Faster and Stronger: When ANN-SNN Conversion Meets Parallel Spiking Calculation
Authors: Zecheng Hao
Qichao Ma
Kang Chen
Yi Zhang
Zhaofei Yu
Tiejun Huang
Venue: ICML 2025 poster (2025)
Keywords: ANN-SNN Conversion
Parallel Spiking Calculation
Distribution-Aware Error Calibration
Primary area: applications->neuroscience_cognitive_science

Abstract: Spiking Neural Network (SNN), as a brain-inspired and energy-efficient network, is currently facing the pivotal challenge of exploring a suitable and efficient learning framework. The predominant training methodologies, namely Spatial-Temporal Back-propagation (STBP) and ANN-SNN Conversion, are encumbered by substantial training overhead or pronounced inference latency, which impedes the advancement of SNNs in scaling to larger networks and navigating intricate application domains. In this work, we propose a novel parallel conversion learning framework, which establishes a mathematical mapping relationship between each time-step of the parallel spiking neurons and the cumulative spike firing rate. We theoretically validate the lossless and sorting properties of the conversion process, as well as pointing out the optimal shifting distance for each step. Furthermore, by integrating the above framework with the distribution-aware error calibration technique, we can achieve efficient conversion towards more general activation functions or training-free circumstance. Extensive experiments have confirmed the significant performance advantages of our method for various conversion cases under ultra-low time latency. To our best knowledge, this is the first work which jointly utilizes parallel spiking calculation and ANN-SNN Conversion, providing a highly promising approach for SNN supervised training. Code is available at https://github.com/hzc1208/Parallel_Conversion.

Faster and Stronger:
When ANN-SNN Conversion Meets Parallel Spiking Calculation
Zecheng Hao
Qichao Ma
Kang Chen
Yi Zhang?
Zhaofei Yu 13 Tiejun Huang 13
Abstract
1. Introduction
Spiking Neural Network (SNN), as the third generation of neural networks (Maass, 1997), has become academic focus in the domain of brain-inspired intelligence. Unlike traditional Artificial Neural Network (ANN), the network backbone of SNN is composed of alternating synaptic lay- ers and neuron layers. Due to the superior biological plas- ticity and unique firing mechanism of the spiking neuron models, SNNs have great potential in the field of neuro- morphic computing and the internal spike triggering events are extremely sparse. At present, SNNs can be effectively deployed on multiple neuromorphic hardwares and have demonstrated significant advantages in inference power con- sumption (Merolla et al., 2014; Davies et al., 2018; DeBole et al., 2019; Pei et al., 2019).
Spiking Neural Network (SNN), as a brain- inspired and energy-efficient network, is currently facing the pivotal challenge of exploring suit- able and efficient learning framework. The pre- dominant training methodologies, namely Spatial- Temporal Back-propnggatoo (STBP) and ANN- SNN Conversion, are encumbered by substan- tial training overhead or pronounced inference latency, which impedes the advancement of SNNs in scaling to larger networks and navigating intri- cate application domains. In this work, we pro- pose novel parallel conversion learning frame- work, which establishes a mathematical mapping relationship between each time-step of the par- allel spiking neurons and the cumulative spike firing rate. We theoretically validate the lossless and sorting properties of the conversion process, as well as pointing out the optimal shifting dis- tance for each step. Furthermore, by integrating the above framework with the distribution- error calibration technique, we can achieve ef- ficient conversion towards more general activa- tion functions or training-fire free circumstance. Ex- tensive experiments have confirmed the signifi- cant performance advantages of our method for various conversion cases under ultra-low time la- tency. To our best knowledge, this is the first work which jointly utilizes parallel spiking calculation and ANN-SNN Conversion, providing highly promising approach for SNN supervised training. Code is available at https: /tt////ttttttt httpgggtthuhh.oo com/ hzcl 208 Paaral 1 e Lateeel_oooeereeeeee Conversion.
How to train effective spiking models remains a core topic faced by researchers in the SNN community. The current two mainstream training methods, Spatial-Tempone Back- propagation (STBP) (Wu et al., 2018; Neftci et al., 2019) and ANN-SNN Conversion (Cao et al., 2015; Bu et al., 2022), each have their own advantages and deficiencies, as described in Tab. Among them, one can obtain SNN models under ultra-low time latency (e.g. S 4 ~ time- steps) through STBP training, but it requires significant costs in terms of training speed and GPU memory overhead (Yao et al., 2022). Therefore, STBP will struggle greatly for network backbones with larger parameter scale and training time-steps. In addition, when STBP does not fuse global information in the time dimension or adopts fewer time- steps, the performance upper- bound of the trained SNNs still have gap with that of the pretrained ANNs (Hao et al., 2024b).
The idea of ANN-SNN Conversion is to establish mathe- matical mapping relationship between the activation layer of ANNs and the neuron layer of SNNs, so as to replace the activation function modules in pretrained ANNs with corresponding spiking neurons layer by layer, then obtain the converted SNNs. Under this learning framework, the calculation of SNNs only involve the model inference stage, resulting in less training burden and superior performance consistent with pretrained ANNs. But the drawback is that the converted SNN usually requires higher time latency to
"School of Computer Science, Peking University, Beijing, China "China Mobile Research Institule, Beijing, China Institute for Artificial Intelligence, Peking University, Beijing, China. Cor- respondence to: Zhaofci Yu <yuzf12@pp @ki.ecduuu........
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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When ANN-SNN Conversion Meets Parallel Spiking Calculation
Table I: Comparison of various supervised learning methods for SNNs.
Method
Act. Fune.
Train. Free
Train. Speed
Train. Mem.
Inf. Lat.
Inf. Speed
Inf. Acc.
STBP'Training Training
Surro. Func.
X
Slow
Large
Ultra Low
Slow
Low
ReLU
Fast
Small
Ultra High
Slow
High
ANN-SNN Conversion
QCFS
X
Fast
Small
High
Slow
High
Conversion Rect.
QCFS
X
Fast
Small
Low
Slow
High
QCFS
Fast
Small
Ultra Low
Fast
High
This Work
ReLU
/
N/A
N/A
Low
Fast
High
reach the ANN-level inference accuracy, especially when using original ReLU ANN directly as the foundation model to achieve the so-called training-firee conversion (Li et al., 2021a; Bu et al., 2024). To tackle this problem, researchers have proposed a series of conversion rectification strategies from multiple perspectives, further compressing the infer- ence latency to a small number of time-steps (Wang al., 2022; Hao et al., 2023b). In addition, due the fact that the converted SNNs obtained from current conversion schemes are generally based on Integrate-and-Firt (IF) neurons, the inference process of SNNs are limited by serial calculation, which further amplifies the harm of time latency.
top-1 accuracy of 72.90% on ImageNet- Ik, ResNet-34 within merely 4 time-steps.
2. Related Works
STBP training for SNNs. As a significant learning algo- rithm that can achieve relatively superior performance for SNNs within ultra-low time latency, Wu et al. (2018) and Neftei al. (2019) integrated Back-propagation through Time (BPTT) with surrogate gradient to pioneer the con- cept of STBP. On this basis, researchers have successively combined STBP algorithm with novel BatchNorm (BN) lay- ers (Zheng et al., 2021; Jiang et al., 2024), residual blocks (Fang et al., 2021: Hu et al., 2024), objective learning func- tions (Li et al., 2021b; Deng al., 2022; Guo et al., 2022), multi-dimennional attention mechanisms (Qiu et al., 2024), Transformer blocks (Zhou al., 2023; Shi et al., 2024) and advanced spiking models (Yao et al., 2022; Hao et al., 2024a), thereby extending SNN models to various appli- cation scenarios (Ren et al., 2023; Liao et al., 2024; Yao et al., 2024). In addition, to effectively optimize GPU mem- ory overhead and power consumption of STBP training, multiple variant learning frameworks have been further ex- plored, such time-based learning (Mostafa, 2017) and online learning (Xiao et al., 2022). However, at present, aforementioned schemes still have bottlenecks in learning performance.
Recently, parallel spiking neuron (Fang et al., 2023) is fa- vored by researchers due to its high-speed calculation ability, but current research around is generally limited to the field of STBP Training. In fact, the training precision of parallel neurons heavily relies on parameter initialization and can- not effectively contribute to the training memory explosion problem of SNNs. Instead, it is likely to play a crucial role in the conversion series methods with higher time latency. In this work, we innovatively combine ANN-SNN Con- version with parallel computing propose lossless and high-speed universal parallel conversion framework. The specific contributions are as follows:
We utilize parallel neurons to map the cumulative spike firing numbers predicted by pretrained ANNs within specific time period step by step. and theoretically prove the lossless property of the above process.
ANN-SNN Conversion. Compared to STBP training, ANN- SNN Conversion merely needs to replace the activation function modules of the pretrained ANN model with spik- ing neurons layer by layer to obtain the converted SNN (Cao et al., 2015; Diehl et al., 2015; Sengupta et al., 2019), which not only economizes training load, but also ensures that the converted SNN has sufficienlly superior performance upper-bound. Rueckauer al. (2017) and Han et al. (2020) realized that the soft-reset mechanism is more suitable for conversion learning algorithms, while Deng & Gu (2021) proposed shiftable ReLU function to better adapt the dis- tribution of the spike firing rate. Based on the above find- ings, Bu et al. (2022) proposed an advanced quantization activation function and theoretically validated its ability to losslessly simulate the average firing rate within any time latency from the perspective of mathematical expectation.
We derive the step-wise optimal shifting distance and sorting properties of parallel inference from a math- ematical perspective, expanding the applicability of parallel conversion and optimizing its computational overhead.
We propose a universal learning framework that can achieve effective parallel conversion regardless of (i) the type of activation function used (ii) whether the simulated and actual time-steps are equal.
Experiments have demonstrated the superior perfor- mance of our method for both conventional and training-fres free conversion. For example, we achieve
2

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When ANN-SNN Conversion Meets Parallel Spiking Calculation
However, despite achieving better performance than STBP within sufficient time-steps for the same network backbone (Li et al., 2022), converted SNNs still suffer from significant performance degradation under the condition of ultra-low latency (Rathi & Roy, 2021). Therefore, subsequent re- searchers further proposed more radical error rectification strategies, including setting silent states for specific neurons (Hao et al.. 2023a), calibrating forward temporal bias (Wu al., 2024), shifting initial membrane potential (Hao al., 2023b), as well as introducing burst and signed spikes (Li & 7eng, 2022; Wang et al., 2022).
spike computing:
1
X
1
PRE = A'T,,
A
: (2)
(19
Here A' E RTXT, As the dynamic equation of the LIF neuron at the t-th time-step can also be rewritten as vyRE = EX)
( when we ig- nore the influence of the previous spike firing sequence |s'.1 ..... sb((-11) on the current time-step, the equation will degenerate into the form of Eq.(2), which can finish the calculation process of T time-steps in parallel at once. How- ever, when X is not a small value (e.g. X = 1), the contribu- tion of the previous spike sequence to the current time-step (i.e. - (2)) the calculation result of the above parallel scheme deviate from that of vanilla LIF neuron. In addition, when A' is set as learnable parameters (e.g. in STBP training), some potential inappropriate values (e.g. Vi.j E [1,T]. A < 0) may lead to the problem of gradient vamishing.
Training-Free Conversion. How to effectively convert un- processed ANNs into SNNs with the lowest possible time latency has also become a recent academic focus in the field of conversion learning. Han & Roy (2020) proposed novel Samporal-SSiich-Codiiee
scheme to cut down the time latency and number of addition operations during the SNN inference stage. From the perspectives of calibrat- ing bias and initial membrane potential, Li et al. (202 designed two sets of pipelines to further enhance the per- formance of converted SNNs within dozens of time-steps. Bu et al. (2024) analyzed the upper-bound of the layer-wise conversion error, then pointed out training-free threshold balancing strategy, which can be applied to various visual tasks on networks with sequential structure.
cannot be directly ignored, causing
ANN-SNN Conversion. Vanilla conversion methods are generally based on the approximate linear transformation re- lationship of the average spike firing rates from pre-synaptic and post-synaptic layers. Specifically, when combine the charging and resetting process mentioned in Eq.(1), we will have:
3. Preliminaries
Spiking Neuron Models. Leaky Integrate-ande Fin-Fee (LIF) neuron is the most commonly-used spiking foundation model in the domain of SNN supervised training. Within simulation period consisting of T time-steps, Vt E [1,T], the LIF neuron will undergo three phases: receiving input current 1 firing spikes s and resetting potential UpRE- which can be described the following equations:
s = (1) (v..t -(pl) -Nel---))- (3)
Then, if we consider IF neuron and calculate the average firing situation along time dimension for both sides of the equation, we can further obtain:
1.t
F.T = (1)(1-)) ULT v
(4)
Lt UPRE- = 10) + I,.,, whe = VèRE- s
Here we use p.. = ΣI sht00/1 denote the average firing rate. Bu et al. (2022) further pointed out that when v4.0 = 02/2 and assuming that the spike sequence is uni- formly distributed in time dimension, we can utilize the (QCFS) function to simulate the average spike firing rate within any number of time-steps:
[1, upRe 2 0¹
tle = (0 s/ie= =
(1)
0, otherwise
following
Here uii and off respectively denote the membrane po- tential before and after firing spikes. X' and 0' regulate the potential leakage degree and firing threshold. IF neuron is special form of the LIF neuron when X 1. w' repre- sents the synaptic weight. As the spike firing process of the LIF neuron depends on the value of the previous membrane potential, the calculation procedure in each layer is serial, which limits the inference speed of SNNs. To address this issue, Fang et al. (2023) proposed the concept of parallel
0¹ _Clip T
W4
I.T QCFS
.o.F). (5)
0
Here T and efd respectively represents the simulation time period and shift term in QCFS function. Whether T is equal to T or not, when s = =8 82/2, roces and F.7 always maintain equivalence from the perspective of mathematical expectation.
3

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When ANN-SNN Conversion Meets Parallel Spiking Calculation
image/ text/ video
17
RelU @
(-PS
Traditional Comersionn:
IP
Otns
(b)
Stem
0
high time-latency performance degradation
ZWyyhee aill
Stage 1: Blocks x
26
Stage 2: Blocks 4
Ouase
Stage 3: Blocks x 6
ultra- time- lotency
T
lossless conversion
Conw 1 & BN
parallel computing
x-th step
Time-stap (0-T)
W W
trainiing free conversion
ReL. U & QCPS
Cosv 3x3 & BN
Ret.U & QCPS
Conv 1 & BN
8" 8/1
Ref.U & QCPS
T
T
I
8
Slage 4: Blocks
Fiei1
2-21
Avg Pool
Fsp
8
Head
css seg. det.
Figure 1: The overall framework of parallel conversion. Here (a) depicts the activation functions in ANNs, (b) shows the sorting property of parallel spiking neurons in the firing phase, and (c) describes the specific process of parallel inference.
4. Methods
or not at this time-step, we can derive:
4.1. Establishing an Equivalent Mapping Relationship between Spiking Parallel Inference and QCFS
a dt (1 0
T
- = cli
x(['-++1
For traditional conversion framework, spiking neurons gen- erally require a higher time latency (i.e. larger T) to make the error term (u'-² )// (4) approach zero, thereby achieving the layer-wise output alignment between the pretrained ANN and converted SNN. Considering the inherent serial computing property of LIF neurons, the total time cost of SNN inference stage will be further exacerbated. Unlike previous approaches, here we attempt to explore the mathematical mapping relationship between parallel spiking neurons and ANN activation functions. Intuitively, a larger average input current (1-)( will cause spiking neu- rons to emit spikes earlier. Therefore, for a QCFS function with T quantization levels, at the z-th time-step (a [1, will judge whether the total number of firing spikes is not less than T + 1, as shown in 1-1.I.
(7) indicates that when (1 > (T- x 1)0'. we will have L. > 8", then neurons will emit spikes to the posterior layer; Otherwise, spiking neurons will remain silent. Therefore, for (T x + 2) W4r(--1),T > 1)0', spiking neurons will continuously fire spikes from the z-th step to the 7' step, with total firing count of T-r+1, 1, which is completely consistent with the simulated result of the corresponding QCFS ANN.
(T
However, it worth noting that the calculation in (7. is based on the assumption that the input current completely follows uniform distribution (i.e. Vx [1, I'.. (i),(-)) From the above analysis, one find that the spike sequence transmitted from the I-th layer to the |+ 1-th layer [s !'..,''TT) clearly does not satisfy the condition of uniform distribution. To effectively regulate the distribution of the input current layer by layer, we introduce the concept of conversion premise controling matrix: A = + 1, 7'xT as shown Fig.
Specifically, we first define a primary parallel conversion matrix by refering to (2):
c
2
1
A POST
(6)
For each layer in the converted SNN, the input current is first projected into uniformly distributed state through A and then transformed into spike sequence consistent with the ANN prediction through A and parallel spiking neuron. We perform re- parameterization fusion for A and A losT to obtain the final parallel conversion matrix A A
clT
To simplify the calculation, we assume that the ratio of the input current obtained at the r-th time-step is c/ Since we need determine whether (( 2 (T - x + 1)0'

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When ANN-SNN Conversion Meets Parallel Spiking Calculation
Subsequently, can also losslessly convert DA-QCFS function into parallel spiking neurons. The specific process has been described in Algorithm 1.
Apc = APOST A
I-I
T-
T
(8)
PRE
Algorithm The overall pseudo-code for universal parallel conversion
Require:
Pretrained ANN model JANN with L layers; orig- inal activation function (QCFS or ClipReLU) gox (.) and layer-wise output TOA actual activation function (DA-QCFS) gbx (-) and layer-wise output DA cali- bration dataset D; mean function along the channel dimension p(();; learning momentum a.
Next, we will consider the transformation towards the shift term in QCFS function 1Fi.. For multi-step parallel inference, v/ plays a role similar to the initial membrane potential, but the contribution of el to different time-steps is obviously various. We theoretically prove the optimal value of the shift term, which can achieve lossless conversion from QCFS function to SNN parallel inference:
I.T.
Ensure: Converted Parallel SNN model fSNN- # Stage I: Parameter Initialization for I 11to to L do
Theorem 4.1. For stepss parallel inference in the I-th layer, we use b' to denote the corresponding shift term, here b' E R², When the pretrained ANN adopts QCFS function in (5, the following cases, we will derive the optimal
[ANN ANN-9DA 0 SANN- Tox--ox.00 .
fANN- DA = 0
SANN- = 0
value of the shift term: b'
w T
v¹
end for
T-H+1
# Stage II: Layer-wise Error Calibration for (Image, Label) in D do for 1 to L do
(i) T T, then have I..T 1.
TQCFS-
(ii) If T
+
T
and 2/d = 0' /2, then we have
1.T
1.T TQCFS)
+QTFs)= O.
e/RB
W FoA
(1-1) W' (1-1)
fANN-
fANN- (1 a) of
Refering to (5) and Eq,( calculate the origi- nal and actual activation output OA FDA through SANN- P0s (.) and JANN- TANN-9bA() I.T
4.2. Towards Universal Conversion Error Rectification
Theorem 4. (ii) indicates that under the condition of receiv- ing uniform data distribution, even if the simulated time latency î is not equal to the actual inference latency T, from the perspective of mathematical expectation, the con- version error can still be cut down to zero. However, on the one hand, the input data may not necessarily follow a uniform distribution in reality; on the other hand, there may be significant distribution gap across different chan- nels. Therefore, further rectify the conversion error under arbitrary data distribution and time latency, we propose Distribution-ANe Aware QCFS (DA-QCFS) function:
eOST = ( 'A
TANN.ObA = fA + (11 at e
end for end for # Stage III: Parallel Conversion for /
to do for t 1 to T do fsNN-b JAN sh o² 2[T [+1)
SaNN
+
T-11
end for fSNN. W fANN..W W
J.f DA
0 +'+b Clip / (W4r(-11). + tbb y +b
Set A according to (8)
...T
fSNN. PRE JANN Ibx O²
ssNN BroST = fANN- IDA. 0² + fANN.ODA end for
Here W/DA ob E CRC, which are the learnable shifting and scaling factors of DA-QCFS function (C² denotes the total number of channels). For each layer, along the channel dimension, we respectively calculate the mean conversion errors e/2E: f/OTT before and after the activation function, which are then used update db vbb iteratively. The overall learning process of t/aa adopts the idea of greedy algorithm. The goal of each iterative update is to make the distribution of the average firing rate during ac- tual inference closer to the distribution simulated by the pretrained ANN, thereby reducing the precision loss when converting from the original model.
# Stage IV: Parallel Inference for 1 to L, 1-1-1 1 T do I' = fsNN. (1g(1-1) fsNN f 0
if A + fsNN.. 2 O then
Fire spikes: s' =
else
Keep slient: s' = end if
end for Return fSNN (W, Apc, b, OrRe, GpoST).
It worth noting that the above algorithm is also applicable
5

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late A/c 1' + b If g/ 1, the next search interval will be squeezed to |ptr',. mid], otherwise it will be updated to [mid - 1, pt Finally, we will derive the time-step tли at which the first spike is emitted. Then, we can directly and transmit to the next When ANN-SNN Conversion Meets Parallel Spiking Calculation
Table 2:
Detailed experimental configuration for universal parallel conversion framework.
Conversion Cases
Need Thre. Rec.
Need Calib.
A
pe.sh
b' .saape
0 Shape
0 rost
QCFS (T = T) QCFS (T + T) ReLU
x
T.T
[T.
scalar
scalar
T,T
[T. C1
scalar
C.
[T.
[C,]
[C,]
to the training-free -ree conversion for pretrained ReLU ANNs. Compared to QCFS ANN family, which is specifically de- signed for conversion learning, large number of models in the ANN community are typically based on vanilla ReLU function. The data distribution based on ReLU is more irreg- ular and has a larger numerical range, which is more difficult to achieve precise conversion under low time latency. Here we propose stree-stage training free conversion frame- work:
4.3. Optimizing the Calculation Overhead of Spiking Parallel Inference
In the previous discussion, we have pointed out that for the parallel conversion matrix in (q) the calculation intention of ATC is to determine whether the total number of firing spikes within T time-steps is not less than T x + 1. That is to say. if parallel neurons emit spikes at the æ-th step, they will continue to emit spikes from the x + 1-th step to the Th step. Therefore, to further optimize the computational overhead and inference speed, we can leverage this sorting property and apply the binary search technique in the parallel inference stage.
From ReLU to ClipReLU. For each layer, we utilize the calibration dataset to record the histor- ical maximum activation value within each chan- nel, then set it 0 achieve the transformation from ReI.U(.) max(0,-) to ClipRel.U(,,000) min (max(0, -0, 0").
Specifically, under the initial state, we respectively set lower- bound and upper-bound pointers ptr(,, ptrrt for the search interval, where ptr = 1, 1,p, = T. In each subsequent search, we select the mid = ptr +pr: -th step and calcu-
From ClipReLU DA-QCFS. As shown in Algo- rithm for the specified inference time T, we will replace ClipReLU (set IOA) with T-level initialized DA-QCFS (set as DbA) Due to the fact that the ac- tual data distribution may be irregular, then we adopt layer-wise error calibration to enhance the inference performance within T time-steps as much as possible.
set gt gl.tm = 1, 1, g.1: synaptic layer.
In addition, during the actual inference process, we can choose 1,... T--"I"" T (' rather than
A I. Obviously, the above schemes are computationally equivalent, but the Hadamard product can further reduce the total number charging operations from O to OTT).
From DA-QCES to parallel spiking neuron. Specif- ically, as illustrated in Algorithm 1, vhA and &e can be merged together in the bias term; for ob. we can achieve mathematical equivalent mapping by setting pre-threshoid P/ and post-threshold 6poST-
Overall, by combining the above two optimization tech- niques, compared to vanilla LIF neuron, we can achieve the calculation of charging phase within OTT) and derive the complete spike firing sequence within only O(log TT), without the need for additional reset phase.
Overall, we utilize a unified foundational framework for pre- trained ANNs based on QCFS (T = T, T + T) or ReLU, with the only difference being whether additional threshold recording (ReLU- + ClipReLU) and error calibration stages (ClipReLU/QCFS + DA-QCFS) are introduced. Among them, threshold recording has accuracy loss the cali- bration dataset, error calibration aims to reduce the error to zero from the level of mathematical expectation, while par- allel conversion is completely lossless for any data distribu- tion. The detailed comparison of the above three conversion cases has been listed in Tab.2.
5. Experiments
Consistent with previous conversion learning works, we con- duct performance validation CIFAR (Krizhevsky et al., 2009) and ImageNet (Deng et al., 2009) datasets by using two types of network backbones, VGG (Simonyan & Zis- serman, 2014) and ResNet (He et al., 2016). We selected multiple methods including STBP Training (Li et al., 2021b, Dspike; Guo al., 2022, RecDis; Yao al., 2022, GLIF;
6

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When ANN-SNN Conversion Meets Parallel Spiking Calculation
Table 3: Comparison of previous state-of-ther -frtearr learning methods. f denotes adopting the error calibration technique.
Dataset
Method
Type
ANN Acc. (%)
Arch.
T
SNN Acc.
OPT
ANN-SNN Conversion
93.51
VGG-16
32
88.79
QCFS
ANN-SNN Conversion
95.52
VGG-16
2, 4, 8
91.18, 93,96, 94.95
SNM
Conversion Rect.
94.09
VGG-16
93.43
SRP
Conversion Rect.
95.52
VGG-16
6 (4+2)
94.47
CIFAR-10
Ours
Parallel Conversion
95,43
VGG-16
2,4
94.16, 95.50
QCFS
ANN-SNN Conversion
91.77
ResNet-20
2, 4,4,8
73.20, 83.75, 89.55
SRP
Conversion Rect.
91.77
ResNet-20
(4+2)
88.73
Ours
Parallel Conversion
91.67
ResNet-20
2.4
87.42, 91.58
OPT
ANN-SNN Conversion
70.21
VGGi-6
32
56.16
QCFS
ANN-SNN Conversion
76.28
VGG-16
2,
63.79,
69.62, 73.96
SNM
Conversion Rect.
74.13
VGG-16
32
71.80
SRP
Conversion Rect.
76.28
VGG-16
(4+2)
74.31
CIFAR-100
Ours
Parallel Conversion
76.11
VGG-16
2,
72.71, 75.98
QCFS
ANN-SNN Conversion
69.94
ResNet-20
4, 8, 16
55.37, 67.33 34.14,
SRP
Conversion Rect.
69.94
ResNet-20
6 (4+2)
53.96
Ours
Parallel Conversion
69.57
ResNet-20
4,8
65.31, 69.62
OPT
ANN-SNN Conversion
72.40
VGG-16
54.92
QCFS
ANN-SNN Conversion
74.29
VGG-16
8, 16, 32
19.12,
50.97, 68.47
SNM
Conversion Rect.
73.18
VGG-16
32
64.78
Burst
Conversion Rect.
74.27
VGGG-6
32
70.61
COS
Conversion Rect.
74.19
VGG-16
10 (8+2)
70.59
Ours
Parallel Conversion
74.23
VGG-16
4, 8, 16
71.23, 73.92, 74.26
Ours
Parallel Conversion
74.23
VGG-16
71.75
RecDis
STBP Training
ResNet-34
67.33
ImageNet-1k
Dspike
STBP Training
ResNett33
68.19
GLIF
STBP Training
ResNet-34
67.52
TAB
STBP Training
ResNet-34
67.78
OPT
ANN-SNN Conversion
70.95
ResNet-34
64
59.52
QCFS
ANN-SNN Conversion
74.32
ResNet-34
8, 16, 32
35.06, 59.35, 69.37
COS
Conversion Rect.
74.22
ResNet-34
10 (8+2)
72.66
Ours
Parallel Conversion
74.30
ResNet-34
4, 8
67.28, 74.32
Ours
Parallel Conversion
74.30
ResNet-34
72.90
Jiang et al., 2024, TAB), ANN-SNN Conversion (Deng Gu, 2021, OPT; Bu al., 2022, QCFS), Conversion Rectification (Li & Zeng. 2022, Burst; Wang et al., 2022, SNM; Hao et al., 2023a. SRP; Hao al., 2023b, COS), and Training-Free Conversion (Li et al., 2021a, SNNC; Bu et al., 2024, TBC) as comparison targets. The detailed experimen- tal configuration provided in Appendix.
T T T, especially for complex datasets and deeper network backbones, the additional utilization of layer-wing wise error cali- bration will further enhance the performance of SNNs under ultra-low latency.
Compared with other types of learning methods, our ap- proach has achieved significant advantages, even surpassing the memory-hungry STBP methods, which means that the parallel conversion scheme may open up a third path for the domain of SNN supervised learning besides STBP and ANN-SNN Conversion. For instance, we achieve 73.92% for ImageNet- Ik, VGG-16 within 8 time-steps, which ex- ceeds the performance of COS (T 10) by 3.33% and is at least 3.31% higher than the reported accuracies of remain- ing methods even extending the inference latency by 4x (i.e. 32).
5.1. Comparison with Previous state-of-the-ane Works
In Tab.3, we choose QCFS ANNs as the pretrained base models, and the hyper-parameter settings of QCFS func- tion are the same as (Bu et al., 2022) (T' = for CIFAR- 100/ImageNet-Ik ResNet-20/34; T 16 for ImagNet- 11, VGG-16; π 4 for the remaining cases). One can note that when the inference latency T is equal to the simulation latency T. the performance of converted SNNs is generally at the same level as that of the corresponding ANNs. When

---

When ANN-SNN Conversion Meets Parallel Spiking Calculation
Table 4: Comparison of training-free conversion algorithms on ImageNet- Ik dataset. i denotes utilizing fine-tuning training.
Method
Arch.
ANN Acc.(%)
T T=
T 16
T T= 32
T 64
TBC
ResNet-18
69.76
50.65 (-19.11)
64.79 (-4.97)
SNNC-LP
ResNet-34
75.66
50.21 (-25.45)
63.66 (-12.00)
SNNC-APt
ResNet-34
75.66
64.54 (-11.12)
71.12 (-4.54)
TBC
ResNet-34
73.31
59.03 (-14.28)
70.47 (-2.84)
ResNet-18
69.76
55.18 (-14.58)
66.26 (-3.50)
69.05 (-0.71)
69.54 (-0.22)
ResNet-34
73.31
50.67 (-22.64)
68.04 (-5.27)
72.46 (-0.85)
73.03 (-0.28)
Ours
ResNet-50
76.12
64.16 (-11.96)
73.59 (-2.53)
75.71 (-0.41)
76.04 (-0.08)
ResNet-101
77.38
60.59
(-16.79)
73.86 (-3.52)
76.42 (-0.96)
77.01 (-0.37)
0.6
panilell inference (this work)
0.30
35
serial inference (IP Neumo)
30
0.5
Imanee per second
0.25
Acelenaion Ratio
50
04
0.20
25
Aediattion
0.15
20
Image per
0.3
20
0.10
0.2
15
0.05
10
0.00
T-8
T-16
T-32
T-64
T-8
T-16
T-32
T-64
(a) ResNet-18
(b) ResNet-34
20.0
1.50
25
Image per seoo0d
0.6-
17.5
1.55
2.00
Acdleratonn
Image per
10.0
0.50
7.5
025
0.00
T-8
T-16
T-32
T-64
T-8
T-16
T-32
T-64
ResNet-50
ResNet-101
Figure 2: Comparison of parallel and serial inference speeds on ImageNet- lk dataset.
5.2. Performance Validation of Training-Free Parallel Conversion
5.3. Analysis of Parallel Inference Speed
As illustrated in Fig.2, we compare our parallel inference with the serial inference based on vanilla IF neuron. One can note that our scheme generally achieves 19 ~ 38x acceler- ation ratio when 2 32, even for the very deep network backbone (2 100 layers). It is worth noting that the con- version error may be further amplified for complex network backbones task scenarios, which leads to more severe time latency and performance degradation. Therefore, if we respectively consider the converted SNNs after adopt- ing our method and traditional conversion framework at the same performance level, the actual advantages we achieve in terms of inference speed will become more remarkable. More experimental results be found in Appendix.
We further investigate the parallel inference capability of our method under the condition of training free conversion, as illustrated Tab.4. One can find that our method can reduce the accuracy loss of conversion learning to 1% within 32 time-steps and achieve better performance than previous schemes with only half of their inference latency. For example, we achieve accuracies of 66.26% (68.6% (.4%%) on ResNet-18(34) within 16 steps, which exceeds the corre- sponding results of TBC within 32 steps by 15.61 % and 9.01%, respectively. In addition, it worth noting that even if the number of network layers increases to over 100 (e.g. ResNet-101), also rapidly squeeze the accuracy loss within the same time latency, preventing the conversion enror from being exacerbated as the network becomes deeper.
training-free conversion framework
8

---

When ANN-SNN Conversion Meets Parallel Spiking Calculation
6. Conclusion
DeBole, M. V., Taba, B., Amir, A., Akopyan, F., Andreopou-
los, A., Risk, W. P., Kusnitz, J., Otero, C. O., Nayak, T. K., Appuswamy, R., et al. TrueNorth: Accelerating from zero to 64 million neurons in 10 years. Computer, 52(5):20-29,2)) 2019. 2019.
In this paper, we propose a novel concept of parallel conver- sion and theoretically establish its mathematical equivalent relationship with the general activation function modules. Extensive experiments have validated that our scheme out- performs existing routes in SNN supervised learning in terms of inference performance and speed, which provides a brand-new approach for obtaining efficient SNN models.
Deng, J., Socher, R., Li, and Li, F. Imagenet: A large-scale hierarchical image database. In IEEE Confer- ence on Computer Vision and Pattern Recognition, 2009,
Acknowledgments
Deng, S. and Gu, S. Optimal conversion conventional artificial neural networks to spiking neural networks. In International Conference on Learning Representations, 2021.
This work supported by the National Natural Sci- ence Foundation of China (62422601, U24B20140, and 62088102), Beijing Municipal Science and Technology Program (Z241 100004224004), Beijing Nova Program (20230484362, 20240484703), and National Key Labora- tory for Multimedia Information Processing.
Deng, S., Li, Y., Zhang, S., and Gu, S. Temporal effi- cient training of spiking neural network via gradient re- weighting. International Conference Learning Repre- sentations, 2022.
Impact Statement
Vries, T. and Taylor, G. W. Improved regularization of convolutional neural networks with cutout. arXiv preprint arXiv:/08..04552 2017.
This paper presents work whose goal is to advance the field of SNN supervised learning. There are many potential soci- etal consequences of our work, none which we feel must be specifically highlighted here.
Diehl, P. U., Neil, D., Binas, J., Cook, M., Liu, S.-C., and Pfeiffer, M. Fast-classifyingg high-accuracy spiking deep networks through weight and threshold balancing. In International Joint Conference on Neural Networks, pp. 1-8. IEEE, 2015.
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When ANN-SNN Conversion Meets Parallel Spiking Calculation
A. Appendix
A.1. Proof of Theorem 4.1
Theorem 4.1. For steps parallel inference in the 1-th layer, we use b' to denote the corresponding shift term, here
b' RR. When the pretrained ANN adopts QCFS function in Eq.(5), for the following cases, we will derive the optimal
value of the shift term: b' =
T-2+1
(i) If = T, then we have pl.T" QCCSS
(ii) IfT + T and v 0¹ /2, then we have E (1ir (1.:2-ro0c 1.7
-OCFFS =0
Proof. (i) For I' W1T(--1,TT E [10 - w/t (Ac + 130 -²) Ak E [1, from Eq.(S) we can derive that J.T k0 /T.
Forrs
When consider s (A I' bb 2 8¹ will have:
s
7-1
7-1
I +
gr
1
T
T
T
(1
+
2/d
2 00)
(SI)
T x+=
T
T x-++1
Combining with W1T. E
ho' T V'
(k+1)0' ) 1
we further have:
kd
kd
(k 1)0
(I: + 1)0'
kgg
$ A
b'
T-++1 ... (k + 1)0¹
T
... T x-x+1
T
s' (ArcI' +b' 2 0²) + 5²
0 1
(S2)
firing spikes
Finally, we will derive p.T
1.T JQCFS kd /T.
(ii) Since QCFS function has the property of E FOCFS
IT
I.. TOCFS)
when 2i¹ = 00 /2. as mentioned in (Bu et al., 2022).
combining with the conclusion of (i), we can have:
E
IT
J.f TCCFS)
E LT
1. FOCFS)
+ E
ITT [FOCFS
1.7 TQCFS) = 0 + 0 =0
(S3)
Among them, ,.T satisfy the assumption mentioned in (Bu et al., 2022) that the input current follows a uniform distribution within multiple
Focrs maintains lossless conversion under any precondition, while FOCFS - r FQCFs needs to
JTT
1.
I.F
sub-intervals.
A.2. Detailed Experimental Configuration
For pretrained QCFS ANN models, we use SGD optimizer (Bottou, 2012), the optimization strategy of Cosine Anneal-
ing (Loshchilov & Hutter, 2017) and data augmentation techniques VDeVries & Taylor, 2017: Cubuk et al., 2019), the corresponding dyper-paramees
settings are: ir = 0.1, wd = 5 x 10-4 4 for CIFAR-10, ir 0.02, wd = 5 x 10-4 for CIFAR-100 and 1r = 0.1, wd = 1 x 10-4 for ImageNet- k. The specific network structure is consistent with (Bu et al., 2022). Regarding the error calibration technique, we utilize the training dataset as the calibration data to iterate for 1 epoch. The learning momentum a mentioned in Algorithm is set to 0.99.
For ReLU ResNet family in Tab.4, we replace all ReLU modules except for Stem with ClipReLU, DA-QCFS, and parallel spiking neurons in sequence. The inference speeds Fig.2 and Fig.S1 are measured on single NVIDIA RTX 4090 GPU.
12

---

When ANN-SNN Conversion Meets Parallel Spiking Calculation
panallll inforence (this work)
0.125
(IP Neuron)
Imsge per second
0.06
scral inference (IF Nouren)
74
0.100
(this work)
100
72
Acenteey
Aqauray
0.073
68
0.050
0.025
40
64
0.00
0.000
T-2
T-8
T-16
T-4
T
T-16
T-32
(a) CIFAR-100, VGG-16
(b) CIFAR-100, ResNet-20
0.30
0.125
0.25
Image per 8ec0nd
Aonuray
0.20
60
Accuacy
0.075
0.15
50
0.050
0.10
0.025
0.05
0.000
T-8
T-16
T-32
0.00
T-4
T-8
T-16
T-32
(c) ImageNet-Ik, VGG-16
(d) ImageNet-Ik ResNet-34
Figure $1: Comparison of parallel/serial inference speeds and performance on QCFS ANN models.
Among them, the inference speed of IF neuron is calculated on subset the test dataset (1000 images). In addition, experimental results reported in Tab.4, Fig.2 and Fig.S1 utilize (T) acceleration optimization in the charging phase.
A.3. Comprehensive Analysis based on Inference Speed and Performance
As shown Fig.SI, we make comprehensive comparison between parallel and serial inference in terms of speed and learning accuracy. The serial inference performance under the QCFS conversion framework utilizes the accuracies reported in (Bu et al., 2022). For relatively simple cases (i.e. CIFAR-100 dataset), IF neuron requires approximately 4x time latency of parallel conversion to reach the comparable accuracy, which makes our method achieve 15 23x actual acceleration ratio.
For more complex scenarios (i.e. ImageNet- Ik dataset), the ratio of time latency between neuron and parallel spiking neuron the same performance level will further increase. Considering that our scheme can ensure lossless conversion within specific time latency, this may lead greater potential for parallel conversion more challenging cases.
13


Reviews:
[{"review_id": "HXcLIff5eV", "reviewer": "Reviewer_72NY", "summary": "This work presents a novel route for SNN supervised learning by jointly adopting ANN-SNN Conversion and parallel calculation. The main contributions of the paper include the proof of optimal shifting distance, further promotion of parallel conversion framework based on QCFS, and experimental demonstration on various benchmarks.", "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": "## To Reviewer 72NY\n\nWe sincerely appreciate your recognition for the novelty and experimental effectiveness of this work. We will strive to address your concerns in detail in the following section:\n\n> The discussion on threshold recording and error calibration techniques is not sufficient.\n\n**A1:** Thanks for the question. In this work, threshold recording is used to confirm the initial maximum threshold and effectively utilize the distribution of input current, as QCFS explicitly provides learnable thresholds during the pre-training stage of ANN, threshold recording is only used in training-free conversion based cases. The motivation of error calibration lies in the fact that QCFS can only eliminate conversion errors ($T\\neq\\tilde{T}$) when the input current follows a uniform distribution, as shown in Theorem 4.1(ii). However, since the assumed condition may not be fully satisfied in practical situations, additional error calibration can further enhance the performance of converted SNNs under low time latency (where ClipReLU can also be considered as a case of $\\tilde{T}\\gg T$).\n\n> Which calculation step does the “sorting property” save in terms of computational cost?\n\n**A2:** The sorting property actually effectively saves multiplication operations in $\\Lambda_\\text{PC}^l\\mathbf{I}^l+\\mathbf{b}^l$ and comparison operations between $\\Lambda_\\text{PC}^l\\mathbf{I}^l+\\mathbf{b}^l$ and $\\theta^l$. Specifically, when we utilize the sorting property, it actually only involves calculation related to $\\Lambda_\\text{PC}^{l,\\text{idx}}\\mathbf{I}^l+\\mathbf{b}^{l,\\text{idx}}\\geq\\theta^{l,\\text{idx}}$, where $\\text{idx},\\text{len(idx)}=O(\\log T)$ is the index time-step set selected by the sorting property.\n\n> How are the corresponding throughput rates calculated?\n\n**A3:** We randomly select a subset of data (1000 images) to calculate the average inference time for the above two schemes. We choose scientific tools to calculate the precise time and the specific process has been submitted into the supplementary materials. For serial inference, we feed data into the SNN backbone at each time-step, while parallel inference packages consecutive $T$ time-steps into a batch and feeds it into the network all at once.\n\n> For ResNet-50 and ResNet-101, it seems that their Acceleration Ratio do not further increase like other cases?\n\n**A4:** Thanks for this insightful comment. Due to the fact that $T$ time-steps will be passed into the corresponding network backbone at once during parallel inference, for experimental cases with large model parameter quantity or time-steps, the required hardware memory is large and the utilization rate tends to be saturated. Therefore, under a environment with limited hardware support, the corresponding acceleration ratio may not further increase. However, even so, the advantage of parallel conversion is very obvious when $T\\geq 32$ (e.g. the corresponding acceleration ratio exceeds $17.5\\times$ for Fig 2.c-d). In addition, due to the theoretically lossless property of our method, in practical scenarios, we usually only need a small number of time-steps to achieve the same level of performance as the pretrained ANN for the converted SNN.\n\n> The authors' proof of the theorem in Appendix is somewhat concise.\n\n**A5:** Thanks for the suggestion. We will further improve the relevant proof process in the final submission.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "I have checked the relevant proof", "experimental_designs_or_analyses": "I have checked the experimental results about the Accuracy and Acceleration Ratio of this method.", "relation_to_broader_scientific_literature": "This work investigates a new conversion method that combines the performance advantages of ANN-SNN conversion with the low-latency advantage of STBP Training in the inference stage. It is a new learning route in SNN field.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "Strengths\n1. The narrative logic of this work is clear. Experiments have shown that parallel conversion has significant advantages in accuracy and acceleration ratio compared to traditional conversion methods.\nWeaknesses：\n1. The discussion on threshold recording and error calibration techniques is not sufficient. For example, as shown in Table 2, the authors need to further explain why some cases require the use of the above two techniques, while others do not?\n2. In Section 4.3, the author needs to clarify more clearly which calculation step does the “sorting property” save in terms of computational cost?", "other_comments_or_suggestions": "The authors' proof of the theorem in Appendix is somewhat concise, and more additional explanation can be introduced to enhance its readability.", "questions_for_authors": "1: In Section 5.3 (Figure 2) and Appendix A.2 (Figure S1), how are the corresponding throughput rates calculated for serial inference based on IF model and parallel inference based on parallel spiking model? Please clarify it.\n2: For ResNet-50 and ResNet-101 (Figure 2.c-2.d), it seems that their corresponding Acceleration Ratio do not further increase like other cases when the number of time-steps is large ($T\\geq 32$). What is the specific reason for this? Does it means the proposed method work only for low-latency SNNs?", "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": "dpyPBTrjKM", "reviewer": "Reviewer_HMDR", "summary": "This paper propose a parallel ANN-SNN conversion framework. The author firstly categorizes and summarizes various conversion paradigms in the field of ANN-SNN conversion learning, then proposes an efficient conversion method based on parallel spiking computing, which relate each time-step to the cumulative spike firing rate. Experimental results show that the proposed methods can achieve SOTA performance on several benchmark datasets.", "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": "## To Reviewer HMDR\n\nWe would like to thank for your acknowledgement about our approach in terms of theoretical analysis and performance advantages, we will provide further answers and clarifications for your questions and concerns.\n\n> Can this method be generalized to other tasks?\n\nThanks for this comment. To validate the generalization ability of our method on visual tasks, we further conduct experimental verification on semantic segmentation tasks. We attempt training-free parallel conversion based on DA-QCFS for Pascal VOC dataset [1] and ResNet50-FCN/DeepLabv3 structure [2, 3], as shown in Tab. R1. Experimental results indicate that our scheme can also achieve approximately lossless parallel conversion in segmentation tasks.\n\n**Table R1:** Experimental results of training-free conversion on Pascal VOC dataset.\n\n|       Arch.        | Metric (%) |  ANN  |  T=8  | T=16  | T=32  |\n| :----------------: | :--------: | :---: | :---: | :---: | :---: |\n|    ResNet50-FCN    | Pixel Acc. | 88.76 | 86.99 | 88.12 | 88.60 |\n|    ResNet50-FCN    |    mIOU    | 51.93 | 46.71 | 49.70 | 51.25 |\n| ResNet50-DeepLabv3 | Pixel Acc. | 91.46 | 89.87 | 91.21 | 91.38 |\n| ResNet50-DeepLabv3 |    mIOU    | 63.03 | 58.91 | 62.48 | 62.72 |\n\n\n\n> The analysis of Parallel Conversion for Transformer-based SNNs?\n\n**A2:** Thanks for the comment. The most critical difference between Transformer and CNN is the matrix multiplication between multi-branch inputs (e.g. $\\mathbf{Q}^l{\\mathbf{K}^l}^{\\top}, \\text{Attn}^l\\mathbf{V}^l$). If we directly insert QCFS functions after $\\mathbf{Q}^l$ and $\\mathbf{K}^l$ weight layers in the pre-training stage of ANN, and then replace QCFS modules with parallel spiking neurons $\\text{SN}(\\cdot)$ in the SNN inference stage, this may introduce $O(T^2)$ computational complexity within the self-attention modules. Therefore, we can consider pre-calculating the average input current for one of the branches (e.g. $\\mathbf{I}^{l,\\text{avg}}_Q$) and then calculating the attention score $\\mathbf{I}^{l,\\text{avg}}_Q \\text{SN}({\\mathbf{I}^l_K}^{\\top})$ to maintain the computational complexity at $O(T)$. It is worth noting that at this point, parallel conversion will still maintain its unique lossless and sorting properties on Transformer-based SNNs.\n\n> The proposed method needs to train an ANN with quantization activation function, which brings training costs.\n\n**A3:** For parallel conversion based on QCFS ANN, we usually need to complete the pre-training process of the quantized ANN model. However, our method also validate its effectiveness in training-free conversion cases. We can directly obtain the corresponding converted SNN model through utilizing quantization, error calibration, and parallel neuron replacement on an open-source and training-free ANN checkpoint.\n\n> The specific differences between Conversion Rectification and Parallel Conversion from the perspectives of performance and calculation overhead?\n\n**A4:** Thanks for the question.  The concept of Conversion Rectification usually refers to the relevant schemes for secondary optimization of the converted SNN model in the inference stage, aiming to reduce the representation gap between pre-trained ANNs and converted SNNs. The previous related works were generally based on IF neuron and its variants, and most of the works cannot guarantee the complete elimination of conversion errors in theory. Compared to these methods, our parallel conversion has faster inference speed and the property of lossless conversion . Additionally, due to its small number of time-steps, it can always keep the calculation overhead within a reasonable range.\n\n[1] The PASCAL Visual Object Classes (VOC) Challenge, IJCV, 2010.\n\n[2] Fully convolutional networks for semantic segmentation. CVPR, 2015.\n\n[3] Rethinking Atrous Convolution for Semantic Image Segmentation, 2017.", "claims_and_evidence": "YES", "methods_and_evaluation_criteria": "yES", "theoretical_claims": "The theoretical claims and proofs have been validated.", "experimental_designs_or_analyses": "The experimental comparison with previous SOTA methods has been checked.", "relation_to_broader_scientific_literature": "The academic theme of this work is related to the ANN-SNN Conversion learning with high efficiency, the author respectively considers solutions for the non-uniform problem of the spike sequence and the simulated average firing rate.", "essential_references_not_discussed": "nO", "other_strengths_and_weaknesses": "Strengths\n1.The theoretical analysis of the lossless property is solid.\n2.The authors point out the non-uniform problem for both $[\\mathbf{s}^{l,1},…,\\mathbf{s}^{l,T}]$ and $\\mathbf{r}^{l,T}, \\mathbf{r}^{l,\\tilde{T}}, T \\neq \\tilde{T}$, which is the foundation to establish theuniversal parallel conversion framework .\n3.Compared to previous works, the performance advantage of parallel conversion is remarkable.\n\nWeaknesses\n1.The authors mainly focus on the classification performance of SNNs. Can this method be generalized to other tasks?\n2.The author has verified the effectiveness of Parallel Conversion on CNN backbone. However, it lacks the test on Transformer-based SNNs. I suggest to add the analysis to make the contribution of this work more comprehensive.\n3.The proposed method needs to train an ANN with quantization activation function, which brings training costs.", "other_comments_or_suggestions": "For more comments or suggestions, please refer to the “Other Strengths And Weaknesses” section.", "questions_for_authors": "As shown in Tab.1, the author further divides the concept of conversion learning into ANN-SNN Conversion (ReLU or QCFS), Conversion Rectification and Parallel Conversion. I am curious about the specific differences between Conversion Rectification and Parallel Conversion? For example, from the perspectives of performance and calculation overhead, etc.", "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": "ZHjHulfiV5", "reviewer": "Reviewer_nBwe", "summary": "This work introduces a novel parallel conversion learning framework that establishes a mathematical mapping between each time step of parallel spiking neurons and the cumulative spike firing rate. The lossless and sorting properties of the conversion process are theoretically validated, and the optimal shifting distance for each step is identified. Additionally, it integrates distribution-aware error calibration to further improve accuracy.  Moreover,  the proposed framework achieves a top-1 accuracy of 72.90% on ImageNet-1k using ResNet-34 within only 4 time-steps, showcasing significant performance improvements in both conventional and training-free conversion scenarios.", "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": "## To Reviewer nBwe\n\nWe are delighted that you think that our method is well written and organized, as well as being validated in both theoretical and experimental dimensions. We will discuss your questions in detail in the following content.\n\n> The difference between the conversion method in this paper and I-LIF.\n\n**A1:** Thanks for the question. From the perspective of conversion error, I-LIF transmits integer spikes during the training stage and can switch to vanilla LIF neurons during the inference stage. However, this can only ensure that I-LIF satisfies the input current assumption consistent with the QCFS function in the sub-slices composed of every $D$ time-steps ($D$ denotes the maximum integer spike value), and cannot fully achieve lossless conversion. In addition, I-LIF is commonly used in the field of STBP training. In comparison, parallel conversion is a learning framework specifically designed for ANN-SNN Conversion and has the property of lossless conversion.\n\nFrom the perspective of calculation mechanism, I-LIF, as an enhanced version of the vanilla LIF model, still consists of three processes: charging, firing and resetting. The overall computing process is serial and has a temporal direction. In comparison, our scheme adopts parallel spiking calculation, saving the processes of charging and resetting, and enabling more efficient SNN inference.\n\n>  Whether the spike trains in this paper can be adjusted at will?\n\n**A2:** For ANN-SNN Conversion, the key to learning lies in the average spike firing rate. As shown in Eq.8, our $\\Lambda_\\text{PC}^l$ is formed by the fusion of $\\Lambda_\\text{PRE}^l$ and $\\Lambda_\\text{POST}^l$, thus possessing the ability to homogenize the distribution of input current. In other words, theoretically, arbitrarily shuffling the order of the output spike sequence $\\mathbf{s}^{(l-1)}$ will not affect the prediction of the average spike firing rate $\\mathbf{r}^{l,T}$ in the next layer.\n\nFrom the perspective of adjusting the length of the spike sequence and the number of firing spikes, by combining the calibration scheme discussed in Sec 4.2 and Eq.9, we can arbitrarily adjust the length of the spike sequence and ensure that the converted SNN model has advanced performance within any time period.\n\n> It remains an open question whether the proposed parallel transformation can be applied to the Transformer architecture.\n\n**A3:** Thanks for the comment. Assuming that the input currents through $\\mathbf{Q}^l,\\mathbf{K}^l,\\mathbf{V}^l$ are respectively $\\mathbf{I}_Q^l,\\mathbf{I}_K^l,\\mathbf{I}_V^l\\in\\mathbb{R}^T$. If the input current is directly passed through the corresponding parallel spiking neurons $\\text{SN}(\\cdot)$ and the attention score is calculated, it will introduce potential computational complexity of $O(T^2)$. Therefore, one viable solution is to pre-calculate the average input current $\\mathbf{I}_K^{l,\\text{avg}},\\mathbf{I}_V^{l,\\text{avg}}\\in\\mathbb{R}$, then complete the calculation for $\\left(\\text{SN}(\\mathbf{I}_Q^l){\\mathbf{I}_K^{l,\\text{avg}}}^{\\top}\\right)\\mathbf{I}_V^{l,\\text{avg}}$.\n\nAt this point, one can note that the computational complexity of each step is at the level of $O(T)$ and always maintains $\\mathbf{r}^{l,T}=\\sum_t\\mathbf{s}^{l,t}$. When $\\mathbf{r}^{(l-1),T}=\\sum_t\\mathbf{s}^{(l-1),t}$, $\\mathbf{I}^{l,x}=\\Lambda_\\text{PRE}^l\\mathbf{W}^l\\mathbf{s}^{(l-1)}=\\mathbf{W}^l\\mathbf{r}^{(l-1),T}, \\forall x\\in[1,T]$ holds, ensuring that the input current entering parallel neurons satisfies the distribution assumption and guarantees the precision of predicting the average spike firing rate layer by layer during the conversion process.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "Yes", "experimental_designs_or_analyses": "Yes", "relation_to_broader_scientific_literature": "N/A", "essential_references_not_discussed": "[1] Scaling spike-driven transformer with efficient spike firing approximation training. IEEE T-PAMI 2025.", "other_strengths_and_weaknesses": "Strengths :\n\n1. This paper proposes a low-time-step train-free ANN2SNN method to reduce the SNN training burden and inference cost.\n\n2. Well-written and organized.\n\n3. This work establishes a mathematical mapping between parallel spiking neurons and cumulative spike firing rates, theoretically validates the lossless and sorting properties of the conversion process, and derives the optimal shifting distance for each step.\n\nWeaknesses:\n\n1. The proposed parallel transformation is limited to the convolutional architecture, and it remains an open question whether it can be applied to the Transformer architecture.\n\n2. The proposed parallel transformation can only convert fixed ANN architectures, and the characteristics of SNNs such as spike-driven may not be guaranteed during conversion.", "other_comments_or_suggestions": "1. Please discuss in detail the difference between the conversion method in this paper and I-LIF [1], and whether the spike trains in this paper can be adjusted at will.\n\n2. The proposed parallel transformation is limited to the convolutional architecture, and it remains an open question whether it can be applied to the Transformer architecture.\n\n\n\n\n\n[1] Scaling spike-driven transformer with efficient spike firing approximation training. IEEE T-PAMI 2025.", "questions_for_authors": "1. Please discuss in detail the difference between the conversion method in this paper and I-LIF [1], and whether the spike trains in this paper can be adjusted at will.\n\n2. The proposed parallel transformation is limited to the convolutional architecture, and it remains an open question whether it can be applied to the Transformer architecture.\n\n\n\n\n\n[1] Scaling spike-driven transformer with efficient spike firing approximation training. IEEE T-PAMI 2025.", "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": "XmKE1Xlv9i", "reviewer": "Reviewer_mMJc", "summary": "This paper innovatively combines parallel spiking calculation with ANN-SNN Conversion to propose a high-performance and ultra-low-latency parallel conversion framework, which can also be applied in more general conversion scenarios (e.g. ReLU, QCFS with different quantization level). Experimental results have demonstrated that the superiority of the proposed method in terms of inference speed and performance.", "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": "## To Reviewer mMJc\n\nWe are pleased that you recognize the relevant content of this work in terms of theoretical claims and experimental validation, as well as pointing out that our method provides a new perspective for SNN supervised learning. We will elaborate on your questions and comments.\n\n> The authors can compare the specific computational overhead of vanilla IF model and parallel model in more detail from the perspective of operands (ADD, MUL)\n\n**A1:** Thanks for the question. For the vanilla IF model, the inter-layer computation (assuming the synaptic layer is a fully-connected layer $[C,C]$) involves $O(T_\\text{IF} NC^2)$ multiplication/addition operations, here $N,T_\\text{IF}$ respectively denote the total number of tokens and time-steps. The intra-layer calculation involves charging, firing and resetting, with a total of approximately $2T_\\text{IF}$ addition and $T_\\text{IF}$ comparison operands for each neuron. \n\nFor the parallel spiking model, the inter-layer computation is consistent with that of the IF model, while the intra-layer calculation can be combined with various optimization techniques proposed in Section 4.3. Specifically, when we convert $\\mathbf{\\Lambda}^l_\\text{PC} \\mathbf{I}^l$ to $[\\frac{1}{T_\\text{PC}},...,\\frac{1}{T_\\text{PC}-x+1},...,1]\\odot\\sum_t\\mathbf{W}^l\\mathbf{s}^{(l-1)}$, only $T_\\text{PC}$ addition operands are involved, where $[\\frac{1}{T_\\text{PC}},...,\\frac{1}{T_\\text{PC}-x+1},...,1]$ can be further fused with $\\theta^{l,t}$ at each time-step. This step involves $T_\\text{PC}$ comparison operands. However, due to the existence of sorting property, the comparison operand can actually be further reduced to $O(\\log T_\\text{PC})$. Overall, using parallel conversion framework can save approximately $2T_\\text{IF}-T_\\text{PC}$ addition and $T_\\text{IF}-O(\\log T_\\text{PC})$ comparison operands for each neuron layer, $O(T_\\text{IF} NC^2)-O(T_\\text{PC} NC^2)$ multiplication/addition operations for each synaptic layer, as well as achieving more superior inference performance and speed. Generally speaking, when traditional ANN-SNN Conversion reaches the same level of performance as Parallel Conversion, one can find that $T_\\text{IF}\\gg T_\\text{PC}$.\n\n> What are the differences between the DA-QCFS based calibration method proposed in this work and SNNC-LP(AP)?\n\n**A2:** Thanks for the comment. SNNC-LP(AP) is committed to extremely low-cost error calibration from pre-trained ANNs to converted SNNs, where the average spike firing rate used for calibration is based on the assumption of uniform input current distribution. Due to SNNC-LP(AP) still using the vanilla IF model in the inference stage, there is still a gap between the estimated firing rate after calibration and the actual firing rate layer by layer.\nIn comparison, the motivation of our calibration method is to achieve efficient inference of SNN under any time latency. Since parallel spiking calculation can satisfy the assumption of input current distribution, the process of replacing the rectified DA-QCFS module with parallel spiking neurons is lossless. The goal of calibration is to regulate the distribution of input current within a specified number of time-steps, so that the estimated firing rate of each layer is aligned with the highest learning accuracy as much as possible, thereby preparing for the parallel conversion process in advance.", "claims_and_evidence": "The theoretical claim (e.g. Theorem 4.1) made in the submission is supported by convincing experimental validation.", "methods_and_evaluation_criteria": "The derivation of the step-wise optimal shift term and the layer-wise error calibration based on DA-QCFS function ensure the fidelity of the conversion process.", "theoretical_claims": "I have checked the correctness of the proof for theoretical claims in this paper.", "experimental_designs_or_analyses": "According to Table 3-4 and Figure 2, compared to traditional conversion methods, parallel conversion achieves more superior performance within the same time latency.", "relation_to_broader_scientific_literature": "This paper provides a new perspective for further exploring the supervised learning schemes of SNNs (ANN-SNN Conversion, STBP Training, etc).", "essential_references_not_discussed": "At present, no previous work has been found to be omitted or improperly cited in this paper.", "other_strengths_and_weaknesses": "Strengths:\nThis paper explores the parallel spiking computation model from the perspective of conversion learning, establishing an equivalent mathematical mapping relationship between each time-step and the corresponding cumulative spike firing rate, which can also be considered as revealing the performance upper-bound of the parallel spiking model from another perspective. In addition, the authors further analyze the optimal value of the shift term and recognize the potential layer-by-layer distribution problem of the spike sequence, thus extending the proposed method to a more general conversion framework.\nWeaknesses:\nIn Section 4.3, the authors mention that the computational cost of parallel conversion can be further optimized. I suggest that the authors can compare the specific computational overhead of vanilla IF model and parallel model in more detail from the perspective of operands (ADD, MUL), so as to make the parallel conversion scheme more convincing.", "other_comments_or_suggestions": "The parallel conversion framework explores the performance upper-bound of parallel spiking computing (both precision and speed) from a new perspective.", "questions_for_authors": "SNNC-LP(AP) has also utilized an error calibration scheme before. What are the differences between the DA-QCFS based calibration method proposed in this work and SNNC-LP(AP)?\n\nLi,Y., Deng,S., Dong,X., Gong,R., and Gu,S. A free lunch from ANN: Towards efficient, accurate spiking neural networks calibration. In International Conference on Machine Learning, 2021.", "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 presents a novel and technically rigorous framework for parallel ANN-SNN conversion, combining parallel spiking computation with distribution-aware calibration. The key contributions include: (1) a mathematically grounded mapping between time-steps and cumulative spike firing rates; (2) theoretical validation of the lossless and sorting properties of the conversion process; (3) integration of an efficient error calibration technique to improve accuracy across various quantization levels and training regimes; and (4) strong empirical results on standard classification and segmentation benchmarks, with particular emphasis on ultra-low-latency inference.

The reviewers were generally positive, with three reviewers recommending acceptance (score: 4) and one reviewer leaning toward acceptance (score: 3). All acknowledged the strong theoretical contributions, clear writing, and empirical superiority of the proposed method compared to existing ANN-SNN conversion frameworks.

Strengths noted by reviewers include:

* Well-structured mathematical formulation and proof of conversion properties.

* Significant reduction in latency and computational cost, demonstrated across multiple architectures and datasets.

* Support for both training-free and training-based settings, with practical implementation details included in the supplementary material.

* Generalization beyond classification to semantic segmentation tasks, improving the perceived applicability of the method.

Concerns raised by reviewers were adequately addressed in the rebuttal:

* The authors provided detailed explanations regarding error calibration use cases, the impact of sorting properties, and implementation details of throughput measurements.

* Clarified the method’s applicability to Transformer-based SNNs and addressed differences with prior works like I-LIF and SNNC-LP(AP).

* Quantified computational savings (ADD/MUL/comparisons) compared to vanilla IF models, reinforcing the efficiency claims.

* Demonstrated the method’s generalization on segmentation tasks and discussed future directions for more diverse architectures.

Overall, the paper proposes a well-founded and practically impactful advancement in SNN training and inference. The rebuttal was thoughtful and resolved the reviewers’ concerns effectively, and the discussion reflects maturity in theoretical and empirical SNN research.
Decision: Accept (poster)