TTFSFormer: A TTFS-based Lossless Conversion of Spiking Transformer
Authors: Lusen Zhao
Zihan Huang
Jianhao Ding
Zhaofei Yu
Venue: ICML 2025 poster (2025)
Keywords: spiking neural networks
ANN-SNN conversion
time-to-first spike
spiking transformer
Primary area: applications->neuroscience_cognitive_science

Abstract: ANN-to-SNN conversion has emerged as a key approach to train Spiking Neural Networks (SNNs), particularly for Transformer architectures, as it maps pre-trained ANN parameters to SNN equivalents without requiring retraining, thereby preserving ANN accuracy while eliminating training costs. Among various coding methods used in ANN-to-SNN conversion, time-to-first-spike (TTFS) coding, which allows each neuron to at most one spike, offers significantly lower energy consumption. However, while previous TTFS-based SNNs have achieved comparable performance with convolutional ANNs, the attention mechanism and nonlinear layers in Transformer architectures remains a challenge by existing SNNs with TTFS coding. This paper proposes a new neuron structure for TTFS coding that expands its representational range and enhances the capability to process nonlinear functions, along with detailed designs of nonlinear neurons for different layers in Transformer. Experimental results on different models demonstrate that our proposed method can achieve high accuracy with significantly lower energy consumption. To the best of our knowledge, this is the first work to focus on converting Transformer to SNN with TTFS coding.

TTFSFormer: A ITFF-basee Lossless Conversion of Spiking Transformer
Lusen Zhao Zihan Huang'
Jianhao Ding' Zhaofei Yu
Abstract
for communication between neurons instead of numerical values. Compared to traditional Artificial Neural Networks (ANNs), SNNs achieve higher energy efficiency due to the sparsity of event- signaling, particularly on neuromor- phic hardware (Davies et al., 2018; DeBole et al., 2019; Pei et al., 2019).
ANN-to-SNN conversion has emerged as a key approach to train Spiking Neural Networks (SNNs), particularly for Transformer architec- tures, as maps pre-trained ANN parameters SNN equivalents without requiring retraining. thereby preserving ANN accuracy while elim- inating training costs. Among various coding methods used in ANN-to-SNN conversion, fime-tofirst-spike (TTFS) coding, which allows each neuron at most one spike, offers signif- icantly lower energy consumption. However, while previous TTFS-based SNNs have achieved comparable performance with convolutional ANNs, the attention mechanism and nonlinear layers in Transformer architectures remains a challenge by existing SNNs with TTFS coding. This paper proposes a new neuron structure for TTFS coding that expands its representational range and enhances the capability to process nonlinear functions, along with detailed designs of nonlinear neurons for different layers in Transformer. Experimental results on different models demonstrate that our proposed method can achieve high accuracy with significantly lower energy consumption. To the best of our knowledge, this is the first work to focus on converting Transformer to SNN with TTFS coding. The source code of the proposed method is available at https: github. com/ ForestoonTheaan//TEEE
The Transformer architecture (Vaswani al., 2017) has been demonstrating its strong ability in wide range of tasks with its special self-attention mechanism, from natural language processing to computer vision (Dosovitskiy et al., 2020), Recent efforts to integrate Transformers with SNNs seek to combine the information processing ability of Transformers with the energy efficiency SNNs, achieving promising results in many tasks (Wang et al., 2023; Yao et al., 2023).
Currently, there are primary approaches for training spiking transformers: direct training and ANN-10-SNN con- version. Direct training methods (Yao et al., 2023; Zhou et al., 2023b;a) rely on surrogate gradients (Neftci et al., 2019) to perform backpropagation on networks, which ap- proximates the non-differentiable spike series with continu- ous functions (e.g., sigmoid or tanh) during gradient compu- tation. However, direct training of large-scale SNNs from scratch (Yao et al., 2023; Zhou et al., 2023a) requires high computational resources, posing major challenge in its scalability and efficiency. In contrast, ANN-to-SNN con- version (Wang et al., 2023; Jiang et al., 2024; Huang et al., 2024) maps pre-trained ANN parameters to SNN counter- parts without requiring retraining, thereby preserving ANN accuracy while eliminating training costs. However, pre- vious Transformer- to IN-SNN methods primarily rely on rate coding, where information is encoded through spike counts over time. A key limitation is that precise value represen- tation often requires multiple spikes, which reduces energy efficiency.
git.
1. Introduction
Spiking Neural Networks (SNNs), known as the third gener- ation of neural networks (Maass, 1996), are promising due their low computational cost and biological plausibility. Inspired by biological neurons, SNNs utilize binary spikes
Recent evidence from neuroscience suggests that biolog- ical neural systems encode information not only through firing rates but also via precise spike timing (Gütig & Som- polinsky, 2006; Montemurro et al., 2008; Park et al., 2019). Temporal coding methods leverage this observation by repre- senting values through spike timing rather than spike counts. Notably, fiiett--irst-spike (TTFS) coding achieves high energy efficiency by encoding information in the latency of single spike (Rueckauer & Liu, 2018). However, TTFS-
Peking University, China. Correspondence to: Zhaofei Yu <yuzf12 @wt.@epu.uu..........
Proceedings of the 4rnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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TTFSFormer: A TTFS-based Lossless Conversion of Spiking Transformer
based ANN-to-SNN approaches have far been limited to Multi-Layer Perceptrons (MLPs) and Convolutional Neural Network (CNN). In this work, we propose the first TTFS coding framework for Transformer conversion, which si- multaneously maintains high accuracy and reduces energy consumption through precise spike timing. Our main contri- butions are summarized as follows.
two primary representation methods in SNNs: rate-based encoding and temporal bbased encoding.
Rate-based SNNs map the value to the frequency of spikes. Specifically, if a neuron emits N spikes over T time steps, NN it represents the value T E [0. 1]. Rate coding has been widely adopted in previous studies, demonstrating compara- ble performance ANNs, including both directly trained SNNs and those converted from ANNs. However, rate- coding typically requires multiple time steps to efficiently approximate the value with spikes, which results in higher energy consumption.
We analyze the limitations of the representation ability of previous ITFS-basee methods.
We propose generalized type of TTFS- based neuron, enabling the lossless conversion of all layers in the Transformer architecture into an SNN while signifi- cantly reducing energy consumption.
Temporal- -base SNNs, inspired by the temporal informa- tion observed in biological neural systems, map the value to the timing of spikes. These methods include time-to-first spike (Thorpe et al., 2001), reverse coding (Zhang et al., 2019; Park et al., 2020), phase coding (Montemurro et al., 2008) and burst coding (Park et al., 2019). TTFS repre- sents the value by the exact time of the single spike emitted, where a higher value results in an earlier spike. Reverse coding (Zhang et al., 2019; Park et al., 2020), in contrast, make the convention that the stronger the input stimulus is, the later the corresponding neuron fires spike. Phase coding generates the post-synaptic potential (PSP) based on the phase of periodic oscillatory function. Burst coding encodes information through sequence of spikes with short inter-spike intervals. Temporal- methods are typically more energy-efficient than rate-based methods, as they re- quire fewer spikes to represent a value. However, despite the variety of temporal- SNNs, previous studies have largely focused on simple network architectures, such as MLPs and CNNs.
We evaluate our method on various pre-trained Trans- former models, including VIT and EVA, using the ImageNet- IK dataset. Experimental results demon- strate that our approach achieves performance compa- rable to ANN counterparts. Specifically, the accuracy loss of the converted ViT and EVA models, across different parameter sizes, remains below 0.1% with precise representation of TTFS spike timing.
To the best of our knowledge, this is the first work to explore TTFS-based SNNs within the Transformer architecture.
2. Related Works
2.1. Transformer for Visual Tasks
With its specialized attention mechanism that captures con- textual information, the Transformer (Vaswani et al., 2017) has become dominant across various fields of machine learn- ing, including natural language processing and computer vi- sion. By dividing an image into blocks and converting them into tokens, the Vision Transformer (ViT) (Dosovitskiy et al., 2020) successfully adapted the Transformer architecture for visual tasks, effectively processing spatial information. The EVA model (Fang et al., 2023; 2024) further introduced ad- ditional techniques, such as the gated linear unit and various activation functions, significantly enhancing performance.
2.3. ANN-to-SNN Conversion
To address the challenges posed by the non-differentiable spike generation function in SNN training, the ANN- to-SNN conversion method effectively leverages well- established techniques from ANN training to achieve high performance. Cao et al. (2015) initially proposed obtain- ing an SNN by training an ANN and then converting it. The resulting SNN conveys information through spike rates, commonly referred to a rate-based SNN. Building on this, Diehl et al. (2015) reduced the accuracy gap between the source ANN and the converted SNN through weight normal- ization. Subsequent studies have further narrowed this gap by employing tailored activation functions or specialized adjustments to spiking neurons (Ding et al., 2021; Bu et al., 2022: Hao et al., 2023). It is important to note that these approaches are primarily based on deep CNNs.
2.2. Spikes Coding Methods in SNN
One of the key differences between SNNs and ANNs that SNNs use spikes to transmit information between layers, whereas ANNs rely on Moating-point numbers or integers. The representation method, which defines the mapping be- tween the value and the pattern of emitted spikes, plays crucial role in both encoding external inputs and decoding model predictions. This makes it a critical issue in SNN ar- chitectures. Considering the tra between performance and energy efficiency, previous studies have focused on
With the growing significance of Transformer architectures across various tasks (Dosovitskiy et al., 2020; Fang et al., 2023), recent studies have also explored rate-based con- verted SNN Transformers. Wang et al. (2023) were the first
2

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TTFSFormer: A TTFS-based Lossless Conversion of Spiking Transformer
apply the conversion method on Transformer architec- tures. Jiang et al. (2024) introduced the Spatio-Temporal Approximation (STA) method, which approximates nonlin- ear operations using multiple neurons, referred to as the universal group operator. STA bridges the gap between Transformers and SNNs but results in higher energy con- sumption and increased latency. Huang et al. (2024) further improved the performance by incorporating an expectation compensation module (ECM) and multi-threshun neurons, achieving lower accuracy loss with fewer time steps. How- ever, multiplication operations still remain present in the activation layers.
ensuring that the corresponding value remains within [0, 1..
3.2. TTFS-based Neurons
Inspired by biological neurons, ITFS-basee neurons receive spikes from the previous layer and maintain membrane po- tential V that evolves over time. Once the potential reaches the threshold 6, the neuron emits spike. The temporal dy- namics of the membrane potential in a TTFS-base -baed neuron can be described by the following equation:
N v(t) = Σ di
d
While rate-based conversion has demonstrated high per- formance, some ANN-to-SNN conversions also leverage temporal-basee encoding methods. Rueckauer et al. (2018) first proposed several temporal- conversion methods. Zhang et al. (2019) explored the effective conversion of deeper ANNs into SNNs using TTFS coding, and Park et al. (2020) further improved the performance. Previous TTFS-based studies introduced conversion errors across lay- ers until Stanojevic et al. (2023; 2024) demonstrated an ex- act mapping from ReLU network to SNN. Building on this, they further developed a brased training method. How- ever, while TTFS-basce SNNs can achieve performance comparable to their corresponding CNN models, no previ- ous TTFS-based SNN has involved Transformer architec- ture, which can achieve superior task performance.
w wkK(t - (.) +C,
(2)
where t; represents the presynaptic spike time of the i-th neuron in the previous layer, and w; is the corresponding synaptic weight. Each presynaptic spike induces a postsy- naptic potential (PSP). modeled by the kernel function (.). C is a constant, and T represents the time constant.
Various kernel functions have been proposed for construct- ing TTFS-based SNNs. Stanojevic et al. (2023) utilized the Heaviside function as the kernel function to establish an exact mapping from ReLU neurons to TTFS- based neurons:
K(t - t.) = H(( - t.) = 1[t t, 2 0j,
(3)
where I[() denotes the indicator function. The use of the Heaviside function enforces a linear relationship between presynaptic spike times and their corresponding postsynap- tic spikes, making it challenging to construct complex non- linear mappings.
3. Preliminaries
In this section, we introduce key techniques from previous studies that implement TTFS encoding and enable TTFS- based ANN-to-SNN conversion. These techniques address the challenges of directly training SNNs while leveraging the advantages of TTFS encoding.
Another recent work by Goltz et al. employed the current- based (CuBa) neuron model (Göltz et al., 2021), where the kerne function is defined as:
3.1. TTES Encoding
K (.)) = H(t - 4.) exp(
(4)
Inspired by biological observations that precise spike tim- ing is important for communications between neurons, TTFS-based SNNs can operate with at most one spike per time window per neuron by utilizing precise spike timing, achieving higher energy efficiency compared to rate-based SNNs (Rueckauer& & Liu, 2018).
where т is a constant. This kernel function, also known as the alpha-PSP response function, facilitates the gradi- ent computation with respect to spike times. Goltz al. constructed a TTFS-based SNN using the CuBa neuron model and directly trained the network. However, the SNNs were only evaluated on small datasets, and their scalability remains unverified.
Recent studies have adopted a linear relationship between input values and spike times, effectively enabling the con- version of ReLU-based ANNs to SNNs while preserving accuracy and computational efficiency (Stanojevic et al., 2023; 2024). The linear relationship of TTFS between the spike time t and the represented value x: is defined as
3.3. TaFS-based ANN-to-SNN Conversion Method
The TTFS-based ANN-to-SNN conversion method requires precise spike timing to represent the layer-by-layee activa- tions of deep ANNs. Currently, an exact conversion ap- proach involves dividing the activation process of spiking neurons into two stages: the receiving stage and the emit- ting stage. During the receiving stage, the neuron receives
tmax t
(1)
fmax
fmin
where (Mmin [max] defines the available range of spike times,
3

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TTFSFormer: A ITTES-bascl Lossless Conversion of Spiking Transformer
performance than ReLU. Extending the representational range is necessary for effective TTFS-based conversion.
Secondly, the existing TTFS- based conversion methods struggic to handle the attention mechanism and Layer Norm in Transformers. The attention mechanism relies on the softmax operator, which is nonlinear, rendering existing TTFS-based methods inapplicable. Additionally, no TTFS- based implementation of Layer Norm has been proposed in previous studies. Addressing these challenges is essential for adapting TTFS-based SNNs to Transformer models.
Layer (n- 1)
receive
emit
Lasr
receive
emit
Layer fn 1)
receive
emit
time
Figure 1. The pipeline of the receiving and emitting stages.
4. Method: TTFSFormer
spikes from the previous layer, with its activation inhibited by setting a sufficiently large threshold. In the emitting stage, the neuron emits a spike to the next layer once the potential exceeds the threshold. Dividing the activation pro- cess into two stages effectively prevents the severe accuracy loss that occurs in single-stage activation process, where early spike emissions from preceding neurons interfere with the complete processing of incoming information (Rueck- auer & Liu, 2018).
In this section, we propose generalized nonlinear neurons for converting Transformer activation functions. Using these neurons, we construct key Transformer layers and outline the complete conversion process, which we refer to TTFS- Former.
4.1. Neuronal Dynamics in TTFSFormer
To overcome challenges in effectively representing nonlin- ear activations and accommodating extended value ranges, we incorporate two flexible kernel functions in the dynamics of TTFSFormer neurons and introduce the zero reference time mechanism.
An overview of the receiving and emitting process in the network is shown in Figure For convenience, we assume that the receiving stage of layer corresponds exactly to the emitting stage of layer (n 11++ 1). We denote the time range of the receiving stage as [Traa), rol) and the emitting stage as (T(m) emii: I in the n-th layer. Thus, T T and T(() end = -r(att) The membrane potential dynamics of the i-th neuron in layer n are given by (Stanojevic et al., 2023; 2024):
With the initial value V:(m) (Ible) O., the change of the potential of the neuron in layer n satisfies the following equation:
Egg wis
Tii (1 11--11) + c.
(m)
d (m) df 1
(m)
+ E, w
H(t H(t '
1)-1))
E (Teev: T((m) Te )
d v(n) dl
t E Tlaey rlnn)
ul (t- Tr(a)
E [T Tmmit I(()).
((N))
t [T(M) emit T((m)) )
(6)
(5)
(n) where wig are the weights of the n-th layer, (nn is the spike time of the j-th input, the input transform kernel
(n) where A!n) and B(")) are predefined constants, wi repre- sents the synaptic weight, and 1 ffr-1) denotes the spike time of the j-th presynaptic neuron.
(n) Mij is function satisfying (1()) (s) 0, Vs < 0, c(") is a constant, the output transform kernel v.(")) is non- negative function, and (()) is the time constant of the n-th layer.
Despite TTFS-based ANN-to-SNN conversion methods have been explored, their application to Transformers re- mains limited. This limitation arises mainly from two as- pects.
The relation between the spike time +./") in the n-th layer of SNN and the corresponding activation value (n)) in the n--hh layer of ANN is
- T(nd)
First, TTFS- based neuron is limited by its representational range. Using the widely adopted mapping of spike time to values defined in Equation (1), the spike time can only represent values in the range of [o, 1J. which works well for ReLU-based networks. However, Transformer architectures often use complex activation functions like GELU (Hendrycks& & Gimpel, 2016) and SiLU (Elfwing et al., 2018), which retain negative values and offer better
(n) (n) (n)
T(a) ((m)
where the zero reference time T.(n) is manually selected.
A spike at time T(x)) represents and larger value will result in an earlier spike. For simplicity. in the following
discussion we denote g(m) (((7) T(()) as the time step
4

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TTFSFormer: A TTES- based Lossless Conversion of Spiking Transformer
of layer n. We assume the length of the time step is the same across all layers.
V
V
2.86 V 0.73
-0227
By modifying T(a) and 7("), we can adjust the repre- sentational range [a(m), b(r) in layer n flexibly, where T Tend and ((m) T -rim We denote the
a(m)
emit
p(m)
+(m)
difference between these bounds d(n) b(m) a!m).
4.2. Representational Ability of TTFSFormer Neurons
We theoretically prove that TTFSFormer neurons possess the representational capacity to convert Transformer archi- tectures into SNNs by modifying the input and output trans- formation kernels 1), v
3 15
Receiving Stage
Emitting Stage
4.2.1. INPUT TRANSFORM
Figure 2. The dynamics of SiLU neuron, with input range [-3, 3] and output range [-1,3]. By Equation (16), in receiving stage, the potential increases and then decreases, and finally the rate of change tends
v=(")(((())) can be regarded as a linear combination of transformed input values. The coefficient of combination is determined by while the transformation for input values is determined by 7). Here is generalized way to construct for given transformation f.
superseript since only one neuron is involved in emitting stage.
Theorem 4.1. Let Jij : (a(n-1), (m(-1)) + R be differen- tiable functions. If we let
For simplicity, denote the clip function as
< a I r E aa b).
{ fig (FrAn + a(a-11)
(n) (8) Mi (5) = (0
8 P 0
clip(s, a. b)=
(12)
8<0
b.
(8)
fis(a(n-1))
d! = Σ wis d(n-1)
A general method to construct output transform by modify- ing &p is shown in Theorem 4.3.
then the potential at time gr(n) is
Theorem 4.3. Let h A + R be differentiable monotone increasing function, and its inverse h- is well-defied on (a, b). If we let
Vll
(n)
eaiit
Σ
(m) way fey(z)
(9)
v0() 7h' (b-1 (b- +)) , (0,0),
We call the potential at time [-(n) of a neuron in layer n as its accumulated potential. Previous works use identity input transforms, which a special version of Theorem 4.1. Corollary 4.2. In particular, if we let
(13)
0= h hb)-
then the value x represented by the output spike is
(s) H
1] + +a(x-1))
I = clip(h(V a, b).
(14)
(n-1)
(10)
clm) = Σ 1) Wifs
Previous works adopt identity output transform, which is special version of Theorem 4.1.
Then v.(m) (I((n)
Corollary 4.4. particular, if we let (b(s) 4,0 b. (11) then the value x represented by the output spike is
Σ
wiy 2
(x) (n-1)
which is called an identity input transform.
clip V (Temit) a, b).
(15)
which called an identity output transform.
4.2.2. OUTPUT TRANSFORM
Now consider the relation between V (T(())) and the output spike. For simplicity, we omit the subscript and
The identity output transform is equivalent to what used in previous work.
5

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TTFSFormer: A STFSS-asee Lossless Conversion of Spiking Transformer
i.e. log Ei=1 e" can be calculated in single neuron with
log
11 (x) = exp
5
+
ta(o)
kml
((0)
(
n
ea
41
d(u)
(19)
80 (s)
1
exp (b -(1)
7(1)
Jn
where the current layer is layer 1.
Figure 3. Structure of softmax operator for 21, t. Za (black lines). The brown part is the log-sum-exp neuron, with the blue arrows as its input and red arrows as its output.
With the log-sum-exp neuron, we can obtain the softmax operator. We can calculate the logarithm of softmax, i.c.
4.3. Constructing TTFSFormer Layers
log Ljز
I2 log
(20)
The Transformer architecture involves several non-linear layers. In this part, we will design their construction using spiking neurons.
==1
by subtracting the log-sum-exp from Tú. Finally, we can obtain the output after an exponential layer. The whole process is shown in Figure 3.
4.3.1. ACTIVATIONS
Every activation function can be implemented in the input transform stage according to Theorem 4.1. SiLU and GELU are two widely used activations in Transformer architec- tures, which can be constructed in TTFSFormer using the dynamics below.
4.3.3. LAYERNORM
LayerNorm a normalization method widely used in trans- former architecture, achieving better results than Batch- Norm, which is a linear operation. LayerNorm is defined
Corollary 4.5 (Construction of SiL.U/GELU). neuron with input range (a, bl, time step and the identity output transform in Corollary 4 can represent SiLU function with
as
-- E(x)
LayerNorm (x)
7 B. (21)
/Vrr(z) +E
The LayerNorm operator can be obtained by the following parts. Firstly, the mean I can be caleulated directly by single neuron, after which we subtract z from each x;. Then, obtain the variance Var(x) by single neuron with
(>)) I[s 0] (u))
(u+1 -u)((,),
8
1
(16)
where
(zz)
1 e
or GELU function with
(2) (8)
+ (a)
T (0)
erf(
(0)
(22)
(()) = T[s 2 0]
+
v2
(a))
(1)
2
2m
()
(17)
where 5
s, erf(x)
22
dt.
and identity output transform. After that, we can get /Varr= by single neuron with
A full example of SiLU neurons is shown in Figure 2.
1 a(1)) -
(s)
7(1)
(23)
4.3.2. SOFTMAX
(
w((2) =1
d(a) +
Softmax is another important operation in the attention mechanism. The softmax of row vector (I1, ... Fn) is defined as
and identity output transform. Finally, multiply x, with VVr++e" which is discussed in Section 4.3.4.
( 6
Cn
Softmax(z1."". (,n))
4.3.4. MULTIPLICATION
E,
E
Σ, e5
(18)
Multiplication is one of the core operations in the attention mechanism of Transformer. We first consider the multiplica- tion of two neurons 21, 22 E (a) b(0), with which we can implement matrix product and pointwise product directly.
Firstly, we construct the log-sum-exp neuron.
Theorem 4.6. The log-sum-exp of n inputs 31, F2, ... Ans
6

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TTFSFormer: A TTES- Lossless Conversion of Spiking Transformer
Table Comparison between method and previous works ImageNet dataset
Work Spikingformer (Zhou et al., 2023a)
Method
Architecture
Param.
SNN Acc.
ANN Acc.
Spikingformer-85511
29.68M
74.79%
Direct Training
Spikingformer-& 8--6-
66.34M
75.85%
Spike-Driven (Yao al., 2023; 2024)
SpikeDriven- V1 SpikeDriven--2
66.34M
77.07%
Direct Training
55,4M
80.0%
E-Spikeformer (Yao et al., 2025)
E-Spikeformer
83.0M
85.2%
Direct Training
E-Spikfformer
173.0M
86.2%
SRP (Hao et al., 2023)
ResNet-34
21.8M
68.61%
74.32%
CNN-to-SNN
VGG-16
138M
69.43%
74.29%
Lossless TTFS
CNN-to-SNN
ResNet-34
21.8M
75.36%
74.32%
(Stanojevic al., 2023; 2024)
(TTFS-based)
VGG-16
138M
75.66%
74.29%
MST (Wang et al., 2023)
Transformer-to-SNNN
Swin-T(BN)
28.5M
78.51%
89.51 %
STA (Jiang al., 2024)
Transformerrto-SNNN
ViT-B/32
86M
82.79%
85.10%
ECMT (Huang et al., 2024)
ViT-L/16
307M
84.60%
85.83%
Transformer-t-SSNN
EVA-G
1074M
88.60%
88.88%
VIT-S/16
22M
81.45%
81.38%
SpikeZIP-TF (You et al., 2024)
Transformerto-S.NNN
ViT-B/16
86M
82.71%
85.10%
ViT-L/16
307M
83.42%
85.83%
AdaFire (Wang al., 2025)
ViT-S/16
22M
77.09%
81.38%
Burst Coding
ResNet-34
21.8M
75.38%
74.32%
ViT-S/16
22M
81.40%
81.38%
ViT-B/16
86M
85.07%
85.10%
Transformer-o-SNNN (TTFS-based)
ViT-L/16
307M
85.78%
85.83%
TTFSFormer (Ours)
EVA-G
1074M
88.90%
88.88%
EVA02-S
22.1M
85.68%
85.72%
EVA02-L
305M
90.03%
90.05%
Now construct two-layer network that computes their product 22
value. By Theorem 4.1, with
(2) (s) = exp (r0) + +aw) 7o
(26)
Layer I. The neuron on layer I takes T2 [a("),bf ((0) as its input value. Let constant (0) +1 1. By Theorem 4.1, with
for the input y, the identity input transform settings illus- trated in Corollary 4.2 for input 01, and
(s)
-(0] (0)) + c
1 7(0)
(24)
d(1) col)
2c
0
(1)
d(1)
(27)
w
(2)
(2)
w =1 w
w
the accumulated potential is
for y, y, T2 respectively, the accumulated potential is (2) (I z + c² In the output transform, by
((((T(1)) emite ) log(21 + c) + log(#2 + c)
(25)
letting / (s) 7 and ((2) ((2) è² we get the final
log(x122 cz1 cD2 + c?)
output representing 1
By taking the identity output transform illustrated in Corol- lary 4.4, the neuron produces the output = 1og(n102- + cØ1 + cD2 + c²).
5. Experiments
In this section, we evaluate our ITTFS-bace converted SNN methods on the ImageNet- 1k dataset (Deng al., 2009) and
Layer II. The neuron on layer Il takes y, 21, 22 its input

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TTFSFormer: A TTFS-based Lossless Conversion of Spiking Transformer
compare with the corresponding ANNs and other previously proposed SNN methods. Moreover, we estimate the energy efficiency and explore the robustness of our method.
Table 2. Energy consumption for different architectures
Architecture
OSNNN (x109)
ESNN
Bsx
We test the conversion method on various architectures with different model sizes, including ViT (ViT-s, ViT-B, ViT- L) (Dosovitskiy et al., 2020; Steiner et al., 2022) and EVA (EVA-S, EVA-L) (Fang al., 2023; 2024). The weights are sourced from public repositories on Hugging Face. Us- ing pre-trained ANN models, SNNs obtained through Algorithm I in the supplementary material. The detailed results are presented in Table 1, along with comparisons to state-of-the-ar SNN methods.
BANN
ViT-S/16
5.42
4.9mJ
22.3%
ViT-B/16
19.2
17mJ
21.0%
ViT-L/16
65.7
59mJ
20.7%
90
80
Accuracy
70
5.1. Experimental Results
60
Generally speaking, our method achieve comparable perfor- mance to the original ANN architecture, with less than 0. % drop in accuracy. Specifically, we achieve accuracies of 85.8% and 90.0% for the ViT-L/16 and EVA-L architectures respectively. Furthermore, the results of these large models demonstrate the superior scalability of our approach.
50
ViT-S
VIT-B
40
Precise
4096
1024
512
384
Time precision p
Our work outperforms previously proposed SNN Transform- ers. By leveraging pre-trained ANN models, we achieve sig- nificantly higher accuracy than directly trained SNN Trans- formers, while maintaining low computational cost.
Figure 4. Accuracy of VIT under different time precision of TTFS
equation provided in (Rathi & Roy, 2023):
EssN OPSNN EAC
Compared rate-coding based SNN conversion methods Transformer architectures, such as STA (Jiang et al., 2024), ECMT (Huang et al., 2024), and SpikeZIP-TF (You et al., 2024), our proposed method further bridges the gap between the accuracy of SNNs and the original ANN SNNs obtained from rate-coding methods require multiple spikes to approximate the activation value, which creates gap between the activation values of an ANN layer and the mean firing rates of the corresponding SNN layer, especially for non-linear layers. In contrast, the TTFS encoding method conveys the output of layer in a single spike, allowing the next layer to receive complete information as soon as it receives spikes.
(28)
EANN OPANN EMAC
The operation counts OSNNN are summarized in Table 3 in Appendix C. We set EAC 0.9p. and ΣлΑΑ 4.6pJ according to (Horowitz, 2014). The calculated energy con- sumption is shown in Table 2. The results indicates that our method achieves comparable performance to the original ANN architecture with only about 20% energy consump- tion.
5.3. Robustness
In previous sections, the emitting and receiving processes are simulated by passing the time-to-fiss--pile across dif- ferent layers using floating-point values for TTFS. However, due the limitation of hardware implementation, the accu- racy of TTFS can hardly be accurate as 32-bit floating- point numbers. Thus, we explore the robustness of our implementation in this section.
Compared to previous TTFS-based conversion meth- ods (Stanojevic al., 2023; 2024), we successfully integrate Transformer architectures into SNNs by utilizing the pro- posed neuron model and achieve significantly better results than TTFS-based convolutional SNNs.
In hardware implementation, we define the time precision p of TTFS as the ratio of the time step d the maximum error ____ Emax of the simulated values for TTFS, given by p cmm We test the accuracy loss of ViT models under different TTFS time precision, shown in Figure 4. Our method can obtain comparable performance to the original ANN without fine-tuning at a time precision of 1024 or higher. However, the performance declines with decreasing time precision, which requires a trade-off between latency and
5.2. Energy Estimation
Since in TTFS coding, the input activation is encoded into one spike before it reaches the first layer. Consequently, there is no need to perform multiplication operations in the first layer. The energy cost can then be expressed using the
8

---

TTFSFormer: A TTES-based Lossless Conversion of Spiking Transformer
accuracy.
neuromorphic manycore processor with on-chip learning. IEEE Micro, 38(1):82 2018.
6. Conclusion
DeBole, M. V., Taba, B., Amir, A., Akopyan, F,, Andreopou-
In this paper, we propose a novel conversion method of the transformer architecture with TTFS-coding, which is the first work on TTFS-based spiking transformer to our best knowledge. With the proposed structure of general- ized neurons in TTFSFormer, our method is able to convert transformer architecture into SNN with little accuracy loss. Taking full advantage of the energy efficiency of SNN, our method achieves a comparable accuracy to the original ANN architecture with much lower energy cost.
los, A., Risk, W. P., Kusnitz, J., Ortega Otero, C., Nayak, T. K., Appuswamy, R., Carlson, P. J., Cassidy, A. S.. Datta, P., Esser, S. K., Garreau, G. J., Holland, K. L., Lekuch, S., Mastro, M., McKinstry, J., di Nolfo, C., Paulovicks, B., Sawada, J., Schleupen, K., Shaw, B. G., Klamo, J. L., Flickner, M. D., Arthur, J. V., and Modha, D. S. Truenorth: Accelerating from zero to 64 million neurons in 10 years. Computer, 52(5):20-29, 2019.
Deng, J., Dong, W., Socher, R., Li, L.-J., Li, K., and Fei-Fei, L. Imagenet: A large-scale hierarchical image database. 2009 IEEE Conference on Computer Vision and Pat- tern Recognition, pp. 248-255, 2009.
The TTFS-coding demonstrates both strong representational capability in representing information and perfect energy efficiency. The TTFS-coding method might be promis- ing direction for future works. While method focuses on ANN-to-SNN conversion, future works can explore training framework for TTFS-coding transformer SNN.
Diehl, P. U., Neil, D., Binas, J., Cook, M., Liu, S.-C., and Pfeiffer, M. Fast-classifying high-accuracy spiking deep networks through weight and threshold balancing. In 2015 International Joint Conference on Neural Networks (IJCNN). pp. 1-8, 2015.
Acknowledgments
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.
Ding, J., Yu, Z., Tian, Y., and Huang, T. Optimal ANN-SNN conversion for fast and accurate inference deep spiking neural networks. Zhou, Z.-H. (ed.), Proceedings of the Thirtieth International Joint Conference on Artificial In- lelligence, IJCAI-21, pp. 2328-2336. International Joint Conferences on Artificial Intelligence Organization, 8 2021. Main Track.
Impact Statement
This paper presents work whose goal is advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., and Houlsby, N. An image is worth 16x16 words: Transformers for image recognition at scale. CoRR, abs/2010. 11929, 2020.
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TTFSFormer: A TTFS-based Lossless Conversion of Spiking Transformer
Algorithm I Converting ANN into TTFS-based SNN
Input: ANN P.
Select the time step according hardware.
Set the constants [ T + nı and Trln) T((n + ô, where 7 is the tick when simulation begins.
for layer Ln in do
Monitor the range of output X, [an, Dn]. bn -an"
Select the time constant 7(n)
Set T ( + bnr(")
if L, ref
Softmax or L, is LayerNorm then
Simulate the spiking counterpart illustrated in Sections 4.3.2 and 4.3.3. Monitor the range of the output in each intermediate layer.
end if end for
for layer L, in P do
Convert Ln into a Spiking Layer according to Section 4.3.
end for
A. Experiment Details
The whole conversion process is shown in Algorithm 1. We'll discuss some details in this part.
A.1. Setting the Constants
Since we're re using adjustable parameters T and Tret, we can set the Ja, b] such that nearly all outputs lie within the range. More specifically, if the output range is (a, b], we can set
br = Tref Temit,
(29)
aT Trel Teud
which indicates that and Tiet Temit bt.
A.2. Evaluating
Evaluating the SNN is similar ANN except for the conversion between spikes and values. Since the network takes spikes as its input, pixel value x E R is turned to a spike at time t = ( IT. Besides, as the output of the network are actually spikes, the spikes should be turned back into real values. However, in image classification, the prediction given by the index of the earliest spike, and there is no need to convert the spike back into real values.
ref
12

---

TTFSFormer: A TTES-based Lossless Conversion of Spiking Transformer
B. Proof of Theorem
B.1. Proof Theorem 4.1
Proof. Consider the potential change in the receiving stage.
Toin
V (n) (T
Σ
(n) (m)) (t -t- 11 1/1-1)) + c:7²) dt
wiy
Mig
T(a emait
1)
- (l
Foud
Σ
(n)
Tij (s) ds + d(n-1) c.a))
(m)
Wij
p(n-l) and
2oa 1 +)
Σ (n)
mn/n)
Mi (n) (s) ds d(n-1) c..mm)
7(1-1) 1
(30)
fis (يسسー1) alu-11) - (1 fa(n-11)
Σ
why
(n)
+ d(n-1) c.!))
Σ w (faglo)=-1) f()(a(n11)) + d dln)
Σ (o fio(a!u-1)
B.2. Proof of Theorem 4.3
Proof. Denote g = --11 Since h(g(x)) x, we have
x((((z))-g'<>) =
(31)
by taking the derivative of both side.
If the spike is emitted at time E [Tomit, Tend), i.c. the corresponding value E (a, 6). Then
Tomit
0 (Teemit)
j (1s) ds
Trat Tomis 1
r g (D. 8) )) ds
V(Temit)) j
(32)
7
[(b-x)
V(Tomit) 9 (b
7
(TTemi)) g(x) + g(b)
Thus
g(x) = (Teemit)
(33)
which indicates that
x = h(V(Tema)) E (a, b]
(34)
If (TV > b, then ((Temit) > g(b) 0, which means that spike is emitted once the emitting window begins, i.e. at Temit representing the value Tea--Tame 6. If (VVVV(VVenn (Temit)) < a, then the potential at time Tend is (according what we calculated before)
([Temit) + I (s) = (Temit)
8 11 V -g(a) + g(b) < gb( = 0
(35)
which means that there will be no spike, representing the value a.
13

---

TTFSFormer: A TTES-based Lossless Conversion of Spiking Transformer
Table Energy consumption for all layers
Layer
Operand Size
Number of Neurons
Operation Counts
MatMul(A A, B)
A E RRMX and B TR
MN + +1)
MN(3K + 2)
(oftmax(x)
E R
2(N +1)
6
LayerNorma (x)
I E R
3N + 3
9N -
Activation (GELU/SiLU) f(A)
A E R M
MN
MN
C. Detailed Construction of Operators
In this part, we give detailed construction of the operators mentioned before, along with some less important optimization techniques.
C.1. Multiplication
The product of two neurons can be calculated by two-layer network, described in Section 4.3.4.
In the multiplication of matrix A E RM K and matrix B E RR*N, we need M NK neurons in the first layer, each taking Ask Bkj as input for < i S M, < k < K, S S N. In the second layer, we should combine the neuron that shares the same k, i.e. each neuron takes {Aik, Buj. yayl < & < K} as input for s s M, 1 I j S N.. The threshold should be changed into ((2) ((2) K22.
C.2. Softmax
Consider n neurons with input æ1, ". E (a b(0)).
Layer (Optional). The result of softmax wouldn't 't change we subtract a constant for all 24, which can improve the numerical stability of softmax. If we choose subtract max; 24z may need to add layer 0.
More specifically, we can add "maximum" neuron taking #1,-. , In its input, and emit a spike the first time it receives any input spike. The neuron represents the maximum value among all z,. Layer contains n neurons in addition to the maximum neuron, where the i-th neuron do the subtraction of x; and max; Zz.-
Layer The first layer contains neuron described in Theorem 4.6, whose output y = log E, e
Layer II. The second layer contains n neurons, where the i-th neuron takes x; and y its input. With identity input transform and weight for 2; and -1 for y, get the accumulated potential x; y. With
e2 (x) "
(3)
(36)
T Tru Temit 5
(2) log (2)
We get the output
exp
I; - log
=
(37)
2j=1 e
j=l
The result of softmax function must be in (0, 1), so we can set (2) 02) = 1.
14


Reviews:
[{"review_id": "pOfMiGK93I", "reviewer": "Reviewer_Cfcp", "summary": "This paper propose an ANN-SNN conversion method for spiking transformer based on time-to-first-spike (TTFS) method. The author first analyze the limitations of the previous TTFS method, and then propose a generalized TTFS neuron, which make it easier to relate Transformer to its SNN version. Experimental results on ViT and EVA models demonstrate the SOTA performance of the proposed method.", "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": "Thank you for your positive and thoughtful comments. We are encouraged that you find our idea impressive. We are glad you agree that our method achieves SOTA performance with low energy consumption. We would like to address your concerns and questions in the following.\n\n### 1. Please clarify how to compute the energy consumption in Table 2.\n\nThanks for your question. Our energy estimation follows the methodology proposed by [Nitin Rathi and Kaushik Roy,  2020]. For clarity, we analyze operations in a ViT block, categorizing them into **linear** (standard TTFS neuron dynamics, as in prior work) and **non-linear** (novel to our method, with hardware-dependent energy costs). Below is the list of operations (where d=384 or 768 or 1024 for ViT-S/B/L respectively):\n\n\n| Type | Notation of Parameters | Shapes | SNN Ops | ANN Ops |\n| :---: | :---: | :---: | :---: | :---: |\n| LayerNorm | (M, N): Matrix $X \\in \\mathbb{R}^{M \\times N}$ | (197,d), (197,d) | $2 \\cdot 197 \\cdot (9d+1)$ | $2\\cdot 197\\cdot d$ |\n| MatMul | (M, K, N): Matrix $A \\in \\mathbb{R}^{M \\times K},B \\in \\mathbb{R}^{K \\times N}$ | (197,d,197), (197,197,d) | $197 \\cdot [197 \\cdot (3d + 2) + d \\cdot (3\\cdot 197+2)]$ | $2\\cdot 197^{2}\\cdot d$ |\n| SoftMax | (M, N): Matrix $X \\in \\mathbb{R}^{M \\times N}$ | (197,197) | $6 \\cdot 197^{2}$ | $197^{2}$ |\n| GeLU | (M, N): Matrix $X \\in \\mathbb{R}^{M \\times N}$ | (197,4d) | $197 \\cdot 4d$ | $197 \\cdot 4d$ |\n| Linear | (M, K, N): Matrix $X \\in \\mathbb{R}^{M \\times K}$ and weight $W \\in \\mathbb{R}^{K \\times N}$ | (197,d,3d),(197,d,4d),(197,4d,d) | $11\\cdot 197\\cdot d^{2}$ | $11\\cdot 197\\cdot d^{2}$ |\n\n(The number of operations in each SNN layer is analyzed in section 4.3 and appendix C.)\n\nNow we can estimate the energy efficiency:\n\n$$\n\\eta = \\frac{\\text{Energy of SNN}}{\\text{Energy of ANN}}\n= \\frac{(1206d+1578)E_{nl} + 11d^{2}E_{l}}{(11d^{2}+400d+197)E_\\text{MAC}}\n\\approx \\frac{1206 \\cdot E_{nl} + 11d \\cdot E_{l}}{(11d + 400)E_\\text{MAC}}\n$$\n\nwhere $E_\\text{MAC}$ is the energy consumption of one multiply-add operation in ANN, $E_{l}, E_{nl}$ is the energy consumption of one linear and non-linear operation in SNN.\n\nWe use the settings in [Horowitz, 2014], namely $E_{l} = 0.9 \\text{pJ},E_\\text{MAC}=4.6\\text{pJ}$. We assume that $E_{nl} = kE_{l}$, where $k$ is a constant depending on the hardware implementation.\n\nTake ViT-L for example, by letting $d=1024$, we have $\\eta = 0.189 + 0.020k$.\n\nIn our paper, we assume that $k=1$, i.e. the non-linear neuron has the same cost with the linear neuron. We think that a reasonable estimation would be $E_{l} < E_{nl} < E_\\text{MAC}$, for example $k=2$ or $k=3$. Although $k$ may vary according to the hardware implementation, we can conclude that the energy efficiency is between 20\\%-30\\%.\n\n### 2. Could the proposed method be used to other models? Like CNN and ResNet.\n\nThanks for your question. Our work generalizes prior TTFS-based methods from CNNs (consisting of linear, convolutional layers and ReLU) to Transformers. For CNN/ResNet architectures, our model reduces to the linear neuron dynamics described in **Corollary 4.4** and **4.6**, which is almost exactly what existing TTFS approaches (e.g. [Stanojevic et al. 2024]) are. While our method is compatible with CNN architectures, this would not introduce novel improvements for CNNs.\n\n### 3. Whether the proposed method can be generalized to the language task? other visual tasks?\n\nThanks for your inspiring discussion. While our experiments focus on vision tasks, the method is theoretically compatible with standard Transformer architectures in NLP. However, the generalization ability requires further experiments. For example, LLMs are typically larger than vision models, which poses challenges to the scalability of our method. We view this as a promising direction that desires future work. Besides, our method can be applied to regression-based vision tasks like object detection. We will add more discussion.\n\n### 4. Computational cost of the generalized TTFS neuron\n\nThe energy consumption of our non-linear neuron will be similar to or slightly higher than that of the LIF neuron. LIF neurons can be regarded as a special case of non-linear model where the potential change $\\eta,\\psi$ are exponential. When the potential change is not exponential, special hardware design is required, which is expected to have a similar energy cost with LIF neurons.\n\n[Nitin Rathi and Kaushik Roy, 2020] Nitin Rathi and Kaushik Roy. 2020. Diet-SNN: Direct Input Encoding with Leakage and Threshold Optimization in Deep Spiking Neural Networks.\n\n[Horowitz, 2014] M. Horowitz, \"1.1 Computing's energy problem (and what we can do about it),\" 2014 IEEE International Solid-State Circuits Conference Digest of Technical Papers (ISSCC), San Francisco, CA, USA, pp. 10-14\n\n[Stanojevic et al. 2024] Stanojevic, A., Woźniak, S., Bellec, G. et al. High-performance deep spiking neural networks with 0.3 spikes per neuron. Nat Commun 15, 6793 (2024).", "claims_and_evidence": "Yes, it is supported by rigorous theorem derivation and experimental analysis.", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "I have checked the theorem and the proof.", "experimental_designs_or_analyses": "I have checked Section 5.1-5.3.", "relation_to_broader_scientific_literature": "The contribution of this paper is related to spiking neural networks and low-power artificial intelligence.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "Strengths:\n\n1.The idea of using TTSF to implement spiking Transformer is impressive, which can reduce energy consumption in neuromorphic chips.\n\n2.The proposed method achieve SOTA performance with ViT and EVA model.\n\n3.The authors provide rigorous theoretic analysis. \n\nWeakness:\n\n1.The writing needs improvement. The article does not read very coherently, e.g., paragraphs 1-2 of the introduction.\n\n2.The authors need to analyze the computational cost of the generalized TTFS neuron, especially compared to the LIF neuron.\n\n3.This paper focused on improving classification performance of SNN, which in my view, is not the main strength of SNNs. The authors need to analyze other potential advantages. Actually, EVA can be used to other visual tasks. Whether the proposed method can be applied to other visual tasks?", "other_comments_or_suggestions": "See weakness.", "questions_for_authors": "1.Please clarify how to compute the energy consumption in Table 2.\n\n2.Could the proposed method be used to other model? Like CNN and ResNet.\n\n3.Whether the proposed method can be generalized to the language task? I would like to see some discussion on this direction.", "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": "Y109NBISsE", "reviewer": "Reviewer_4BzB", "summary": "The paper introduces a novel approach, TTFSFormer, for converting Transformer architectures into Spiking Neural Networks (SNNs) with Time-to-First-Spike (TTFS) coding. The method addresses the challenge of preserving high accuracy while significantly reducing energy consumption. The authors propose new neuron models and detailed conversion mechanisms to accommodate non-linear activations and complex components like the attention mechanism, which is a significant step in adapting SNNs to Transformer models. Experimental results on the ImageNet-1k dataset show that the method performs comparably to the original ANN architecture with minimal accuracy loss and lower energy costs.", "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": "Thank you for your thoughtful comments. We would like to address your concerns in the following.\n\n### Hardware Implementation\n\nThanks for your question. Since rate-based SNN is currently the most popular coding method, existing neuromorphic chips are specially designed for rate-based algorithms. With existing hardware circuits, one possible workaround is to store the mapping of non-linear functions in hardware storage, and simulate the change of potential. This is easy to implement since the non-linear function is shared in one layer. We hope that there will be neuromorphic chips suitable for TTFS-based SNN models, which will better demonstrate the energy efficiency of temporal coding methods. We will add more discussion in the revised manuscript.\n\n### Scalability Concerns\n\nDifferent from other tasks such as NLP, the size of vision models typically ranges from 80M (such as ViT-B) to 1000M. In order to better demonstrate the scalability of our proposed method, we test our method on **EVA-G** (Giant) with 1.01B parameters in total, which is one of the largest popular pre-trained vision transformers. The experimentable result is shown in the table below.\n\n|  | EVA-G (ANN) | EVA-G (SNN) | EVA-G (SNN, with precision=1024) |\n| --- | --- | --- | --- |\n| Top-1 accuracy | 88.882\\% | 88.898\\% | 88.160\\% |\n| Top-5 accuracy | 98.678\\% | 98.684\\% | 98.440\\% |\n\nThe result shows that our conversion method is still virtually lossless when converting a large vision model, indicating that our method has excellent scalability in vision task.\n\n### Limited Novelty in SNN Design\n\n\nWe agree that the idea of time-to-first-spike (TTFS) coding has been put forward and explored in previous works. Many SNN algorithms, either direct training or conversion, have created convolutional SNN successfully with much lower energy consumption and comparable performance to CNN. However, we would like to clarify that our work is the first to focus on the transformer model with TTFS coding.\n\nOur work mainly focuses on analyzing and solving the challenges encountered in introducing transformer architecture into TTFS-based SNN, which has not been addressed in previous works.\n\n- Challenge 1: Transformer architecture involves plenty of non-linear operations, such as non-ReLU activations, attention, and LayerNorm. However, previous TTFS neuron dynamics are only able to represent piecewise linear functions (Section 3.3).\n- Our Solution 1: We proposed a non-linear neuron model, which introduces non-linearity in SNN. We have theoretically proved that our neuron model has a strong representation ability (Section 4.2). With the proposed neuron model, we can construct Transformer-specific components (in Section 4.3).\n- Challenge 2: Previous TTFS neurons have a small representation range.\n- Our Solution 2: We expand the representation range of TTFS neurons depending on the actual distribution of the input and output values.\n- Challenge 3: Accuracy of converted models.\n- Our Solution 3: We have theoretically proved that our conversion method is lossless. Moreover, we conduct experiments on various vision transformer models (ViT, EVA) with different sizes (from 80M to 1B), showing that our method can achieve SOTA performance in vision tasks.\n\n### Insufficient Comparison\n\nThanks for your suggestion. We add the comparison with more recent works as follows.\n\n| Work | Method | ANN Model | Accuracy |\n| ---- | ------ | --------- | -------- |\n| Adaptive Calibration [Wang et al. 2025] | burst, conversion | ViT | 77.09\\% |\n| E-Spikeformer [Yao et al. 2025] | rate, direct training | - | 86.2\\% |\n| QKFormer [Zhou et al. 2024] | rate, direct training | - | 85.65\\% |\n| Spike-driven V2 [Yao et al. 2024] | rate, direct training | - | 80.0\\% |\n| **Ours** | TTFS, conversion | ViT-L/EVA02-L | 85.8\\%/90.0\\% |\n\nIn **Table 2** of our paper and the table above, direct training refers to training SNN directly through the surrogate gradient method. In **Table 2** of our paper, work not marked with \"TTFS-based\" is rate-based method by default.\n\n[Wang et al. 2025] Ziqing Wang and Yuetong Fang and Jiahang Cao and Hongwei Ren and Renjing Xu, \"Adaptive Calibration: A Unified Conversion Framework of Spiking Neural Network\", AAAI 2025.\n\n[Yao et al. 2025] Man Yao, et al. \"Scaling spike-driven transformer with efficient spike firing approximation training.\" IEEE Transactions on Pattern Analysis and Machine Intelligence (2025).\n\n[Zhou et al. 2024] Chenlin Zhou et al. \"QKFormer: Hierarchical Spiking Transformer using Q-K Attention\", NIPS 2024.\n\n[Yao et al. 2024] Man Yao, et al. \"Spike-driven Transformer V2: Meta Spiking Neural Network Architecture Inspiring the Design of Next-generation Neuromorphic Chips.\", ICLR 2024.", "claims_and_evidence": "no", "methods_and_evaluation_criteria": "Novelty: This is the first work to focus on converting Transformer architectures to SNNs using TTFS encoding, which addresses both energy efficiency and accuracy preservation, two key challenges in SNNs.", "theoretical_claims": "he paper makes an important theoretical contribution by introducing generalized nonlinear neurons for the conversion process, significantly expanding the applicability of TTFS coding to complex architectures like Transformers.", "experimental_designs_or_analyses": "he authors provide strong experimental results, showing that their method performs well on multiple Transformer architectures, including ViT and EVA, with minimal accuracy loss (below 0.1%).", "relation_to_broader_scientific_literature": "While the paper compares TTFSFormer to other SNN methods, there is insufficient comparison with other Transformer-to-SNN methods that leverage different spiking encodings (e.g., rate coding or surrogate gradient methods). A more thorough comparative analysis with state-of-the-art techniques would enhance the paper’s contribution.", "essential_references_not_discussed": "no", "other_strengths_and_weaknesses": "Hardware Realism: The paper focuses primarily on the theoretical model and simulation results but lacks in-depth analysis of hardware implementation or real-world constraints, such as precision or latency in hardware. While the robustness of the model is mentioned, more detailed hardware evaluation would improve the practical impact of the work.\nScalability Concerns: While the method performs well on the tested architectures, the scalability of TTFSFormer to larger, more complex Transformers with more layers and parameters remains unclear. An exploration of how the method scales with model size and complexity would be valuable.\n.", "other_comments_or_suggestions": "Limited Novelty in SNN Design: The paper introduces some interesting neurons and neuron dynamics, but the fundamental idea of TTFS-based SNNs is not entirely new, as it has been explored in other contexts. More emphasis on how the Transformer-specific components are handled would add more value to the novelty claim", "questions_for_authors": "no", "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": {"ethical_review_flag": "Flag this paper for an ethics review."}}, {"review_id": "SYP4oClwM7", "reviewer": "Reviewer_5bT2", "summary": "This paper proposes TTFSFormer, a novel method for converting Transformer architectures into Spiking Neural Networks (SNNs) using Time-to-First-Spike (TTFS) coding. The key innovation lies in designing generalized spiking neurons that address the limitations of prior TTFS-based approaches, particularly their inability to handle nonlinear operations in Transformers (e.g., softmax, LayerNorm). By introducing flexible input/output kernel transformations and a zero-reference time mechanism, TTFSFormer enables lossless conversion of pre-trained Transformers (e.g., ViT, EVA) into SNNs with minimal accuracy loss (<0.1%) and significant energy savings (~20% of ANN energy). Experiments on ImageNet-1K demonstrate state-of-the-art performance among SNN Transformers, outperforming both rate-coding and direct-training methods.", "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": "Thank you for your detailed feedback. We are encouraged that you found our work novel with good results. We would like to address your concerns and questions in the following.\n\n## 1. Table 1 lacks comparisons to very recent TTFS-based methods or advanced rate-coding SNN Transformers.\n\nThanks for your suggestion. We add the comparision with more recent works as follows.\n\n| Work | Method | ANN Model | Accuracy |\n| ---- | ------ | --------- | -------- |\n| Adaptive Calibration [Wang et al. 2025] | burst, conversion | ViT | 77.09\\% |\n| E-Spikeformer [Yao et al. 2025] | rate, direct training | - | 86.2\\% |\n| QKFormer [Zhou et al. 2024] | rate, direct training | - | 85.65\\% |\n| Spike-driven V2 [Yao et al. 2024] | rate, direct training | - | 80.0\\% |\n| **Ours** | TTFS, conversion | ViT-L/EVA02-L | 85.8\\%/90.0\\% |\n\nIn **Table 2** of our paper and the table above, direct training refers to training SNN directly through the surrogate gradient method. In **Table 2** of our paper, work not marked with \"TTFS-based\" is rate-based method by default.\n\n[Wang et al. 2025] Ziqing Wang and Yuetong Fang and Jiahang Cao and Hongwei Ren and Renjing Xu, \"Adaptive Calibration: A Unified Conversion Framework of Spiking Neural Network\", AAAI 2025.\n\n[Yao et al. 2025] Man Yao, et al. \"Scaling spike-driven transformer with efficient spike firing approximation training.\" IEEE Transactions on Pattern Analysis and Machine Intelligence (2025).\n\n[Zhou et al. 2024] Chenlin Zhou et al. \"QKFormer: Hierarchical Spiking Transformer using Q-K Attention\", NIPS 2024.\n\n[Yao et al. 2024] Man Yao, et al. \"Spike-driven Transformer V2: Meta Spiking Neural Network Architecture Inspiring the Design of Next-generation Neuromorphic Chips.\", ICLR 2024.\n\n## 2. Discuss hardware implementation challenges and latency trade-offs of the proposed model could enhance the future work.\n\n### Hardware Implementation Challenge\n\nWe think that potential challenges in hardware implementation include:\n\n- Design special hardware that is compatible with the non-linear neurons proposed in our method. With different dynamics compared with traditional LIF models, the hardware needs a special design in order to fully demonstrate the energy efficiency of our proposed methods.\n- Deal with hardware-related accuracy loss. Although we have proved that our conversion method is theoretically lossless, there will inevitably exist hardware-specific loss, including noise in membrane potential and time bias of TTFS spikes. We have discussed the robustness of our proposed method in Section 5.3, and more analysis is needed for hardware implementation. Fine-tuning is probably needed if the hardware loss is too large.\n\n### Latency Trade-offs\n\nIn our proposed method, there are two separate stages for one layer, namely, the emitting stage and the receiving stage. As proposed in [Park et al. 2020], the two stages can be overlapped in order to reduce the latency, requiring a balance between the conversion loss and latency reduction. Since our work mainly focuses on a lossless conversion method of Transformer architecture, we leave the topic for future works.\n\nWe will add more discussion in the revised version.\n\n## 3. The TTFS could provide advantage in the aspect of low firing rates, hence there could supplement the firing rate comparison and analysis.\n\nThank you for your inspiring question. Compared with previous work on TTFS, each non-linear neuron emits exactly one spike every forward pass. The firing rate is relatively lower than the rate-based method since multiple time steps is needed in rate-based SNN, leading to multiple spikes emitted in one neuron. However, the firing rate is higher than previous work on TTFS-based converted CNN, since we cannot simply ignore those negative values in the network with non-ReLU activation functions and attention mechanisms.\n\nThe firing rate can be further cut down. For example, in activation function SiLU, we can regard $\\mathrm{SiLU}(x) \\approx 0$ for $x \\le -16$ and simply emit no spike, since $\\mathrm{SiLU}(-16) \\approx -1.8 \\times 10^{-6}$ is close to 0. In this way, we can still keep the information carried by values around zero while enhancing energy efficiency.\n\n[Park et al. 2020] S. Park, S. Kim, B. Na and S. Yoon, \"T2FSNN: Deep Spiking Neural Networks with Time-to-First-Spike Coding,\" 2020 57th ACM/IEEE Design Automation Conference (DAC), San Francisco, CA, USA, 2020, pp. 1-6", "claims_and_evidence": "The assertion of lossless conversion (<0.1% accuracy drop) is validated by Table 1 (e.g., ViT-L/16: 85.8% vs. ANN’s 86.0%). Energy efficiency claims are backed by Table 2 (20% ANN energy).", "methods_and_evaluation_criteria": "The method is well-suited for ANN-to-SNN conversion. TTFS coding and kernel transformations directly address nonlinearity challenges in Transformers.\nImageNet-1K is a standard benchmark,", "theoretical_claims": "Theorems 4.1–4.3 and proofs in Appendix B are mathematically sound. Corollaries logically extend the theorems to identity transforms.", "experimental_designs_or_analyses": "Soundness: Training protocols (pre-trained ANN weights, SGD) align with ANN-to-SNN literature. Energy estimation (Eq. 28) follows established metrics (Horowitz, 2014).\n\nLimitation: Robustness tests (Fig. 4) use simulated precision; real-world hardware noise is not considered.", "relation_to_broader_scientific_literature": "TTFSFormer bridges two critical gaps:\n\nTTFS Coding: Extends Stanojevic et al. (2023) to Transformers, enabling nonlinear operations.\n\nSNN Transformers: Outperforms rate-coding methods (e.g., STA ) in energy efficiency while matching ANN accuracy.", "essential_references_not_discussed": "None.", "other_strengths_and_weaknesses": "Strengths:\n\n1. This is the first work to successfully convert Transformer architectures into SNNs using TTFS coding, addressing a critical gap in temporal coding methods.\n\n2. The proposed neurons with input/output kernel transformations (Theorems 4.1, 4.3) enable precise representation of nonlinear operations (e.g., softmax, LayerNorm), a major advancement over prior TTFS methods limited to linear mappings.\n\n3. TTFSFormer achieves ~80% energy reduction compared to ANNs while maintaining near-identical accuracy (e.g., 85.8% for ViT-L/16 vs. ANN’s 86.0%).\n\n4. Rigorous proofs (e.g., Theorem 4.2, Corollary 4.4) validate the equivalence between ANN activations and TTFS-based spike timing, ensuring lossless conversion.\n\nWeakness:\n\n1. Table 1 lacks comparisons to very recent TTFS-based methods or advanced rate-coding SNN Transformers.\n\n2. Discuss hardware implementation challenges and latency trade-offs of the proposed model could enhance the future work.\n\n3. The TTFS could provide advantage in the aspect of low firing rates, hence there could supplement the firing rate comparsion and analysis.", "other_comments_or_suggestions": "None.", "questions_for_authors": "See weakness.", "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": "I1KQCPV2WD", "reviewer": "Reviewer_syoz", "summary": "The work presents a strategy to convert trained ANN transformer models into time-to-first-spike coded SNNs. Specifically, a neuron dynamics model with two flexible kernel functions is used to accurately represent all transformer model operands. It is shown that crucial operations such as SiLU/GELU activation functions, softmax, and LayerNorm can all be expressed with suitable kernels, yielding a conversion algorithm for the entire transformer architecture. The conversion is put to the test empirically, demonstrating reduced loss of precision compared to a wide range of baselines on the ImageNet-1k vision benchmark. Finally, the method is shown to be robust to imprecise spike times and theoretically more energy efficient.\n\n**Update after rebuttal**\nThe authors' response has answered my remaining questions. My rating still stands, good paper!", "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": "Thanks for your suggestions. We would like to address your concerns and questions in the following.\n\n### Code implementation\n\nThank you for your question. Our code will be released with the publication.\n\n### Is there a way to quantify the minimum processing latency of a TTFSFormer neuron block?\n\nThank you for your question. The precision $p$ represents the precision of time in hardware implementation. While the accuracy of our converted model drops with lower precision, the problem can be solved with fine-tuning, as explored in previous works ([Stanojevic et al. 2024]).\n\nThe precision does not reflect the latency of the inference, but a shorter latency leads to a lower precision on a given hardware. However, there are still other techniques that can reduce the hardware latency. In order to further reduce the hardware latency, we can follow the method proposed in [Park et al. 2020], in which the emitting stage and receiving stage can be overlapped in order to reduce the latency. This requires a balance between the conversion loss and latency. Since our work mainly focuses on a lossless conversion method of Transformer architecture, we leave the topic for future works.\n\n### How are the OPs counted for a given transformer architecture?\n\nThank you for your question. We will include a more detailed analysis in future versions of our paper.\n\nWe briefly sketch the computing process in the following. Take one block in ViT as an example.\n- In the converted SNN, we can divide the operations into two categories: non-linear operations and linear operations. **Linear operations** take place in neurons with dynamics described in Corollary 4.4 and 4.6, which is exactly what most previous works on TTFS-based SNN use. **Non-linear operations** are new in our work, and the neurons may require more energy, depending on the hardware implementation.\n- In the original ANN, the energy consumption is measured by the number of multiplication and addition operations.\n\nAll operations are shown below (d = 384 or 768 or 1024 in ViT-S/B/L respectively). We categorize layers according to their type.\n\n| Type | Notation of Parameters | Shapes | SNN Ops | ANN Ops |\n| :---: | :---: | :---: | :---: | :---: |\n| LayerNorm | (M, N): Matrix $X \\in \\mathbb{R}^{M \\times N}$ | (197,d), (197,d) | $2 \\cdot 197 \\cdot (9d+1)$ | $2\\cdot 197\\cdot d$ |\n| MatMul | (M, K, N): Matrix $A \\in \\mathbb{R}^{M \\times K},B \\in \\mathbb{R}^{K \\times N}$ | (197,d,197), (197,197,d) | $197 \\cdot [197 \\cdot (3d + 2) + d \\cdot (3\\cdot 197+2)]$ | $2\\cdot 197^{2}\\cdot d$ |\n| SoftMax | (M, N): Matrix $X \\in \\mathbb{R}^{M \\times N}$ | (197,197) | $6 \\cdot 197^{2}$ | $197^{2}$ |\n| GeLU | (M, N): Matrix $X \\in \\mathbb{R}^{M \\times N}$ | (197,4d) | $197 \\cdot 4d$ | $197 \\cdot 4d$ |\n| Linear | (M, K, N): Matrix $X \\in \\mathbb{R}^{M \\times K}$ and weight $W \\in \\mathbb{R}^{K \\times N}$ | (197,d,3d),(197,d,4d),(197,4d,d) | $11\\cdot 197\\cdot d^{2}$ | $11\\cdot 197\\cdot d^{2}$ |\n\n(The number of operations in each SNN layer is analyzed in section 4.3 and appendix C.)\n\nBy summing up operations in each type of layer, we can finally get the estimated OPs in ANN and SNN. Thus, we have $197 \\cdot (1206d+1578)$ non-linear operations and $197 \\cdot 11d^{2}$ linear operations in one block.\n\nNow we can estimate the energy efficiency by (we divide the energy by 197 simultaneously)\n\n$$\n\\eta = \\frac{\\text{Energy of SNN}}{\\text{Energy of ANN}}\n= \\frac{(1206d+1578)E_{nl} + 11d^{2}E_{l}}{(11d^{2}+400d+197)E_\\text{MAC}}\n\\approx \\frac{1206 \\cdot E_{nl} + 11d \\cdot E_{l}}{(11d + 400)E_\\text{MAC}}\n$$\n\nwhere $E_\\text{MAC}$ is the energy consumption of one multiply-add operation in ANN, $E_{l}, E_{nl}$ is the energy consumption of one linear and non-linear operation in SNN.\n\nWe use the settings in [Horowitz, 2014], namely $E_{l} = 0.9 \\text{pJ},E_\\text{MAC}=4.6\\text{pJ}$. We assume that $E_{nl} = kE_{l}$, where $k$ is a constant depending on the hardware implementation.\n\nTake ViT-L for example, by letting $d=1024$, we have\n$$\n\\eta = 0.189 + 0.020k\n$$\n\nIn our paper, we assume that $k=1$, i.e. the non-linear neuron has the same cost with the linear neuron. We think that a reasonable estimation would be $E_{l} < E_{nl} < E_\\text{MAC}$, for example $k=2$ or $k=3$. Although $k$ may vary according to the hardware implementation, we can conclude that the energy efficiency is between 20\\%-30\\%.\n\n[Stanojevic et al. 2024] Stanojevic, A., Woźniak, S., Bellec, G. et al. High-performance deep spiking neural networks with 0.3 spikes per neuron. Nat Commun 15, 6793 (2024). \n\n[Park et al. 2020] S. Park, S. Kim, B. Na and S. Yoon, \"T2FSNN: Deep Spiking Neural Networks with Time-to-first-spike Coding,\" 2020 57th ACM/IEEE Design Automation Conference (DAC), San Francisco, CA, USA, 2020, pp. 1-6", "claims_and_evidence": "The proposed conversion strategy unlocks significant performance gains over prior baselines as it manages to transform all relevant operators into spiking dynamics without significant loss of accuracy. \n\nTTFS coding is a promising strategy as it typically requires fewer energy-consuming spikes than the more commonly explored rate encoding. However, the advertised \"perfect energy efficiency\" (L434) may not straightforwardly translate into a real-world implementation.", "methods_and_evaluation_criteria": "ViT on ImageNet-1k represents a reasonable proxy for a vision task performance that could be of interest for neuromorphic acceleration.", "theoretical_claims": "I have not carefully checked the conversion proofs.", "experimental_designs_or_analyses": "The accuracy comparison against the baselines is sound.\n\nFor the timing robustness in Figure 4, it is unclear why the plot evaluates for powers of 2 but stops at p=384. Furthermore, it is hard to interpret p in terms of actual inference latency. Is there a way to quantify the minimum processing latency of a TTFSFormer neuron block?", "relation_to_broader_scientific_literature": "Various methods for spiking conversions of transformer architectures have been proposed; this work goes beyond existing strategies by focusing on time-to-first-spike encoding for transformer models. In particular, it addresses lacking support for non-ReLU activation functions, the non-linear softmax operator of the attention mechanisms, as well as missing TTFS-implementations of Layer Norm.", "essential_references_not_discussed": "None", "other_strengths_and_weaknesses": "The paper lacks implementation details, and no source code was provided. I encourage the authors to provide more implementation and hardware details of the experiments and consider releasing source code with the publication.", "other_comments_or_suggestions": "To aid the reader, it's worth expanding on the energy estimation strategy described in Section 5.2. Specifically, how are the OPs counted for a given transformer architecture?  \n\nIt may be worth including the ANN baselines before conversion in Table 1.\n\nL429 \"few\" -> little?\nL430 \"Making\" -> Taking?", "questions_for_authors": "n/a", "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 **TTFSFormer**, a method to convert Transformer models into **Spiking Neural Networks (SNNs)** using **Time-to-First-Spike (TTFS)** coding. The key innovation lies in enabling TTFS-based SNNs to handle the nonlinear operations characteristic of Transformers—e.g., GELU, SoftMax, LayerNorm—via newly designed spiking neuron dynamics with flexible kernel-based transformations. The method achieves minimal accuracy loss (typically <0.1%) while significantly reducing estimated energy consumption (~20%–30%), and is evaluated on models from ViT-S to EVA-G (>1B parameters).

## Strengths
- **Novelty and Scope**: This work demonstrates lossless TTFS conversion for Transformers, extending beyond CNN-focused TTFS methods. The neuron dynamics design is theoretically solid and expands the expressive power of TTFS neurons.
- **Theoretical Rigor**: The manuscript includes well-presented theorems (e.g., Theorems 4.1–4.3), proofs, and corollaries that are largely validated by Reviewer 5bT2. It clearly delineates how TTFSFormer handles each Transformer component.
- **Empirical Results**: Experiments on ImageNet-1k using ViT and EVA models demonstrate near-lossless accuracy and meaningful energy gains. Robustness to spike timing precision is also explored.
- **Rebuttal Quality**: The authors engaged comprehensively with all reviewer concerns, offering detailed clarifications, expanded hardware and latency discussions, additional comparisons to recent work, and plans for code release.

## Weaknesses
- **Writing Quality**: As highlighted by Reviewer Cfcp, the writing—especially in early sections—is at times incoherent and would benefit from thorough editing for clarity and flow.
- **Hardware Realism**: Several reviewers noted the limited discussion of hardware-specific implications (e.g., TTFS neuron latency, noise, or real-world spike timing). The authors responded with helpful elaboration, but empirical validation on actual neuromorphic hardware remains absent.
- **Baseline Comparisons**: While improved in the rebuttal, initial comparisons with recent rate-based or surrogate gradient SNN Transformers were sparse. This has been partly remedied with a supplemental table and additional discussion.

## Rebuttal Assessment
The rebuttal was **constructive and thorough**, addressing nearly all concerns with concrete analyses. Particularly commendable are the discussions around firing rate efficiency, scalability to larger models, and hardware implementation trade-offs. Several reviewers explicitly indicated that their concerns were fully resolved post-rebuttal.

This is a solid and well-motivated contribution to the field of energy-efficient neuromorphic computing and ANN-to-SNN conversion, particularly in expanding the applicability of TTFS coding to complex modern architectures like Transformers.
Decision: Accept (poster)