spike is fired, resulting in firing rate that not equal to the ANN output activation. (d) DTN represents the dual threshold neuron proposed this paper. The dual threshold neuron receives three spike charges
Where 6' is the negative threshold and (t) is the number of spikes fired by neuron at time step t. In order to improve the sensitivity of negative spikes, this paper sets the nega- tive threshold to a small negative value (-le-3 according to experience). Then the membrane dynamics update rule of the IF neuron rewritten as:
because the membrane potential
(i(1) (t 1)+ 400) ('0(v((( - -0) +0'e(0' V((())(N))
(5)
spike (2, 2, 22) at 1, 2, 3, 4. Although it fires 1. the dual threshold neuron model of this paper outputs negative spike at 2. When t = 3, the neuron fires spike. dual threshold neuron model of this paper outputs negative spike at which offsets the residual membrane potential, thereby generating a firing rate cquivalent to that emitted by the ANN.
According to Equation 4 and Equation 5, the IF neuron will fire negative spike to cancel the erroneously fired spike and restore the membrane potential.
3.4. Initialization of Membrane Potential
The complete equivalence between the forwarding process of the ANN and the spike firing rate (or postsynaptic po- tential) of the adjacent layers of the SNN introduced in Chapter A.2 depends on the simulation time step T being
5

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Efficient ANN-SNN Conversion with Error Compensation Learning
large enough so that 1'())= 2 O, 0'(0) Rs 0, which results in T
taken as the target task, and its performance was evaluated the CIFAR-10, CIFAR-100 and ImageNet datasets to validate the effectiveness of our method. Similar to pre- vious work, we use VGG-16, ResNet- 18, and ResNet-20 network structures as the source ANN. And compare the method proposed in this article with other state-of-the-art methods, including RMP from Han et al. (2020), TSC from Han & Roy(2020), ReLUThreshold-S5 -hhiff (RTS) from Deng & G2,2202), RNL from Ding et al.(20) Opt from Bu al.(2),)) Quantization Clip-Floor- Shiff activation function (QCFS) from Bu et al.(20)3), and SNN Conversion with AdvancedPipeline (SNNC-AP) from Li et al.(2021).
T
a long inference time for the SNN when applied to complex data sets. In addition, under the constraint of low lateney, there is an inherent difference between the activation value of the ANN and the average postsynaptic potential of the SNN, which is propagated layer by layer, resulting in significant decrease in the accuracy of the converted SNN. This section will analyze the impact of membrane potential initialization and show that the optimal initialization can achieve the expected error-free ANN to SNN conversion. Since (T) 2 O, the equivalent form of Equation 17 is as follows:
4.1. Comparison with state-of-the-art Methods
d(T))= max (w'-o'i(T) J (TT (0) o) (6)
-
Table 1 shows the performance comparison between the proposed conversion method and the state-of-the-arr ANN- SNN conversion method on CIFAR-10. Among them, the accuracy of the comparison methods is based on the experi- mental data in the original paper, and the best accuracy is highlighted in bold. On the CIFAR-10 dataset, regardless of whether the model is VGG-16, ResNeet- 18, ResNet-22., our method outperforms previous conversion methods at low time steps. Specifically, on VGG-16, the accuracy of our method reached 95.15% 15% at T = 4, which is comparable to the performance of ANN On ResNet-20, the accuracy of our method reached 90.55% % T = 4, which similar to the performance of ANN. On ResNet-18. the accuracy of our method reached 95.99 at T 4. which is also similar to the performance of ANN. These results validate the effectiveness of the method proposed in this paper. It is worth noting that when T = 2, the accuracy of our method on ResNet-15 18 reaches 94.75%, approaching the accuracy of ANN in a very short time step.
T
According to the above formula, the relationship between the average postsynaptic potentials of adjacent layer spike neurons can be rewritten in a new way:
('(T)) = max O0' (=
T-ww (T) +(( o
(7)
gi
From the above formula, we can see that the spike firing rate is discrete, and there is an inherent quantization error between ANN and SNN. This section studies optimal membrane potential initialization method to reduce the con- version error. Specifically, assume that the ReLUU activation of the layer in the ANN is the same as the average postsy- naptic membrane potential of the layer in the SNN, and then compare the outputs of the / layer of the ANN and SNN. For convenience, (=) s("
max(W"-a' .0)
is used to represent the output value of the ANN, and f(=) = f(w'. (T)) = max g'
We also evaluate the performance of our method on the large-scale dataset ImageNet and list the results in Table 2. Our method also outperforms other methods in terms of high accuracy and llt latency. For VGG-16, when T=16, our method achieves 74. 15% accuracy, which is 23% higher than QCFS. For ResNet-34, we achieve 72.37% ac- curacy with only 16 time steps. These results show that our method outperforms previous conversion methods.
( 0 is
# used to represent the output value of the SNN. The expected
T
square difference between a' and o' (T) can be defined as:
0' T 2
+ r (0) 0²
Eg (c]I((t)-
f(+) Es
T
Through mathematical derivation, it is found that f(=)]]
4.2. Effect Evaluation of Dual Threshold Neuron
arg E [(()) -(())f)))] = 2. when the initial mem- ''(0)
To verify the effectiveness of the dual threshold neuron model proposed in this paper, this section gradually applies each part of our method to the transformed SNN. Train 16. ResNet-20, and ResNet-18 using the CIFAR-10 and CIFAR- 100 datasets, and then convert the trained ANN to SNN. Here, this section introduces a set of SNN concepts. SNNa represents the native SNN directly converted from the trained ANN, while SNN represents the SNNa using dual threshold neuron. As shown in Table 3 and Table 5, the
brane potential is set to half the threshold, the expected value of the square conversion error reaches the minimum, thereby minimizing the conversion error.
4. Experiments
To evaluate the effectiveness of the ANN-SNN conversion method proposed in this paper, image classification was
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Efficient ANN-SNN Conversion with Error Compensation Learning
Table J. Comparison of the proposed method with other methods on the CIFAR-10 datasct
Architacture
Method
ANN
T-2
T-1
T=S
T-16
T-32
T-61
RMP
93.67%
60.30%
90.35%
TSC
93.65%
92.7996
KIS
95.72%
76.24%
90,6455
VGG-16
RNI.
92.82%
$7.90%
85. 85.40%
91.15%
Opt
34.57%
00.96%
93.389
94.20%
QCTS
95.52%
91.18%
93.90%
94.95%
95,40%
95.54%
95.55%
Oars
95.23%
93.53%
95.15%
95.41%
95.39%
95.48%
95.43%
TSC
91.42%
ResNet-20
QCFS
91 77%
73.20%
83.75%
89.55%
91,62%
92. 2.%%
92,35%
Ours
91.76%
84.52%
90.55%
92.10%
92,40%
92.43%
92.46%
95 96.466
RNL
93.84%
47.63%
83.95%
91,958
ResNet-18
Opt
96.04%
73.44%6
90.4348
94.822%
93.9216
QCFS
95.04%
75.4416
90.43%
94.82%
93.9226
Ours
96.39%
94.75%
95.99%
96.1%%
96.40%
96.35%
96.39%
Table 2. Comparison of the proposed method with other methods the ImageNet dataset
Architactrre
Method
ANN
T=16
T=32
T=64
T=128
T-256
TSC
70.64%
61.48%
R4
75.66%
0.09%
0.12%
3.19%
47.11%
SNNC-AP
75.66%
64,54%
71.12%
73.45%
74.61%
QCFS
74.32%
59 35%
69.3798
72.85%
73.18%
73.37%
74.36%
72.37%
RMP
73,49%
48.32%
VGG- 16
TSC
73.49%
69.71%
75.36%
70.09%
73.32%
QCFS
74.29%
50.97%
68.47%
72.85%
73.97%
74,229
Ours
73.85%
74.15%
74.29%
74.31
74.32%
dual threshold neuron model improved the performance of the transformed SNN.
in Figure
4.3. Effect of Quantization Steps L
Table Comparison of accuracy between native SNN and SNN using dual threshold neuron model on CIFAR-I0 dataset
In our dual threshold neuron method, the quantization steps L is hyperparameter that affects the accuracy of the con- verted SNN. To better understand the impact of L on SNN performance and determine the optimal value, trained VGG16, ResNet-20, and ResNet- 18 networks with prun- ing function with a learnable threshold À using different quantization steps L. including 2, 4, 8, 16, and 32, and then converted them to SNNs. The results in Table 7 and Figure 4, Figure 6 illustrate the impact on the accuracy of the converted SNNs under different quantization steps L. We found that the accuracy of SNNs at ultra-low latency (within 4 time steps) decreases when the quantization steps I, increases. However, too small quantization step (e.g., 2 time steps) reduces the model capacity and leads to reduced SNN accuracy. The recommended quantization step L is 4 or 8, which can achieve peef-perforancc converted SNNs at small time steps and very large time steps.
Dotuset
Archaecture
SNNG
SMN
VGG--1
91
ResNes-201
73 3..00%
411.32%
96.75%
CIBAR-10
RecNas-18
ResNee-20
83.75%
VGG 16
96 96.95%
95.41%
+0.46%
ResNes
89 50.55%
92.10%
+2.55%
ResNer:
96 826
96.11%
19/29%
The dual threshold neuron model in this article continuously improves the performance of the converted SNN, as shown in Figure 3. On the CIFAR-IA 10 dataset, the SNN@ with the dual threshold neuron model can improve the performance of SNNa. The improvement of Re at T = 2 reaches 19.31 %. It is worth noting that the method proposed in this article achieved comparable accuracy to the source ANN network on the CIFAR-10 dataset at T = 4, and even at a time step of T = 2, the converted SNN achieved high accu- racy. More information on the CIFAR-100 improvement is
7

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Efficient ANN-SNN Conversion with Error Compensation Learning
C:0
500P
5N00
690
80
Sime-oop
Ttmx-dtpp
Time dt
(a)VGG-16 on CIFAR-10
(b)ResNet-20 on CIFAR-10 10
(c)ResNet-18 on CIFAR-10
Figure 3. Evaluation of the dual threshold neuron model CIFAR-10
100
100
079
1-12
140
018
Temworp
VG) on CIFAR-10
(b)ResNet-20 on CIFAR-10
ResNet111 on CIFAR-10
Figure 4, Influence of different quantization steps L on CIFAR-10
4.4. Energy Consumption Analysis
Table 4. Energy consumption analysis using VGG-16 on CIFAR-
On the principle level, SNNs have attracted much attention due to their unique properties. The neurons in SNN only per- form computational operations when spikes occur, resulting in power consumption. In contrast, without spike activation, these neurons do not perform any calculations and therefore do not generate additional power consumption. This low- power characteristic gives SNN significant advantages in hardware deployment, especially in resource constrained en- vironments. In addition, the power consumption of SNN is positively correlated with neuronal spike activity, which pro- computing modes.
100 dataset
ANN
T=2
T=4
T=8
T=16
T=32
Accuracy
76.46%
72.58%
76.50%%
77.14%
77.29%
77.39%
Energy(mJ)
4.170
0.004
0.008
0.017
0.034
0.068
proposed in this article achieved an accuracy of 77.29% at T 16, which very close to the accuracy of the source ANN and only requires 0.034mJ of energy cost, signifi- cantly lower than the energy consumption of 4. 10mJ of the source ANN. The method proposed in this article achieved an accuracy of 76.50% for SNN at T = 4 and only requires O. 1.008mJ of energy cost.
vides the possibility for This means that SNNs can complete complex computing tasks with lower energy consumption and adjust spike emis- sion strategies according to application requirements during design to achieve better energy efficiency ratios. Therefore, the advantages of SNN in power management bring poten- tial benefits for its future technological development and application deployment.
The SNN converted using the method proposed in this arti- cle exhibits excellent energy efficiency. These results clearly demonstrate the high inference performance and energy effi- ciency achieved by the method proposed in this article. The comparison of accuracy and power consumption highlights its effectiveness, allowing the converted SNN to operate in a highly energy-efficient manner while achieving excellent performance.
At the experimental level, in order to further investigate the power consumption of spike neural networks, this section evaluated the energy consumption of the method used in this paper on the CIFAR-100 dataset. This section uses the VGG-16 network structure. According to the analysis, this article uses the synaptic operation (SOP) of SNN to repre- sent the basic number of operations required for classifying an image. Use 77fJ/SOP for SNN and 12.5pJ/FL.O as the power consumption benchmark for ANN (Qiao et al., 2015). The power consumption analysis is shown in Table 4.
5. Conclusion
In this paper, we propose ANN-to-SNN conversion method to achieve high-precision and ultra-low latency deep SNNs. Specifically, we use new activation function to re- place the conventional ReLU activation function in ANN, which is closer to the activation characteristics of SNN while keeping the ANN performance almost unchanged. In ad-
It is worth noting that the SNN converted using the method
8

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Efficient ANN-SNN Conversion with Error Compensation Learning
dition, we propose a dual-threshold neuron that effectively alleviates the quantization error and uneven error that appear in the conversion, while eliminating the clipping error that is re- generated by scaling the threshold. We achieve state-of of- the-art accuracy on CIFAR-10, CIFAR-10 100 and ImageNet datasets with fewer time steps. Our research results not only promote the application neuromorphic hardware, but also lay the foundation for the large-scale practical deployment of SNNs.
conversion for fast and accurate inference in deep spiking neural networks. arXiv preprint arXiv:2 1654, 2021,
Han, B. and Roy, K. Deep spiking neural network: En- ergy efficiency through time based coding. In European conference on computer vision, pp. 388 404. Springer, 2020.
Han, B., Srinivasan, G., and Roy, K. Rmp-snn: Residual membrane potential neuron for enabling deeper high- accuracy and low-latency spiking neural network. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 13558-13567, 2020.
Acknowlegdements
This work was supported by the National Natural Science Foundation of China under Grant (No.62476035, 62206037, 62306274, 61925603, U24B201 40), and in part by the Young Elite Scientists Sponsorship Program by CAST un- der Grant 2024QNRC001, Open Research Program of the National Key Laboratory of Brain-Machine Intelligence, Zhejiang University (No. BMI2400012).
Hao, Z., Bu, T., Ding, J., Huang, T., and Yu, Z. Reduc- ing ann-snn conversion error through residual membrane potential. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pp. 11 11-21, 2023.
Ho, N.-D. and Chang, I.-J. Tel: an ann-to-snn conversion with trainable clipping layers. 2021 58th ACM/EEEE Design Automation Conference (DAC), pp. 793-798. IEEE, 2021.
Impact Statement
This paper presents work whose goal advance the field of Deep Learning. There are many potential societal conse- quences of our work, none which we feel must be specifi- cally highlighted here.
Hubara, I., Courbariaux, M., Soudry, D., Eamiv,,,, R., and
Bengio, Y. Binarized neural networks. Advances in
neural information processing systems, 29, 2016.
Kheradpisheh, S. R. and Masquelier, T. Temporal backprop- agation for spiking neural networks with one spike per neuron. International 2050027, 2020.
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Lee, C., Sarwar, S. S., Panda, P., Srinivasan, G., and Roy, K. Enabling spike-based backpropagation for training deep neural network architectures. Frontiers in neuroscience, 14:497482, 2020.
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Liu, Z., Guan, B., Shang, Y., Yu, Z., Bian, Y., and Yu, Q- Lecalib: Line-based event camera calibration. Measure- ment, 235: 14900, 2024c.
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10

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Efficient ANN-SNN Conversion with Error Compensation Learning
A. PRELIMINARIES
A.I. Neuron Model for SNNs
Spiking neural networks use spiking neurons as their basic computing units, which simulate the natural mechanism of biological neurons communicating through spike trains. In the field of neuroscience research, variety of spiking neuron models have been proposed to accurately simulate the input-output relationship of biological neurons. This section will focus commonly used spiking neuron models: the LIF neuron model and the IF neuron model. Both neuron models used to simplify the description of the spike emission process. The dynamic expression of the LIF neuron is:
dv = (V - Vinst) + ((), V(I) < Va. dt
Among them, (t) represents the membrane potential of the IF neuron at time I, (() represents the input of the neuron at time i, is the membrane time constant, and Vreat is the resting potential. When the membrane potential V (t) exceeds the threshold Vaa time i, the neuron fires a spike, and then the membrane potential V(I) returns the resting potential Vrest- In practical applications, the dynamics need to be discretized. The discretized LIF model is described as:
m' (t) T v 1) + W 21)) s'(t) H(m (f) -8)),
(10)
(1(1) = m1)(1) - (1) -
Among them, ml(() represents the membrane potential of the neuron before the trigger spike at the & time step, (t) represents the membrane potential of the neuron after the trigger spike at the time step, and W represents the weight matrix between the layer and the 1 layer, (t) is the IF neuron in the layer receiving input from the last layer. At the same time, the firing threshold in the layer LIF model is 8¹, H()) is the Heaviside step function, and s'(tt represents the spike output of the layer neuron time I, the element of which equals if there is spike and 0 otherwise. For each element in m (t), if (t) > 0', the neuron will fire spike and update the membrane potential (t). In order to avoid information loss, soft reset mechanism is usually used to update (t) instead of directly resetting it to O, that is, when a spike is triggered, the membrane potential (1)) minus the threshold 0'. In the discretized representation, the resting potential is usually set to 0, so the threshold 0 > LIF neurons strike a balance between computational cost and biological plausibility.
The dynamic expression of IF neurons is:
dV
(V((t) Vrest) + X(t), (tt) < Van dt
(11)
Compared with the LIF model, the IF model simplifies the membrane time constant term, that is, the leakage of membrane potential over time ignored. The discretization description of the IF model is:
m'(t) = v'(t - 1) + w x' (t),
s((1) (mm((1) -1)-0') 0'),
(12)
vt (t) = m'(())))))))))) s()))s((t)) s((()-
This paper uses the IF model for ANN-SNN conversion, which allows neurons to accumulate potential through input current and emit spikes when the threshold is reached. Compared with the LIF model, the IF model does not contain leakage terms, so it is more suitable for converting ANN neurons with rectified linear unit (RcLU) activation function into SNN ncurons, thereby realizing ANN-SNN conversion.
A.2. Principle of ANN-SNN Conversion Method
First, let's look at the relationship between ANN and SNN. Consider a typical ANN with M fully connected layers. The output of the convolutional layer can be expressed as:

---

Efficient ANN-SNN Conversion with Error Compensation Learning
a' = h(hWaaa)) 1= 1,2,.... M
(13)
Among them, the vector a' represents the output of all neurons in the I layer, W represents the weight matrix between the / layer and the - layer, and in(-) is the ReI.U activation function. ReL.U is widely used ANN because of its piecewise linear characteristics, which simplifies the weight update process during training.
For the neuron model of SNN, the IF neuron model is usually used. Since does not have leakage terms and refractory periods, the spike firing rate of the IF neuron in given time window and the activation value of ReLU can be used as a bridge to connect SNN and ANN. In addition, for classification tasks, the maximum activation value of all units in the final output layer is crucial to the classification result, so scaling the spike firing rate of IF neurons in each layer by a constant factor does not affect the classification result. Similar to the approach of Deng et al.(20,)), we assume that if the presynaptic neuron in layer I fires a spike, the postsynaptic neuron in layer receives an unweighted postsynaptic potential 0', that is:
(14)
The key idea of ANN-SNN conversion is map the activation values of simulated neurons in ANN to the firing rate (or average postsynaptic potential) of spiking neurons in SNN. The spatiotemporal dynamics equation of the IF neuron is shown in Equation 12, which represents the neuron charging, discharging, and resetting process. If the IF neuron in the layer receives input x²' (t) from the last layer, the discrete function between the impulses in the layer and the layer can be obtained by superimposing the equation:
J' (1) -1)-v'( (1- w' -
(15)
Equation 15 describes the basic function of the spike neuron used in the ANN-SNN conversion. Summing Equation 15 from time 1 to T and dividing T on both sides, we get:
J ((T)--1) T
W DT (i)
2i=1=
E
(i)o'
(16)
If (T) Els ((1) is used to represent the average postsynaptic potential from 0 to T. and Equation 14 is substituted into Equation 16, can obtain:
B'(T)= = 1 (T) (0)
(17)
T
Equation 17 describes the relationship between the average postsynaptic potentials of neurons in adjacent layers. Note
s'(T) that (T) 2 0. If the initial membrane potential v0))) is set to zero and the residual term T is ignored when the simulation time step long enough, the converted SNN has almost the same activation function as the source ANN (Equation 13). However, higher time step T' results in longer inference latency, which hinders the practical application of SNNs. Therefore, this paper aims to achieve gegh-performance ANN-SNN conversion with extremely low latency.
Table 5. Comparison of accuracy between native SNN and SNN using dual threshold neuron model on CIFAR-100 dataset
Dataset
T
Architecture
SNNa
SNN0
AAce
VGG-16
63.79%
72.58%
+8.79%
ResNet-20
19.96%
42.91%
+22.95%
ResNet-18
70.79%
75.11%
+4.32%
VGG-16
69.62%
76.50%
+6.88%
ResNet-20
34.14%
61.63%
+27.49%
CIFAR-IOM 100
ResNet-18
75.67%
78.81%
+3.14%
VGG-16
73.97%
77.14%
+3.17%
8
ResNet-20
55.37%
67.31%
+11.94%
ResNet-18
78.48%
79.48%
+1.00%
12

---

Efficient ANN-SNN Conversion with Error Compensation Learning
B. Comparison on C1FAR-100 Dataset
evaluated the performance of our method on CIFAR-100 and listed the results Table Our method also outperforms other methods in terms of high accuracy and ultra-low latency. It is worth noting that when T 2, our method achieved an accuracy of 72.58% for VGGI6, which is 8.79% higher than the suboptimal QCFS method. When the time step is only method achieves accuracy of 76.50%, which is similar the accuracy of the source ANN. The results indicate that the method proposed in this paper outperforms previous conversion methods in both accuracy and ultra-low latency.
Table 6. Comparison of the proposed method with other methods on the CIFAR-100 dataset
Architacture
Method
ANN
T=2
T=4
T=8
T-16
T=32
T=64
SNNC-AP
77.89%
73.55%
76.64%
RTS
70.62%
65.94%
69.80%
70.35%
VGG-16
QCFS
76.28%
63.79%
69.62%
73.97%
76.24%
77.01% %
77.10%
Ours 76.46% %
72.58% %
76.50%
77.14%
77.29 %
77.39%
77.28% %
RMP
68.72%
27.64%
46.91%
ResNet-20
QCFS
69.94%
19.96%
34.14 14%
55.37%
67.33%
69.82%
70.49%
Ours 68.58%
42.91 %
61.63%
67.31 %
68.65 %
69.15
69.36 %
SNNC-AP
77.16%
76.32%
77.29%
RTS
67.08%
63.73%
68, 40%
69.27 69.27%
ResNet-18
QCFS
78.80%
70.79%
75.67%
78.48%
79. 79.48%
79.62%
79.54%
Ours
79.09 %
75.11% %
78.81% %
79.48%
79.45 %
79.55
79.50 %
C. Effect Evaluation of Dual Threshold Neuron on CIFAR-100 Dataset
Table 5 reports the comparison of accuracy between native SNN and SNN using dual threshold neuron model on CIFAR-100 dataset.
6.4
0.0
(G) on CIFAR-100
(b)ResNet-220 on CIFAR-100
Re)sesNet- on CIFAR-100
Figure 5. Evaluation of the dual threshold neuron model on CIFAR-100
D. Effect of Quantization Steps L
Table 7 summarizes the performance of converted SNNs with varying quantization steps I. and time-steps T, For VGG-16 and quantization steps L 2, we achieve an accuracy of 94.35% on CIFAR-10 dataset and an accuracy of 73.78% on CIFAR-108 100 dataset with time-steps.
13

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Efficient ANN-SNN Conversion with Error Compensation Learning
1-3
Tensworp
Va)V on CIFAR-100
(b)ResNet-20 on CIFAR-100
(c)ResNet-18 CIFAR-100
Figure 6. Influence of different quantization steps L CIFAR-100
Table 7. Influence of different quantization steps on the CIFAR 10 dataset
Architacture
Quantization Steps
ANN
T=1
T=2
T=4
T=8
T=16
T=32
T=64
L=2
94.71%
85.33%
94.35%
95.04%
95.05%
95.01%
95.05%
95.05%
L=4
95.23%
87.27%
93.53%
95.15%
95.41%
95.39%
95.48%
95.43%
VGG-16
I==8
95.41 %
66.82%
91.40%
95.18%
95.37%
95.23%
95.28%
95.27%
1.=16
95.59%
24.46%
89.65%
95.14%
95.45%
95.59%
95.56%
95.66%
L=32
95.59%
11.96%
88.12%
94.86%
95.43%
95.50%
95.55%
95.58%
L=2
88.56%
78.77%
87.54%
89.83%
90.07%
89.95%
90.08%
90.11%
1,=4
91.76%
67.31 %
84.52%
90.55%
92.10%
92.40%
92.43%
92.46%
ResNet-20
1==
92.89%
51.79%
82.78%
90.96%
92.58%
92.95%
93.03%
93.03%
L=16
93.37%
33.88%
66.05%
88.74%
92.95%
93.32%
93.34%
93.41%
L=32
93.53%
20.18%
54.94%
86.15%
92.24%
93.29%
93.42%
93.41%
1.=2
95.21 %
91.91 %
95.05%
95.62%
95.72%
95.64%
95.67%
95.66%
1,=4
96.39%
89.27% %
94.75%
95.99%
96. 1
96.40%
96.35%
96.39%
ResNet-18
L=8
96.33%
84.29%
93.79%
95.89%
96.31%
96.25%
96.27%
96.27%
L=16
96.59%
77.71% 5
92.91 1
95.78%
96.40%
96.53%
96.56%
96.58%
L=32
96.51% %
67.58%
90.77%
95.36%
96.17%
96.52%
96.41 %
96.43%
Table 8. Influence of different quantization steps the CIFAR- dataset
Architacture
Quantization Steps
ANN
T=1
T=2
T=4
T=8
T=16
T=32
T=64
L=2
74.63%
65.70%
73.78%
75.70%
76.01%
76.06%
75.95%
76.01%
L=4
76.46%
58.39%
72.58%
76.50%
77.14%
77.29%
77.39%
77.28%
VGG-16
L=8
77.32%
46.37%
69.07%
76.03%
77.41%
77.44%
77.46%
77.45%
L=16
77.67% %
32.32%
65.19 15.19%
75.24%
77.09%
77.66%
77.58%
77.50%
L=32
77.83%
21.73%
61.12%
75.32%
77.74%
77.75%
77.77%
77.82%
L=2
59.06%
42.80%
56.83%
59.78%
59.73%
59.95%
59.65%
59.44%
L=4
65.29%
28.17%
54.00%
63.03%
65.88%
66.46%
66.71%
66.66%
ResNet-20
L=
68.58%
13.83%
42.91%
61.63%
67.31%
68.65%
69.15%
69.36%
L=16
69.29%
8.07%
30.28%
60.14%
67.40%
69.11%
69.4 69.44%
69.50%
L=32
70.22%
5.15%
22.24%
54.08%
67.36%
69.69%
70.04% %
70.20%
L=2
77.75%
68.65%
77.23%
79.21 %
79.49%
79.44%
79.49%
79.52%
1,=4
79.09%
60.82%
75.11%
78.81%
79.48%
79.45%
79.55%
79.50%
ResNet-18
1
79.44%
47.62%
71.09%
77.84%
79.59%
79.73%
79.73%
79.49%
L=16
80.33%
37.39%
67.77%
78.02%
79.95%
80.25%
80.26%
80.24%
L=322
80.04%
21.89%
62.60%
76.80%
79.69%
80.10%
80.04%
80.03%
14


Reviews:
[{"review_id": "XjzWsQ8epI", "reviewer": "Reviewer_UJ5r", "summary": "This paper proposes an efficient ANN-to-SNN conversion method that significantly reduces conversion errors and inference latency. The key contributions include: A learnable threshold clipping function to mitigate clipping errors. Dual-threshold neurons to dynamically reduce quantization errors. Optimized membrane potential initialization to minimize unevenness errors. The approach achieves state-of-the-art accuracy on CIFAR-10, CIFAR-100, and ImageNet with only a few time steps, making it practical for low-power hardware applications.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer’s insightful comments and constructive feedback. Below, we address the concerns raised and clarify the contributions of our work\n\n## **Response to Weaknesses**\n\n### 1. Computational Overhead of Dual-Threshold Neurons\n\nThanks for your feedback. We find that the additional threshold brings little computations cost per neuron due to the event-driven nature of SNNs. As shown in Table 1, we evaluated the computational cost in terms of energy consumption and synaptic operations (SOPs) to show the Computational Overhead of Dual-Threshold Neurons. The results show that the Dual-Threshold Neurons almost introduce no extra energy consumption especially in small time steps (T =2 and 4). And other large time steps only introduce limited energy consumption. Therefore, our method significantly reduces energy consumption compared to standard ANNs while maintaining competitive accuracy at ultra-low latency.\n\n**Table 1. Computational Overhead of Dual-Threshold Neurons using VGG-16 on CIFAR-100 dataset**\n\n|   |             | ANN   | T=2   | T=4   | T=8   | T=16  | T=32  |\n| - | - | - | - | - | - | - | - |\n| **without Dual Threshold Neuron** | Energy (mJ) | 4.170 | 0.004 | 0.007 | 0.015 | 0.031 | 0.052 |\n| **with Dual Threshold Neuron**    | Energy (mJ) | 4.170 | 0.004 | 0.008 | 0.017 | 0.034 | 0.068 |\n\n### 2. Generalization Beyond Image Classification\nWe appreciate the suggestion to discuss how our method extends beyond static image classification tasks. Our conversion approach is designed to be broadly applicable, and the learnable threshold clipping function, dual-threshold neurons, and optimized membrane potential initialization can benefit event-driven data processing tasks, such as neuromorphic vision processing, speech recognition, and reinforcement learning.\nAlthough this work focuses on image classification benchmarks for fair comparison with prior ANN-SNN conversion methods, our approach can be extended to other spatiotemporal data. Specifically, the dual-threshold mechanism helps mitigate quantization errors in temporally sparse spike sequences, which is beneficial for event-driven data processing. We will explore these applications in subsequent work.\n\n### 3. Reference Formatting\nWe acknowledge the oversight regarding outdated references and have updated the bibliography to reflect officially published versions of cited works where applicable in the revision.\n\n## **Response to Questions for Authors**\n### 1. How does the learnable threshold clipping function adapt across different network depths?\n\nThanks for your feedback. The learnable threshold clipping function is trained alongside ANNs’ weights and adjust dynamically per layer. During training, it learns to match the optimal activation statistics of each layer, ensuring smooth ANN-to-SNN conversion.\nFor deeper networks, the function effectively scales the thresholds based on the range of activation distributions, which helps mitigate conversion errors. Empirical results demonstrate that this adaptation enables high accuracy even for deeper models like ResNet-34 on ImageNet (e.g., For VGG-16, when T=16, our method achieves 74.15% accuracy, which is 23.18% higher than QCFS. For ResNet-34, we achieve 72.37% accuracy with only 16 time steps.)\n\n### 2. How does the clipping function compare to other activation function alternatives, such as threshold scaling techniques?\nThanks for your feedback. Our learnable threshold clipping function provides a more flexible and data-driven alternative to static threshold scaling. Unlike predefined threshold adjustments (e.g., RMP, Opt), our function dynamically learns the optimal threshold mappings, reducing reliance on manual heuristics.\nWe conducted additional experiments comparing our method with existing threshold scaling approaches, such as RTS and QCFS. Using the ResNet-18 model on the CIFAR-10 dataset, our method achieves an accuracy of 94.75% with only two time steps, 19.31% higher than QCFS, while RTS achieves an accuracy of 84.06% at T=32. The results show that our approach consistently outperforms prior methods across different datasets and network architectures while maintaining ultra-low latency.\n### 3. Does the dual-threshold neuron introduce additional computational overhead during inference?\nAs mentioned earlier, the dual-threshold mechanism slightly increases per-neuron computation. However, since SNNs are event-driven and avoid redundant computations, the overall increase is negligible compared to conventional ANN operations.\nWe measured the impact on inference latency and found that our method achieves faster convergence with fewer time steps (e.g., T=2 on CIFAR-10 with ResNet-18 at 94.75% accuracy). This efficiency gain compensates for the minor computational overhead. Additionally, the power consumption analysis (Table 1) suggest that our method maintains a highly efficient energy profile.", "claims_and_evidence": "The paper claims that the proposed ANN-to-SNN conversion achieves high accuracy and ultra-low latency, with experimental results showing competitive accuracy using just two time steps (e.g., 94.75% on CIFAR-10 with ResNet-18). The claims are supported by detailed mathematical formulations and empirical evaluations on benchmark datasets​.", "methods_and_evaluation_criteria": "The methods and evaluation criteria are well-aligned with the problem domain. The study uses CIFAR-10, CIFAR-100, and ImageNet datasets, standard for ANN-SNN conversion. Compares performance with existing state-of-the-art methods, including RMP, TSC, RTS, Opt, QCFS, and SNNC-AP. Evaluates accuracy at different time steps to assess efficiency​.", "theoretical_claims": "The paper derives mathematical formulations for ANN-SNN conversion errors (clipping, quantization, and unevenness). The proofs appear correct, and the derivation of the optimal membrane potential initialization (reducing conversion errors) follows a logical framework​.", "experimental_designs_or_analyses": "The experiments are well-structured, using widely recognized benchmarks and multiple ANN architectures. However, additional ablation studies on different network depths could further strengthen the conclusions​.", "relation_to_broader_scientific_literature": "This paper is based on prior ANN-SNN conversion techniques", "essential_references_not_discussed": "The paper cites relevant ANN-SNN conversion works but does not explicitly mention some recent hybrid training techniques that combine backpropagation-through-time (BPTT) with ANN-SNN conversion. Including such references would provide a more comprehensive background​", "other_strengths_and_weaknesses": "Strengths\n1. Novel approach combining error compensation learning with ANN-SNN conversion.\n2. Achieves high accuracy at ultra-low latency (T=2).\n3. Comprehensive comparison with state-of-the-art methods.\n4. Strong theoretical foundation and experimental validation.\n\nWeaknesses\n1. Computational overhead of dual-threshold neurons – The introduction of dual-threshold mechanisms could increase computation, which might reduce efficiency on resource-constrained hardware. A quantitative study on computational costs would be useful.\n2. Limited discussion on generalization beyond image classification – The study focuses on static image tasks, but ANN-SNN conversion is also crucial for event-driven data, speech recognition, and reinforcement learning. A discussion on how the method generalizes to such tasks would be beneficial.", "other_comments_or_suggestions": "In the reference list, many entries are still in the arXiv format even though those works have been officially published. Please make sure to update them accordingly.", "questions_for_authors": "1. How does the learnable threshold clipping function adapt across different network depths?\n2. How does the clipping function compare to other activation function alternatives, such as threshold scaling techniques?\n3. Does the dual-threshold neuron introduce additional computational overhead during inference?", "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": "ML6rlzBQk2", "reviewer": "Reviewer_9nCj", "summary": "This paper proposes a new ANN-SNN Conversion framework by combining a learnable threshold clipping function, dual-threshold spiking neurons, and an optimal membrane potential initialization strategy.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer’s insightful comments and constructive feedback. Below, we address the concerns raised and clarify the contributions of our work.\n\n### 1. Difference Between Dual-Threshold Neurons and Spiking Models in [1, 2]\n\nThanks for your feedback. Our design is fundamentally different from the spiking models in [1, 2]. While these approaches adjust the firing threshold or employ additional bias terms to mitigate transition errors, our dual-threshold neuron explicitly distinguishes between over-release at positive membrane potentials and under-utilization at negative membrane potentials. As discussed in Sections 3.3 and 4.2, this design not only compensates for quantization errors but also addresses the problem of non-uniform errors, a challenge that becomes critical at ultra-low latency (e.g., 2 time steps). Our dual-threshold neuron is theoretically demonstrated in Section 3.3 and empirically validated in Tables 3 and 5, showing significant accuracy improvements (e.g., 19.31% improvement over ResNet-18 at T=2 on CIFAR-10), highlighting the effectiveness of our approach compared to previous models.\n\n### 2. Difference Between Learnable Threshold Clipping and QCFS [3]\n\nThe learnable threshold clipping function in our work (augmented with an optimal membrane potential initialization strategy) is significantly different from the QCFS function [3]. QCFS focuses on reducing the translation error by optimizing the activation quantization process. However, our approach employs the learnable threshold that maps directly to the SNN firing threshold. This ensures that the clipping error is minimized in a unified framework, and importantly, our initialization (as derived in Section 3.4) minimizes the expected squared translation error by setting the initial membrane potential to half the threshold. QCFS does not address this joint consideration of clipping, quantization, and non-uniform errors. Our approach achieves superior performance (e.g., 94.75% accuracy at T=2, compared to 75.44% for QCFS in Table 1). This adaptability is critical for ultra-low latency SNNs, as shown in Section 4.1.\n\n### 3. Applicability to Transformer-Based SNNs\n\nWhile our current experiments focus on VGG and ResNet architectures, the principles of error compensation learning of adaptive thresholds and dual-threshold dynamics are generalizable and adaptable. Because the adaptive thresholds and dual-threshold dynamics also could be applied to the spiking neuron models in the Transformer-Based SNNs. We acknowledge that transformer-based SNNs pose unique challenges (e.g., attention mechanisms) and would explore this direction in future work.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "The design of dual-threshold spiking neuron effectively reduces conversion errors from both theoretical and experimental perspectives.", "theoretical_claims": "I have checked the theoretical claims in Sec. 3.1-3.4.", "experimental_designs_or_analyses": "I have checked experimental designs mentioned in Section 4.", "relation_to_broader_scientific_literature": "The research field of this work is related to the fast and efficient ANN-SNN Conversion learning in the SNN community.", "essential_references_not_discussed": "Not found yet", "other_strengths_and_weaknesses": "1. As shown in Sec.3.1 and Sec.3.3, this paper systematically summarizes the conversion errors caused by different reasons and explores corresponding solutions. The error compensation learning strategy has demonstrated its superior performance within fewer time-steps.\n\n2. To make the contribution of this work more convincing, it seems that the authors need to argue the difference between the dual-threshold neurons and the spiking models mentioned in [1, 2]. In addition, the specific difference between learnable threshold clipping function (with optimal membrane potential initialization) and QCFS function [3] may also need further discussion.\n\n3. The applicability of this method to transformer-based SNNs may deserve further exploration.\n\n[1] Li C, et al. Quantization framework for fast spiking neural networks. Frontiers in Neuroscience, 2022.\n\n[2] Li Y, et al. Spiking neural networks with consistent mapping relations allow high-accuracy inference. Information Sciences, 2024.\n\n[3] Bu T, et al. Optimal ANN-SNN conversion for high-accuracy and ultra-low-latency spiking neural networks. ICLR 2022.", "other_comments_or_suggestions": "See Strengths And Weaknesses Section.", "questions_for_authors": "See Strengths And Weaknesses Section.", "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": "lLzoMaf7nw", "reviewer": "Reviewer_Yubt", "summary": "This paper focuses on ANN-to-SNN conversion methods and proposes three techniques to mitigate conversion errors. The first technique, a clipping function, is introduced to replace the ReLU activation in ANNs, thereby improving their compatibility for conversion to SNNs. The second technique, the Dual Threshold Neuron, develops a novel pulse function and a membrane potential update rule for the IF neuron. The third technique involves membrane potential initialization, which provides a principled value for initializing the membrane potential. Experimental results demonstrate that these techniques enable better performance within fewer time steps and provide an analysis of the effectiveness of key settings.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer’s insightful comments and constructive feedback. Below, we address the concerns raised and clarify the contributions of our work.\n\n## **Response to Weaknesses**\n\n### 1. Fixed Hyperparameter Choices\n\nWhile our method uses empirically determined hyperparameters (e.g., negative threshold $\\theta'$ =-1e-3, membrane potential initialized at $\\frac{\\theta}{2}$), these choices are rigorously validated through ablation studies (Tables 3, 5, and 7). For instance, initializing $v^l(0)=\\frac{\\theta^l}{2}$ minimizes the expected conversion error (Eq. 8). We acknowledge the potential benefits of adaptive mechanisms. Future work will explore data-driven tuning (e.g., layer-wise threshold learning) to further enhance flexibility.\n\n### 2. Scalability to Deeper Architectures\n\nOur experiments focus on widely adopted networks (VGG-16, ResNet-18/20/34) for fair comparison with previous work. We further validate our method on ResNet-50 architecture (on CIFAR-10 and CIFAR-100 datasets). The results are shown in the following Table. On the CIFAR-10 dataset, our method achieves an accuracy of 96.05% when T=4. While on the CIFAR-100 dataset, when the time step is only 4, our method achieves an accuracy of 80.51%, which is similar to the accuracy of the source ANN. This demonstrates that our framework is robust even in deeper architectures. Moreover, the optimal membrane potential initialization and error compensation in the theoretical foundation (Section 3.4) also ensure consistent performance across network depths.\n\n**Table 1. Accuracy of ResNet-50 on CIFAR-10 and CIFAR-100 datasets**\n\n| Dataset   | Architecture | ANN   | T=2   | T=4   | T=8   | T=16  | T=32  |\n| --------- | ------------ | ----- | ----- | ----- | ----- | ----- | ----- |\n| CIFAR-10  | ResNet-50    | 96.44 | 90.37 | 96.05 | 96.25 | 96.17 | 96.24 |\n| CIFAR-100 | ResNet-50    | 81.48 | 73.00 | 80.51 | 80.98 | 80.85 | 81.06 |\n\n### 3. Applications Beyond Image Classification\n\nAlthough our current experiments focus on VGG and ResNet architectures, the error compensation learning principles of adaptive threshold and dual threshold neurons are generalizable and adaptable. Adaptive threshold and dual threshold neurons can also be applied to event-driven tasks (e.g., video recognition, neuromorphic perception). We will explore dynamic data applications in subsequent work.\n\n## **Response to Questions for Authors**\n\n### 1. Impact of Negative Threshold Selection\n\nThe negative threshold $\\theta^{\\prime}$=-1e-3 balances activation symmetry and stability. A smaller $\\theta^{\\prime}$ (e.g., -1e-4) reduces sensitivity to minor fluctuations, while a larger $\\theta^{\\prime}$ (e.g., -0.1) risks over-activation. Our experiments (Figure 3, Table 3) show $\\theta^{\\prime}$=-1e-3 optimally mitigates uneven error without destabilizing training.\n\n### 2. Membrane Potential Initialization at half the threshold\n\nThis choice stems from minimizing the expected conversion error (Eq. 8). Mathematically, initializing $v^l(0)=\\frac{\\theta^l}{2}$ achieves the least squares fit between ANN activations and SNN firing rates. Empirical results (Table 1, T=2) suggest that it reduces quantization error by 19.31% in ResNet-18.", "claims_and_evidence": "The paper claims high accuracy and ultra-low latency for ANN-to-SNN conversion. These claims are supported by:\nMathematical analysis of conversion errors (clipping, quantization, uneven activation).\nExperimental validation across multiple datasets and architectures (VGG-16, ResNet-18, ResNet-34).\nComparative results showing superior performance over existing methods (e.g., QCFS, Opt, RTS)​.", "methods_and_evaluation_criteria": "1. The paper analyzes the causes of three types errors in ANN-to-SNN conversion through case studies.\n2. The paper examines the reasons for significant errors when the time step T is few. It further designs solutions and validates them through experiments.", "theoretical_claims": "The paper presents a theoretical framework for ANN-SNN conversion, focusing on:\n1. Mathematical modeling of conversion errors and their impact.\n2. Optimal membrane potential initialization, derived to minimize error propagation.\n3. Dual-threshold neuron mechanism, analyzed for improving activation consistency.", "experimental_designs_or_analyses": "The experiments are comprehensive and well-executed. The study:\n1. Uses multiple network architectures (e.g., VGG-16, ResNet-18, ResNet-34).\n2. Evaluates accuracy under varying time steps (T=2, 4, 8, 16, etc.).\n3. Conducts ablation studies on dual-threshold neurons and quantization methods.\nA potential improvement would be including real-world deployment results on neuromorphic hardware​.", "relation_to_broader_scientific_literature": "This work builds upon prior ANN-SNN conversion research. It advances the field by proposing error compensation learning, improving conversion accuracy at ultra-low latency.", "essential_references_not_discussed": "The paper covers major ANN-SNN conversion studies.", "other_strengths_and_weaknesses": "Strengths\n1. The proposed method achieves state-of-the-art accuracy on CIFAR-10 and ImageNet, thereby further advancing the research in ANN-to-SNN conversion.\n2. Innovative combination of threshold learning, dual-threshold neurons, and optimized initialization.\n3. Energy efficiency analysis supports practical deployment.\n\nWeaknesses\n1. Fixed hyperparameter choices without adaptive mechanisms – The method fixes thresholds and membrane potential initialization values, but allowing adaptive, data-driven tuning of these parameters might further improve accuracy and stability.\n2. Potential numerical instability in deeper architectures – While the method is validated on ResNet-18/34, performance on very deep models (e.g., ResNet-50, Vision Transformers) is unclear. The scalability of the approach to deeper networks needs further exploration.", "other_comments_or_suggestions": "Expand on potential applications beyond static image classification.", "questions_for_authors": "1. How does the choice of the negative threshold value impact overall network stability and performance?\n2. What guided the choice of initializing the membrane potential at half the threshold?", "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:

Meta-review: This paper proposes an ANN-to-SNN conversion framework that addresses three common sources of conversion error: clipping, quantization, and uneven membrane potential dynamics. The method introduces a learnable threshold clipping function, dual-threshold spiking neurons, and an optimized membrane potential initialization strategy. Empirical evaluations on CIFAR-10, CIFAR-100, and ImageNet, across architectures such as VGG and ResNet, demonstrate competitive accuracy with low inference latency (as few as two time steps).

## Strengths  
- **Well-defined technical scope**: The paper focuses on quantifiable sources of ANN-SNN conversion error and proposes targeted techniques to address them, each with theoretical justifications and practical relevance.
- **Efficiency and performance**: The method achieves high accuracy at ultra-low latency, outperforming several existing conversion methods. Notably, the method attains 94.75% accuracy on CIFAR-10 with ResNet-18 at T=2, which is significantly higher than several baselines.
- **Comprehensive evaluation**: The empirical study includes multiple datasets and architectures, and the authors provide additional results on ResNet-50 in the rebuttal to demonstrate scalability.
- **Clarifications in rebuttal**: The rebuttal addresses computational overhead concerns, clarifies methodological differences from prior works such as QCFS, and adds discussion on generalization beyond static image tasks.

## Weaknesses  
- **Task generalization**: The experiments are limited to static image classification. While the authors suggest that the techniques are generalizable, there is no empirical support for their application to dynamic or event-driven tasks.
- **Fixed parameter settings**: The current implementation uses fixed values for certain parameters (e.g., negative threshold, initialization point), which may limit adaptability across network architectures or tasks. The authors acknowledge this and suggest future extensions with adaptive mechanisms.
- **Positioning with prior work**: Although differences from related methods are discussed in the rebuttal, more detailed comparisons with closely related techniques (especially QCFS and threshold-scaling approaches) could help clarify the specific contributions.

## Rebuttal Assessment  
The rebuttal is constructive and addresses reviewer concerns in detail. Additional results on deeper models, clarification of dual-threshold mechanisms, and theoretical distinctions from prior work help clarify the scope and novelty of the contributions. Reviewers generally noted that their concerns were resolved.
Decision: Accept (poster)