Unveiling the Spatial-temporal Effective Receptive Fields of Spiking Neural Networks
Authors: Jieyuan Zhang
Xiaolong Zhou
Shuai Wang
Wenjie Wei
Hanwen Liu
Qian Sun
Malu Zhang
Yang Yang
Haizhou Li
Venue: NeurIPS 2025 poster ()
Keywords: Spiking Neural Networks
Effective Receptive Fields
Visual long-sequence modeling
Primary area: neuroscience_and_cognitive_science

Abstract: Spiking Neural Networks (SNNs) demonstrate significant potential for energy-efficient neuromorphic computing through an event-driven paradigm. While training methods and computational models have greatly advanced, SNNs struggle to achieve competitive performance in visual long-sequence modeling tasks. In artificial neural networks, the effective receptive field (ERF) serves as a valuable tool for analyzing feature extraction capabilities in visual long-sequence modeling. Inspired by this, we introduce the Spatio-Temporal Effective Receptive Field (ST-ERF) to analyze the ERF distributions across various Transformer-based SNNs. Based on the proposed ST-ERF, we reveal that these models suffer from establishing a robust global ST-ERF, thereby limiting their visual feature modeling capabilities. To overcome this issue, we propose two novel channel-mixer architectures: \underline{m}ulti-\underline{l}ayer-\underline{p}erceptron-based m\underline{ixer} (MLPixer) and \underline{s}plash-and-\underline{r}econstruct \underline{b}lock (SRB). These architectures enhance global spatial ERF through all timesteps in early network stages of Transformer-based SNNs, improving performance on challenging visual long-sequence modeling tasks. Extensive experiments conducted on the Meta-SDT variants and across object detection and semantic segmentation tasks further validate the effectiveness of our proposed method. Beyond these specific applications, we believe the proposed ST-ERF framework can provide valuable insights for designing and optimizing SNN architectures across a broader range of tasks. The code is available at \href{https://github.com/EricZhang1412/Spatial-temporal-ERF}{\faGithub~EricZhang1412/Spatial-temporal-ERF}.

Unveiling the Spatial-temporal Effective Receptive Fields of Spiking Neural Networks
Jieyuan Zhang', Xiaolong Zhou', Shuai Wang' Wenjie Wei', Hanwen Liu', Qian Sun', Malu Zhang! Yang Yang', Haizhou L
University of Electronic Science and Technology of China, Thh Chinese University of Hong Kong, Shenzhen, Shenzhen Loop Area Institute
Abstract
Spiking Neural Networks (SNNs) demonstrate significant potential for energy- efficient neuromorphic computing through an event-driven paradigm. While train- ing methods and computational models have greatly advanced, SNNs struggle modeling tasks. In artifi-
achieve competitive performance in visual long-sequent cial neural networks, the effective receptive field (ERF) serves as valuable tool for analyzing feature extraction capabilities in visual long-sequence modeling. Inspired by this, we introduce the Spatio- Temporal Effective Receptive Field (ST-ERF) to analyze the ERF distributions across various Transformer-bas based SNNs. Based the proposed ST-ERF, we reveal that these models suffer from establishing robust global ST-ERF, thereby limiting their visual feature modeling capabilities. To overcome this issue, we propose two novel channel-mixer architectures: multi- seee-pperceptron-basee mixer (MLPixer) and splash-ann--ecoonstruu block (SRB). These architectures enhance global spatial ERF through all timesteps in early net- SNNs. improving performance on challenging
work stages of Transformer-bast visual Long-sequence modeling tasks. Extensive experiments conducted on the Meta-SDT variants and across object detection and semantic segmentation tasks further validate the effectiveness of our proposed method. Beyond these specific applications, we believe the proposed ST-ERF framework can provide valuable insights for designing and optimizing SNN architectures across a broader range of tasks. The code is available at O EricZhangg hat.ha/nnnnaaltttpataetemmoorraa
Introduction
Spiking Neural Networks (SNNs) 2 have emerged as prominent research focus, characterized by binary spike activation that offers high sparsity, event-driven processing B 4. and biological
plausibility (5). Recent advances in encoding schemes [6] 7 g training methodologies [9] [0]
and neuromorphic hardware
[I]
have enabled SNNs to achieve remarkable success in
diverse tasks, including image processing [14 15 16,, point/event analysis [17] [8] language
understanding 19 20 211, and speech processing 22 24. Nonetheless, SNNs still struggle to
achieve performance comparable to their Artificial Neural Networks (ANNs) counterparts in visual long-sequence modeling tasks.
Compared to conventional image classification, visual long-sequence modeling tasks 25 26 demand spatially dense outputs with prediction scales several orders of magnitude higher. This paradigm requires architectures capable of modeling long-range spatial dependencies, which are essential for
"Correspodingg author:
Emaluzhang @uestc.edu.cn
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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F
Neural Network
(8)
[b]
F(:0)
Learnalle parameters
Gradient Slimuli
Dacay Factor
Effective Receplive
Spatial feediorward
Visuel Stmuli
ANN
Temporal feadforward
Splikigg Neuron
Reset Fundiin
Visual field left eye
R
y E
Spallal Effective
Receptive Flokt of JF
Optic nerve Laft eye
SNN
(..
((:0)
Visual field of right eye
Right eye
ProPP
FRR
Temporal Effective Receptive Field of F
Gradient Slimuli
x R,
I2
Figure 1: (a) The human visual field. (b) ERF in ANNs. (c) ST-EEF in SNNs. It extends the ERF to the temporal dimension, thus facilitating a comprehensive analysis of feature extraction in SNNs.
achieving competitive performance 225
The Transformer 227 architecture introduces a self-attention
mechanism that enables effective modeling of long-range spatial dependencies (28
29
30
Motivated
by this, recent studies have proposed various Transformer-basee SNNS [31
achieving notable progress in visual long-sequence tasks [15]. However, simply combining Transformers
32
33
34
with SNNs may lead to suboptimal designs without fully considering the intrinsic spatio-tempone
dynamics of spiking neurons. To bridge this gap, more structured and interpretable framework is required to examine how SNNs model spatio-temporal dependencies. In this context, receptive field (RF) analysis offers concrete lens through which their feature extraction capacity and attention allocation can be theoretically characterized.
In neuroscience, the RF represents the region of sensory input that can modulate neuron's 's activ- ity [35]. Borrowing this concept, the deep learning community defines a neuron's RF as the region of the input that influence its output (36). with its size determined by network topology. However, this topology-basee based definition treats all positions within the RF equally, ignoring the learnable weights that determine the actual contribution of each input location. To refine this problem, researchers proposed the effective receptive field (ERF) (37] to quantify input features' contributions to output features via gradient analysis. Unlike topology-basee faithful characterization of the network's feature extraction patterns. However, such framework cannot be directly applied SNNs due to the intrinsic spatio-temporal dynamics of spiking neurons. Therefore, we introduce the Opatial-Tempory Effective Receptive Field (ST-ERF) framework, which quantifies input feature contributions across spatio-temporal locations to characterize SNNs' feature extraction patterns. By jointly modeling temporal dependencies and spatial relationships, ST-ERF facilitates comprehensive analysis of information processing SNNs.
RF, gradient-based ERF provides a more
Based on the proposed ST-ERF, we analyze various Transformer- based SNNs and identify that existing models fail to establish effective global receptive fields across all timesteps. This limitation stems from the prevalent use of convolutional channel-mixers, which inherently introduce locality bias (88. Despite facilitating efficient local feature extraction and long-range sparse modeling, this architectural design fundamentally constrains the long-range dense spatial interactions necessary for effective visual seg-seeuence modeling in SNNs. Building on these insights, we propose two novel channel-mixe architectures: multi-layer-perceen wwwppppern-ebeeeeeeeeeeeee and-roconstruct block (SRB). These designs use pixel-wise MLPs to keep spatial features separate when mixing channels, which reduces locality bias and improves the global receptive field in early stages of Transformer- based SNNs. Extensive experiments demonstrate the effectiveness of our methods on visual long-sequence tasks. Specially, on COCO 2017 object detection and ADE20K semantic segmentation, our Meta-SDT-Base 33 with SRB achieves 48.9% API, and 43.7% mloU, respectively, while maintaining a smaller model size. These results surpass sfate-of-the- art Transformer-based SNNs, thereby validating our ST-ERF analysis and further advancing SNNs in visual long-sequened sequence modeling. Our main contributions are listed as follows:
mixer (MLPixer) and splash-

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We propose the ST-ERF framework, extending the traditional ERF concept to the temporal dimension with rigorous mathematical formalization. ST-ERF systematically quantifies how input features at different spatial and temporal locations contribute to output features. This provides theoretical tool for understanding and optimizing feature extraction in SNNs.
We analyze various Transformer- based SNNs using the ST-ERF framework, revealing a critical limitation that existing models fail to establish global ERF across all timesteps. To overcome this issue, we introduce two novel channel mixer designs: MLPixer and SRB, enabling Transformer-based SNNs fully exploit their global modeling potential of long-range dependencies.
We conduct extensive experiments on visual long-sequence modeling tasks and demonstrate that our method achieves superior performance. For instance, our Meta-SDT-Base with SRB achieves 48.9% AP on COCO 2017 detection and 43.7% mIoU ADE20K segmentation. It significantly outperforms existing state-of-the-ar Transformer-basee SNNs while using a smaller model size. These results strongly support the validity of our ST-ERF theoretical analysis and demonstrate the effectiveness of the proposed architectural designs.
2
Related Works
2.1 Receptive Field in Neural Networks
The human visual system perceives the external world through the visual fields of both eyes. As illustrated in Figure aa), each eye covers specific region of the visual space, and these regions partially overlap in the center to enable binocular vision. Neurons along the visual pathway respond selectively stimuli within their RFs. Over the past decades, the RF theory has profoundly influ- enced our understanding of how the brain filters and integrates visual information across spatial locations 33) Inspired by the RF theory, deep neural networks adopt a similar principle by charac- terizing hierarchical ERFs that capture progressively abstract representations of input data. As shown in [ the ERF [37 formalizes this process by analyzing how spatial stimuli contribute to network activations. ERF has motivated extensive research at different architectural levels, from understanding basic operators 40 to designing higher-level modules and network structures such as Adaptive Receptive Fields [11, RF-Next 422, and AutoRF 43] RF-based analysis has also driven advances in computational efficiency for lightweight architectures, influencing the development of CNN-based MobileNet variants [44 45 46) and MLP-based networks such as MLP-Mixer [47) and TSMixer [48). Building on these insights, this work extends the ERF concept to SNNs, offering a theoretical framework for analyzing and optimizing their spatio-temporal feature extraction processes.
2.2 Visual Long-sequence Modeling in SNNs
Visual long- long-sequence modeling refers tasks that require multiple predictions per image, rather than a single-label classification 49 These tasks mainly include detection, segmentation, video understanding, and on (25]. As these tasks involve modeling complex spatial and temporal dependencies, they demand architectures capable of capturing long-range contextual information. Transformer has become the dominant paradigm for visual long-sequence modeling owing to its global self-attention mechanism and flexible scalability. However, such models still suffer from high computational costs, primarily due the quadratic complexity of self-attention, dense prediction requirements, and high-resolution inputs [50]. Recently, leveraging the sparse spike-driven nature of SNNs has emerged as a promising direction to mitigate these computational costs. Spike-driven Transformer series 551, 33 [2) adapt the standard Metaformer into an SNN framework for object detection and semantic segmentation, demonstrating the feasibility of SNNs dense prediction tasks. Spike2Former [15] integrates normalized integer leaky- manky-and-ng -nd--and---iee -nd-integrated firing (NI-LIF) neurons and spike-driven deformable attention to achieve competitive performance on segmentation benchmarks while maintaining low energy consumption. Despite these advancements, SNNs still lag behind ANNs in visual long-sequence modeling. This underscores the need for deeper investigation into SNNs' spatio-temporal bottlenecks and architectural optimization.
3

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3 Theoretical Analysis of Spatio-temporal Effective Receptive Field
In this section, we first introduce the concept of ERF in conventional ANNs. Subsequently, we extend this conventional ERF into the temporal dimension to characterize the ST-ERF in SNNs. Finally, we introduce a loss-derived method to efficiently compute ST-ERF in SNNs.
3.1
ERF in ANNS
The concept of the ERF has been widely adopted to analyze how input features contribute to network activations and how such influences of a single channel per layer, Luo et al. [37] mathematically characterized how each input feature contributes to the output of neural network layer. It can be defined as follows:
distributed within the RF 40 41]. Under the assumption
())m))))))
FRF [[,..)) x]
(1)
where x E RI is the input feature and y E R2 is the output feature. In this manner, the ERF measures the partial derivative of an output feature ((m,,) E y with respect to each input feature Ji(..) within a given layer. As illustrated in Figure bb), the ERF of given network F(; () describes the input regions that contribute to particular output activation.
As shown in Eq. ① the ERF can be computed at any output location. However, most studies evaluate the ERF at the central output feature V/(0,0) by assigning a unit gradient to this location [53 54). This practice establishes centered and symmetric reference, ensuring stable and comparable visualization results. In this work, we also follow the setting of [37] and adopt the ERF at the central output feature B(o.0) as the evaluation metric.
3.2 ST-ERF in SNNs
Due to the inherent temporal dynamics, SNNs require additional consideration of the input at each timestep. To address this, we formally define the ST-ERF (i.e., (RF().T)). Firstly, we redefine the mapping relationship of SNNs. Consider SNN layer with learnable parameters that maps input spike features x(1 T] E IR, to output spike features y[1 T R2:
y(1 7| F(x(1: F): R2 - R.g.
(2)
Its ERF needs to account not only for the accumulation across spatial dimensions but also for that across temporal dimensions. Specifically, (RF(S.T) E R can be expressed as:
0y(m,)) [x,] Oz - 7]" S 1
ERF(S (S.T) (U)m,)) (4,5)
(3)
Accordingly, (RF(S.T) quantifies how much each input feature B(c,)[t - r] E x at a previous timestep t contributes to a specific output feature 3(m,)) [t] E y. Based on this definition, the spatial ERF (i.c., ERF(S) can be seen the weighted average of the ST-ERFs over all timesteps:
T 1-1
ERF(S) (1-5) ((mm))) x] =
w(t, T) ERF(S,T) (i.))
(( [t]:,,
T
[=1 T=U
where w(t, T) represents the relative contribution of the input with delay 7 at time to the output. The specific form of w r) depends on the neuronal dynamics and network architecture. For example, (LIF) neurons, inputs closer to the current time step may have higher
in Leaky Eiegrate-and-Fiin influence due to the decay of membrane potential over time.
The temporal ERF (i.c., ERF(T) can be seen as the integration over the spatial dimensions of ST-ERF to indicate the contribution of inputs different timesteps the final output:
FRF( [r:x] = ΣΣ FRF (RR(S.T)
(S,T)
(K.) (3) [T)
As shown in Figure ()), we visualize an example of the ST-ERF. Similar to conventional ERF analysis, we focus on the center of the feature map at a specific timestep (e.g., the final timestep in Fig. [c) to analyze the spatio-temporal feature representations in an SNN. Depending on the purpose of analysis, one may investigate the spatial distribution of the ST-ERF at a given timestep (spatial ERF) or its temporal distribution across one more layers (temporal ERF).

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3.3 Loss-Derived Calculation for ST-ERFss
Based on Eq. B computing the ST-ERF SNNs requires evaluating first-order derivatives of outputs with respect to all input features. To obtain the ST-ERF conveniently, we introduce the loss-derived calculation method efficiently compute using Py PyTorch's Automatic Differentiation functionality. Consider a SNN with input spike features s s-1 output spike features s at the /-th layer, and an arbitrary loss function The spatial ERF of SNNs can be easily obtained by calculating the average of the gradient of the loss with respect to input features at position (i. j) across all timesteps T. Specifically, it can be computed as follows:
ERE (1.)) (1.1) ((.00)
Σ
T
as
(0.0) [t]
Σ
Oc
when'l,
dc
[1, - 00
T
0s 1
0s
otherwise
(1.))
(6)
The temporal ERF of SNNs can be obtained by calculating the sum of the gradient of the loss function with respect to input features at timestep across all spatial positions. It can be computed as:
ast [T]
OC
OC
ERE (T)
ΣΣ 1J
Σ J 05
when vi,j.
1. (7)
T-
T-
(1.))
Ōs
Proof can be found in Appendix A We refer to the conditions in Eq. 66 and 7 gradient stimuli.
Based on this proposition, we could easily obtain the spatial and temporal ERF with automatic back-propagation without an explicit loss function.
4 Problem Analysis on Transformer-based SNNs using ST-ERF
In this section, we use the ST-ERF framework to analyze existing Transformer-based SNNs and identify their limitations in visual long-sequence modeling tasks.
4.1 Different ST-ERF Behaviors in Transformer--asee SNNs
We apply the ST-ERF framework to analyze Transformer-based SNNs' spatial ERF behaviors across all timesteps. Specifically, we compared two groups of architectures(a: ViT-like architecture group and b: Meta-architecture group) with their ANN counterparts to investigate the differences in the formation their spatial ERFs. For the loss-derived calculation, we set the central patch across all channels and timesteps in the output tensor the gradient stimuli (uniform values of 1), then perform automatic back prok-propagation. Each experiment comprised 60 iterations using randomly sampled input tensors under standard normal distribution (μ の² 1). Note that average the ST-ERE over all timesteps to obtain a clear visualization.
(a)
(b)
ANN
SNN
ANN
SNN
VIT-B
SDT-V1 (8-384)
CAFomer-s18
Meta-SDT-S
Figure 2: Comparison of spatial ERF with ANN Vision Transformers and ST-ERF with different Transformer-bart SNNs. (a) ViT-like architecture comparison group: ViT-B and SDT-V1. (b) Meta-architecture comparison group: CAFormer-s18 and counterpart Meta-SDT-S.
The comparison of ViT-like architectures is illustrated in Figure a).. Compared with the classic ViT-B, SDT-VI exhibits more centrally concentrated yet markedly narrower spatial ERF, This
5

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observation suggests that the architectural modifications in SDT-VI may restrict the receptive field's spatial extent, thereby enhancing its attention on local spatial dependencies. In fact, SDT-VI adopts fundamentally different strategy from the vanilla VíT in the patch splitring stage. Specifically, SDT-VI employs the Spike Patch Splitting (SPS) module, consisting a Patch Splitting Module (PSM) to linearly project the input image and a Relative Position Embedding (RPE) (55) block to generate the latent position information. The SPS module incorporates multiple convolutional layers at the early stage of the network, facilitating low-level spatial features extraction from input images.
The comparison of aettttrrciisss is illustrated in Figure b).. Although Meta-SDT exhibits ERF behaviors similar to those of its ANN counterparts, it also struggles to maintain long-range feature attention. This limitation can be attributed the additional employment of convolutional layers, which tend to emphasize localized features rather than global spatial contexts. Compared with CAFormer, Meta-SID SDD introduces the Re- ne-parameterization Convolution (RepConv) to perform the linear projection of queries, keys, and values[51]. This design enhances local feature extraction, yet it inherently constrains the model's capacity to aggregate information across distant spatial regions. Together, these findings suggest that the convolutional operations enhances local feature sensitivity but poses challenges for maintaining long-range spatial coherence in Transformer-based SNNs.
4.2 Visual Long-sequence Modeling Needs Global ST-ERF
Visual mung-sequence modeling tasks often involve dense predictions across an entire image, requiring the processing of thousands of input tokens [25]. Therefore, capturing long-range dependencies and global context is crucial for achieving accurate and robust representations [57]. Prior studies have found that vision models with global receptive fields often excel at segmentation and detection, for instance when using self-attention mechanisms as Transformer architectures [57] (58). In contrast, architectures lacking global context integration tend to struggle. While early convolutional layers excel at extracting low-level structural patterns [59]. their locality inherently limits the capacity to capture
dependencies, making them suboptimal for visual long-sequence tasks.
However, despite the need for global spatial awareness in visual uen-sequence modeling. Transformers-basee based SNNs still fail to achieve truly global ST-ERF. As discussed above, they tend focus heavily on the center and expand to limited size. This contrasts sharply with the expected behavior required for visual limits information aggregation and consequently degrades performance on such scenarios (57)
modeling tasks, where the weak global ST-ERF
Methods
In this section, we propose two novel channel-mixing designs, MLPixer and SRB, which enable Transformer-based SNNs to more effectively capture long-range dependencies. Furthermore, we integrate these modules into the Meta-SDT architecture to enhance performance visual long- sequence modeling tasks.
5.1 Design of Channel Mixer Block
To enhance the global modeling capability of SNN in visual long-sequence tasks, we propose two novel channel mixer designs. The first is the multi-layer perceptron-based mixer (MLPixer), which employs a two-layer MLP structure to more effectively extract global features. It is defined as follows:
MLPixer(X. = (MLPPGONNENNMPP/NXXX)))
(8)
where X E IxTxBxNxD denotes the input of channel mixers in the Transformer block. SN(-) denotes a spiking neuron layer that transforms the input sequence into the spike trains. MLP(-) denotes a langeellayer fully connected (FC) operation, and (N(-)) denotes batch normalization.
Compared with vanilla channel mixers 660 51 that rely on convolution operations, the MLPixer employs two-layer MLP operation to mix features across channels. This design reduces reliance on convolutional operations, mitigating the ERF's bias toward Gaussian-like central concentration and enabling SNNs to capture range dependencies more effectively.

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(9)
(b)
(C)
BN
BN
BN
BN
BN
BN
Figure 3: Comparison between the original channel mixer design and our proposed methods, along with their ST-ERF. For clearer visualization, the ST-ERF is averaged over timesteps. (a) Vanilla convolution-based channel mixer. (b) Proposed MLPixer architecture. (c) Proposed SRB architecture. Obviously, the vanilla convolution-baee channel mixer exhibits a limited ST-ERF, whereas our MLPixer and SRB modules achieve a more global ST-ERF. Moreover, due to the reduced use of convolutions, MLPixer exhibits even broader effective receptive field.
Building on this, further propose the SRB module. It replaces only the second convolution in the channel mixer with a single-layer MLP operation. Specifically, the SRB is defined as follows:
SRB(X) (BNXX)))NNNP(PENNEE
Here, Conv(.) denotes x convolution operation. In this manner, SRB module reduces additional parameters while maintaining performance. To validate the effectiveness of our approach, we visualize the ERFs of the Conv-based mixer, the MLPixer, and the SRB modules.
As shown in Figure 3 a), the vanilla convolution-baset channel mixer exhibits limited ST-ERF. In contrast, the proposed MLPixer and SRB modules demonstrate a more global ST-ERF. Furthermore, the comparison between Figure b) and Figure 3e) further demonstrates that MLPixer exhibits more global ERF. This stems from reduced use of convolutions and further suggests that MLPs provide stronger global modeling capacity than convolutional operators. We will validate the proposed module visual long-sequence modeling tasks in the experiment section.
Architecture
Stage
Stage 2
Stage 3
Stage 4
Down
Conv-based SNN Block
sample
Down
Conv-based
sample
Down
Transformer-
Down
Transforme- SNN Block
Head
SNN Block
SNN Block
SSC
Spike Separañle
PWConw
SSC
SDSA
MLP
Convolatin
PWConw
Linear
BN
Pointwise Convolutin
DWCcnn
Spike-driven Self- Delf-attention
Linear
DWConw
Channel Mixer
BN
Linear
BN
Linear
BN
Deptholse Convilaiion
PWConw
Linear
BN
Linear
BN
EN
Spiking Neuronn Layer
Figure 4: The overall architecture of Meta-SDT, which typically comprises four hierarchical stages. The first two stages use convolution-basel SNN blocks, while the latter two adopt Transformer-SNY blocks. To strengthen the global modeling capacity of SNNs, we introduce two novel channel mixer architectures, MI.Pixer and SRB, replace the convolution based SNN blocks the first two stages.

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5.2 Overall Architecture
To further validate the effectiveness of our approach, we integrate the proposed SRB and MLPixer modules into the CAFormer [60] and Meta-SDT [33 architectures. As shown in Figure 4 these architectures adopt multi-stage design, where the first two stages consist of Conv-based SNN blocks, and the latter two stages comprise Transformer-SNN blocks. In this work, we replace only the operations in the first two stages. Specifically, the first two stages are represented as:
- SSC(X), -X' = Mixer, (X').
(10)
Here, (-) is the channel mixer. In this work. we implement the approach using both the ML.ixer module and the SRB module. Similar to the vanilla channel mixer, our method adopts an up-projection followed by down-projection with nonlinear activation in between, where
c <> represents the intermediate dimensional expansion ratio. SSC(.) is the spike-driven separable convolution block token mixer, it is defined as follows:
SSC(X)
(11)
PWConvi( (-) and (WConv2(-) are pointwise convolutions, DWConv(-) is depthwise convolution. SN(-) denotes the spiking neuron layer. To maintain the spike-driven characteristics of the network, we implement membrane- shortcut residual connection mechanism. Furthermore, Transformer SNN blocks are utilized in Stage 3 and Stage 4, following the same configuration as that of Meta-SDT- We will further verify the effectiveness of the proposed method in the experimental section.
V3 33
6 Experiments
In this section, we validate the effectiveness of our method through visualization and experimental analysis. First, we examine the changes in the ST-ERF after integrating the proposed modules into Meta-SDT, showing that our method achieves stronger global spatial receptive fields across all stages. Second, we evaluate its performance improvement on long-sequence modeling tasks, including object detection and semantic segmentation. Finally, we further investigate the method on complex event modeling tasks to assess its applicability in more challenging scenarios.
6.1 ST-ERF Behavior in Transformer-basee SNNs
In order to study the impact of our proposed block on the receptive field of Mcta-SDT, we compared tevporal-averaged spatial ERFs between our two Meta-SDT variants with previous models. We initialized the central spatial feature across all channels and timesteps in the output tensor as uniform gradient stimuli (value 1). and propagated the gradients backward through the network. Each experiment consisted of 60 iterations with input tensors randomly drawn from standard normal distribution (μ+ = 0, o² 1). 1).
The results are illustrated in Figure 5 Surprisingly, we found that Spikformer exhibits diffuse receptive fields across all stages. The SDT-VI, Mcta-SDT, and QKFormer demonstrate markedly centered distribution that gradually expand as the network deepens, all manifesting a Gaussian like effect. Additionally, we observed dissipation of spatial ERF in SDT-VI I during the final stage. In contrast, proposed two Meta-SDT variants establish robust global spatial receptive fields in the early stages. The MLPixer-Sie SDD establishes a strong global spatial ERF in Stage As the network deepens, its spatial ERF selectively contracts toward specific regions. The ERF behavior in SRB-SDT slightly different, as it only begins to form a preliminary spatial ERF at Stage 2, and this distribution continues to evolve with increasing network depth.
6.2 Performance in Visual Long-sequence Modeling Tasks
We selected two challenging datasets to evaluate performance on classic visual long- uen-seeqence model- ing tasks: object detection and instance segmentation COCO 2017, and semantic segmentation the ADE20K dataset. We choose the Meta-SDT(y33) [В] as the baseline and construct Meta-SDT variants with MLPixer(e4), MLPixer(e6) and SRB(e4).
Performance on COCO 2017 We evaluate the efficacy of the MI.ixer and SRB on Meta-SDT and select the classic and large-scale COCO [61] dataset our benchmark for evaluation. Following
8

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Ours #1
Ours #2
Spikformer (8-512)
SDT-V1 (8-384)
Meta-SDT-S
@KFormer (10-384) MLPixer-SDDT (e 6) SR-SDT-S (e
Evolving through stages
Figure 5: Comparison of temporal-average spatial ERF evolution across stages. From top to hottom Stage through Stage 4. Spikformer shows diffuse receptive fields across all stages. SDT-V1, Meta-SDT, and QKFormer exhibit more centered spatial distributions that gradually expand as depth increases. Our two Meta-SDT variants establish global spatial receptive fields in the early stages.
codehase with a spiking version and then deploy model. We employ the Meta-SDT [33] with two variants the backbone network to extract features, along with fine-tuning Mask R-CNN (63) for object detection and instance segmentation. All backbone networks are pretrained ImageNet-IK [64], while the incremental layers are initialized following [65]. During fine-tuning, we strictly obey the 1x training schedule.
the previous work 51 33 52],
we use the MMdetection
The comparison results of object detection and instance segmentation are shown in Table | Under the same training schedule, both the MLPixer and SRB variants outperforms the baseline across all metrics. More specifically, the SRB variant exceeds the performance of SDTv3-T and SDTv3-B by 10.42% and 4. 1,26% on the APb metric, while maintaining almost the same model size. In conclusion, our approach demonstrates efficacy in object detection and instance segmentation, setting new benchmark for COCO dataset in the SNN domain.
Performance on ADE20K We evaluate the performance of MLPixer and SRB on the semantic segmentation task using the challenging ADE20K dataset [66]. Similar the COCO experiments, utilize the spiking version of MMSegmentation (67 as our codebase and employ the Meta-SDT [33 with two variants as the backbone network. We fine-tune the Semantic FPN framework [68] for semantic segmentation. Backbone networks are initialized with ImageNet- 1K pre-trained weights [64], and new layers follow the initialization scheme of All models are strictly obey the same training schedule for 160k iterations.
As shown in Table both MLPixer and SRB variants surpass the baseline in terms of mloU. The SRB variant improves performance by 3.3% and 2.6% over SDTv3-T and SDTv3-B, respectively, while reducing parameters by 0.3M and 1. 1.2M. The MLPixer(e4) variant achieves the largest parameter reduction of 0.6M and 2.4M, with comparable or superior accuracy to SDTv3-T and SDTv3-B, These results highlight the effectiveness of the proposed modules enhancing semantic segmentation on ADE20K.
6.3 Performance Complex Event Modeling Tasks
Event-based Tracking We evaluate the effectiveness of two channel mixers in the context of event-based tracking, highly challenging yet practically significant application domain for SNNs. Our experiments follow the SDTrack pipeline [18), which employs the Global Trajectory Prompt

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Arch.
#T #P
AP
AP
AP
AP"
A 00
76
Arch.
Ch. Mixer
(aram.(M)
mloU(%)
SDTv3-I 33
25M
35.5
10.2
15.2
33.0
C2d-k3(r4)
4
6.5 BASE
34.9
4 24M
16.2
37.0
11.5
15.2
32,9
12.5
SDTv3
MLPix.(e4)
5,9 (,0.6)
34.9 (70.0)
4 25M
17.5
38.5
13.2
16.2
34.5
13.5
-T
MLPix.(e6)
6.6 (70.1)
35.9 (11.0)
()
4 25M
18.2
39.2
13.8
17.5
34.8
14.3
SRB(c4)
4
6.2 (10.3)
38.2 (13.3)
SDTv3-B 33
4 39M 21.7
46.9
17.0
20.1
41.8
17.5
C2d-k3(e-4
4
20.4 BASE
41.1 BASE
MLPixenee))
4 36M
22.9
47.6
19.2
21.0
43,4
18.3
SDTv3
(ePix.(e4)
4
18.0 (12.4)
42.0 (10.9)
MLPixeNed)
4 39M 25.1
48.8
22.5
21.9
43.5
19.6
-B
MLPix.(c6)
4
20.7 (10.3)
43.4 (12.3)
SR
4 37M 25.8
48.9
22.8
22.5
43.9
20.4
SRB(c4)
(U1.2) 43.7 (12.6)
Table 1: Object detection and instance segmenta- tion with Mask R-CNN COCO val2017. using ImageNet- KK pre-training and x training schedule.
Table 2: Segmentation results on ADE20K based different mixer block, using ImageNet-IK pre-training and 160k iter.
method to convert event streams into event frames. We strictly adhere to the original training protocol, modifying only the backhone by replacing SDTrack with our proposed SDTrack+MLPPP or SDTrrckKSSBB variants. As presented in Table extensive experiments on the FE108 [69 and VisEvent 770 datasets demonstrate that our architectures surpass the original SDTrack in several key metrics. These results confirm that both the MLPixer and SRB designs preserve the Transformers- based SNNs' performance, yet highlight opportunities for further improvement subsequent temporal benchmarks.
Table 3: Performance comparison on event-based object tracking, a challenging yet important application for SNNs. Evaluation is conducted on two benchmark datasets, FE108 and VisEvent.
FE108
669
VisEvent 70
Architecture
Timesteps
Param. (M)
AUC(%)
PR(%)
AUC(%)
PR %
(D-Track(Tiny) [8]
X 1
19.61
56.7
89.1
35.4
48.7
+MLPixer
4
20.21
57.1
89.2
33.7
47.3
+MLPixer (c [c=00 6)
4 4x1 1
22.99
57.9
90.1
34.5
48.9
+SRB (e
4 4x1
21.43
58.2
88.5
33.8
48.0
7
Conclusion
This paper presents ST-ERF as a novel framework for analyzing the spatial-temporal modeling behaviors in SNNs from new perspective. Through this analysis, an inherent limitation in current Transformer- -aased SNN models is identified when applied to visual long- sequeeeeence modeling tasks. To address this limitation, two channel-mixet architectures, MLPixer and SRB, are proposed. Visu- alization of ST-ERF demonstrates that both modules enhance the global receptive field. Extensive experiments on long-sequence modeling tasks, including object detection and semantic segmentation, show that MI.ixer and SRB improve overall performance, with SRB achieving optimal balance between accuracy and model size. Furthermore, the study investigates complex event modeling tasks to assess the applicability of MLPixer and SRB in more challenging scenarios. Overall, the proposed ST-ERF framework offers valuable insights for the design and optimization of SNN architectures across a wide range of tasks.
Acknowledgments
This work is supported in part by the National Natural Science Foundation of China (No. 62220106008 and 022222229999 1432), in part by the Shenzhen Science and Technology Program (Shenzhen 1302006)) and in part by the Program for Guang-
Key Laboratory, Grant No. dong Introducing Innovative, Entrepreneurial Teams, Grant No. 20232T10X044, and in part by the State Key Laboratory of Brain Cognition and Brain-inspired Intelligence Technology, Grant No. SK25000 This work was partially supported by UESTC Kunpeng&Ascant Center of Cultivation.
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Answer: [Yes]
Justification: We mentioned our proposition and properties of ST-ERF and provided a whole set of proofs in Appendix A
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The experimental setting should be presented in the core the paper to a level detail that is necessary appreciate the results and make sense of them.
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Appendix
[s time f. Moreover, notice that [v is non-differentiable. To overcome this problem, Wu al. [9] propose the surrogate function make only the neurons whose membrane potentials close to the A Proof of 3.3
Proof. Leaky Integrate-and-Fire (LIF) model S
2
can be described by the following equations:
v [t] h 1| f( f(w x 1 1)),
(Charging function),
(12)
sf [1] = @vv'() 1))
(Firing function),
(13)
[[ [t)(.. soft reset h [t] [v111(1 s²(1),, hard reset
(Leak-and-resel function),
(14)
where is the decay constant, / is the time step, w is the weight matrix of layer f(-) is the operation that stands for convolution (Conv) or fully connected (FC), x is the input, and (-) denotes the Heaviside step function. When the membrane potential v exceeds the firing threshold 9, the LIF neuron will trigger spike s; otherwise, it remains inactive. After spike emission, the neuron invokes the reset mechanism, where the soft reset function employed. h the membrane potential following the reset function.
For the back- proppaataan of this neuron, we introduce the training process of SNN gradient de- scent and the parameter update method of spatio-temporal pack-propagation (STBP) 9 The accumulated gradients of loss L with respect to weights at layer can be calculated as:
ac Ow!
OC
Os [s
tv dv [c] ow
Öv [
dv ar [ 1] ds ds [
Ov [v
Σ II
0
(v)+
0v
[st+
Ov
[
Ow
(15)
where [t( and v'tt represent the output spikes and membrane potential of the neuron in layer f, at
firing threshold receive nonzero gradients during back sack-propagation.
In this paper, the rectangle function, which has been shown to be effective in gradient descent and may be calculated by:
Øs [1] sign - > Öv [t] a
0
(16)
where a a defined coefficient for controlling the width of the gradient window.
anfa [1]
To compute Σn
( we follow the chain rule with an arbitrary loss C. Consider
Σ 85
ac
(4
Ös
[t]
Σ
dc
OC
(ij)
[t]
Ost
Os
f-1
1
0s (1.))
(17)
Ost (1.)
0s
ΣΣΣ
Oc 0s
ac
Os (0.0)
(o.00) [
ds
0s
as (0.0)
0s
140 100
t=1
(i.j)
(s.)
When the following conditions are met:
ac
1
i - 0,3 0,
Vt E T,
(18)
0s
0
otherwise
(1.)
22

---

We can get:
T
ac
Os
(0.0) [d]
ac
T
ds
0.00
[t]
Σ t=l
(19)
as (1.3)
T
(1,))
T
(13)
The spatial ERF position (i.j) thus be calculated by summing the gradients of the loss with respect to all timesteps.
88 [T] 0e (e T-
For the temporal ERF, we need to compute Σn, applying the chain rule:
We consider Eig
ac
By
0o
[T-
Üs (i.3)
(T)
d
OC
Σ (J
ΣΣ
(20)
85
Os (3:)
[T]
0s f-
(T
i
(i.j)
When the following conditions are met:
vi,
= 1
(21)
Os (i.j)
[
We can simplify:
t5t ( 1-1-11 (.))
dc
Σ 1
ΣΣ 8
(22)
Os
Os
(i.))
i.
The temporal ERF delay r can thus be calculated by summing the gradients of the loss with respect to all spatial positions timestep T T
B Details in Detection and Segmentation Experiments
On ImageNet-1K 1 pretraining, employ three scales of Meta-SDT with three different channel mixer design ((1): Conv-Mixer; (2): MLPixer; (3): SRB) in Table f and utilize hyper-parameters in Table 5 to pre-train models in our paper for further fine-tuning on COCO 2017 and ADE20K datasets. Note that e represents the channel expand ratio (CHW + CHW + CHW).
For COCO 2017 dataset, We utilize the MMDetection 772 framework to implement the existing models and our method. The object detection and instance segmentation framework strictly follows Mask R-CNN, with training schedule of 1x (12 epochs). We use total batch size of 4/GPU, utilize the AdamW optimizer with learning rate of 10-4 and weight decay of 0.05. Images are resized and cropped into 1333 x 800 for training and testing and maintain the ratio. Random horizontal flipping and resize with a ratio of 0.5 was applied for augmentation during training. This pre-training fine-tuning method is commonly used strategy in ANNs.
For ADE20K dataset, utilize the MMSegmentation 773 framework. The training configuration strictly encompasses for 160,000 iterations. The batch size is set to 4/GPU, and the AdamW optimizer tuned x 10-4 and 0.05, respectively.
used, The learning rate and weight decay parameters To speed up training, we warm up the model for 1.5k iterations with a linear decay schedule. All the experiments are conducted on NVIDIA-AID -100 80GB GPUs.
23

---

Table 4: Contigurations of different Meta-SDT Variants.
Stage # Tokens
Layer Specification
Tiny
Medium
Basc
Conv
7x7 stride
Downsampling
Dim
16
24
32
DWConv
7x7 stride
H
W X
SepConv
MLP ratio
2
2
Conv-based SNN block
Cononn+Cony
=
Channel Mixer
(2)MLP4MLP
c 4/6
(3)MLP+Conv
4
Conv
3x3 stride
Downsampling
Dim
32
48
64
DWConv
7x7 stride
H
W X
SepConv
MLP ratio
2
4
Conv-based
SNN block
C)Conn+Conn
=
Channel Mixer
(2MLLP+MLP
c 4/6
(3)MLP+Conv
Conv
3x3 stride
Downsampling
Dim
64
96
128
DWConv
7x7 stride
H
W
SepConv
2
X
ratio
2
8
8
Conv-based SNN block
()Conv+Cony
= 4
Channel Mixer
22MLPP+MIPP
c 4/6
(3)MLP+Conv
4
# Blocks
Conv
3x3 stride
Downsampling
Dim
128
192
256
H
W
3
X
SDSA
RepConv
3x3 stride
16
16
Transformer-basel
Channel MI.
MI.Pratin
SNN block
# Blocks
Conv
3x3 stride
Downsampling
Dim
192
240
360
H
W
4
x
SDSA
RepConv
3x3 stride
16
16
Transformer-based
Channel MLP
MLP ratio
4
SNN block
# Blocks
2
Table 5: Hyper-parameters for pre-training on ImageNet- IK
Hyper-parameter
Settings
Hyper-parameter
Settings
Model size
T/M/B
Timestemp
Epochs Batch size
200
Resolution
2244224
1568
Optimizer
LAMB
Base learning rate
6c-4
Learning rate decay
Cosine
Warmup eopchs
10
Weight decay
0.05
Random augment
9/0.5
Mixup
None
Cutmix
None
Label smoothing
0.1
C
Limitations
This work presents several avenues for future exploration, such as how neuronal dynamics parameters influence ST-ERF in more dynamic and diverse SNNs. Given that one of SNN's ' major successes stems from its inherent membrane potential memory update mechanism, this represents particularly worthwhile direction for deeper investigation. We will further explore the interactions between spiking neurons' neurodynamics and the networks' temporal response in the future. Nevertheless, this work provides viable analytical framework for understanding SNN model behavior, with practical implications for architectural design across various levels of SNNs.
24


Reviews:
[{"review_id": "LUXJDSy2FG", "reviewer": "Reviewer_cNmF", "summary": "This paper proposes a novel framework called the Spatio-Temporal Effective Receptive Field (ST-ERF) to study the learning behavior of both spatial and temporal domains. It discovers two key patterns: spatial patterns are Gaussian-like, and their influence fades predictably over time. Using these findings, the authors analyze existing spiking transformers and then build two new efficient building blocks (MLPixer and SR blocks). Finally, they test these new blocks successfully on tasks requiring processing long sequences of visual data.", "questions": "1. How would ST-ERF behave under other neuron types like Izhikevich or P-LIF? Would the power-law decay pattern still hold?\n\n2. Please provide a clearer explanation of what each subplot (a)-(d) in Figure 5(b) represents. What cause the jagged temporal ERF?", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength:\n1. ​​Introduces a new way (ST-ERF) to understand both spatial and temporal learning in Spiking Neural Networks, filling an important research gap.\n2. ​​Rigorously demonstrates ST-ERF's core findings (Gaussian space, power-law time decay) through comprehensive experiments on synthetic models and real-world tasks.\n3. ​​Designs simple but impactful new blocks (MLPixer, SR Block) that significantly improve SNN performance on demanding long-sequence vision tasks.\n\nWeakness:\n1. Some of the operator notations in equations (especially Eq. (12), (13)) are overloaded or ambiguously defined, making it harder to parse the exact pipeline.\n2. other see questions.", "was_revised": true, "final_justification": "I think the rebuttal did solve my concerns. I would like to see this paper be accepted.", "rebuttal": "> Q1: Some of the operator notations in equations (especially Eq. (12), (13)) are overloaded or ambiguously defined.\n\nA1: We appreciate your feedback regarding the operator notations in equations, particularly Eq. (12) and (13). Here we provide a table summarizing the definitions of the operators used in these equations:\n| Operator | Definition |\n|----------|------------|\n| $\\mathrm{Mixer}_{ch}(\\cdot)$ | Channel mixer block|\n| $\\mathrm{SSC}(\\cdot)$ | Spike-driven Seperable Convolution block |\n| $\\mathrm{BN}(\\cdot)$ | Batch Normalization |\n| $\\mathrm{MLP}(\\cdot)$ | Multi-layer Perceptron Layer |\n| $\\mathbb{SN}(\\cdot)$ | Spiking neuron layer |\n\nWe have revised the manuscript to clarify the definitions of the operators used in these equations. The Eq.(12) and (13) is supposed to be:\n$$\\mathrm{Mixer}_{ch}(\\cdot) = \\mathrm{BN}(\\mathrm{MLP}(\\mathbb{SN}(\\mathrm{BN}(\\mathrm{MLP}(\\mathbb{SN}(\\cdot))))))$$\n\n$$\\mathrm{Mixer}_{ch}(\\cdot) = \\mathrm{BN}(\\mathrm{Conv}(\\mathbb{SN}(\\mathrm{BN}(\\mathrm{MLP}(\\mathbb{SN}(\\cdot))))))$$\n\n\nWe have ensured that all operators are clearly defined and consistently used throughout the manuscript. We hope this clarification addresses your concerns. If you have any further questions or suggestions, please feel free to let us know.\n\n> Q2: ST-ERF behaviors in other spiking neuron models.\n\nA2.1: **Izhikevich's spiking neuron model:**\n\nWe conducted the Temporal ERF framework on Izhikevich's spiking neuron model, which is a well-known model in computational neuroscience. The Izhikevich model is defined by the following equations:\n\n$$\n\\frac{dV}{dt} = 0.04V^2 + 5V + 140 - U + I,\n\\frac{dU}{dt} = a(bV - U)$$\n\n$$if  \\space  V \\geq v_{threshold}, then \\space V \\leftarrow c, U \\leftarrow U + d$$\n\nwhere $V$ is the membrane potential, $U$ is the recovery variable, and $I$ is the input current. The parameters $a$, $b$, $c$, and $d$ are constants that define the specific behavior of the neuron. We discretized the equations using Euler's method and implemented the Izhikevich model in PyTorch and Spikingjelly, which can be formulized as follows:\n\n$v(t + \\Delta t) \\approx v(t) + \\Delta t \\left[ 0.04v(t)^2 + 5v(t) + 140 - u(t) + I(t) \\right]$, \n\n$u(t + \\Delta t) \\approx u(t) + \\Delta t \\left[ a(bv(t) - u(t)) \\right]$\n\n$V \\leftarrow c, U \\leftarrow U + d$\n\nDescription of each parameter is provided in the following table:\n|Parameter|Description|\n|---------|-----------|\n|$a$|Time scale of the recovery variable|\n|$b$|Sensitivity of the recovery variable to the membrane potential|\n|$c$|Reset value of the membrane potential after a spike|\n|$d$|Increment of the recovery variable after a spike|\n|$\\Delta t$ or $tau_{inv}$|Time step for discretization|\n\nBy properly setting the parameters, we can acquire the desired spiking behavior as we discovered in the manuscript. The parameter $\\Delta t$ primarily controls the time resolution of the simulation, and influences the temporal ERF evolution (same as the parameter $\\beta$ in the manuscript). The detailed parameter settings and results are summarized in the following table:\n\n| a | b | c | d | tau_inv | v_threshold | Temporal ERF |\n|---|---|---|---|---------|-------------|--------------|\n| 0.02 | 0.2 | -65.0 | 6.0 | 0.006 | 2.0 | Exponential Decay|\n\nNote that the Izhikevich model can be extremely flexible, and the parameters can be adjusted to achieve various spiking behaviors(e.g. bursting, regular spiking, etc.). And we believe that the exploration of these behaviors using the Temporal ERF framework can provide valuable insights into the dynamics of spiking neural networks. \n\nA2.2: **Parametric LIF:**\n\nWe also conducted the Temporal ERF framework on the Parametric LIF model, which is a variant of the LIF model that incorporates learnable parameters to control the dynamics of the neuron. Because it is a variant of the LIF model, the Temporal ERF is computed in a similar way as described in the manuscript, which follows the exponential attenuation of the membrane potential over time.\n\n**Both the results of Izhikevich's spiking neuron model and the Parametric LIF model demonstrate that the Temporal ERF framework can effectively capture the temporal dynamics of spiking neurons, regardless of the specific neuron model used.** The exponential decay behavior observed in both models aligns with our theoretical framework, confirming the robustness and versatility of the ST-ERF approach. We have included these visual results in the updated manuscript to provide a more comprehensive evaluation of the ST-ERF framework across different spiking neuron models.\n\n> Q3: Provide a clearer explanation of what each subplot (a)-(d) in Figure 5(b) represents. What cause the jagged temporal ERF?\n\nA3.1: We apologize for the lack of clarity in the legend of Figure 5(b). In Figure 5(b), we aimed to illustrate the temporal ERF patterns of Spiking CNNs with different spike activations. We employ a 20-layer deep SCNN network to derive temporal ERFs across four distinct surrogate functions. From subfigures (a) to (d), the surrogate functions are as follows: (a): $\\mathrm{arctan(\\cdot)}$, (b): $\\mathrm{Sigmoid}(\\cdot)$, (c): $\\mathrm{Rect(\\cdot)}$, (d): $\\mathrm{Poly(\\cdot)}$.\n\nIn each subfigure, we visualize the temporal ERF patterns at different decay factors. Considering that the spike activations are achieved by LIF neurons, we can describe the forward process as follows:\n\n$\\mathbf{v}^{\\ell}[t]=\\mathbf{h}^{\\ell}[t-1]+f({\\mathbf{w}^{\\ell}},\\mathbf{x}^{\\ell-1}[t-1]), \\text{(Charging function)}$\n\n$\\mathbf{s}^{\\ell}[t]=\\mathbf{\\Theta}(\\mathbf{v}^{\\ell}[t]-\\vartheta), \\text{(Firing function)}$\n\n$\\mathbf{h}^{\\ell}[t]=\\beta\\mathbf{v}^{\\ell}[t]- \\vartheta \\mathbf{s}^{\\ell}[t], \\text{soft reset}$\n\nAccordingly, the temporal ERF is defined as:\n$$\n\\underset{\\mathcal{T}}{\\mathrm{ERF}}(s^{\\ell}, \\tau) = \\sum_{i,j} \\sum_{\\hat{i},\\hat{j}} \\frac{\\partial s_{(\\hat{i},\\hat{j})}^{\\ell}[T]}{\\partial s_{(i,j)}^{\\ell-1}[T-\\tau]} = \\sum_{i,j} \\frac{\\partial \\mathcal{L}}{\\partial s_{(i,j)}^{\\ell-1}[T-\\tau]}\n$$\n\nwhere $\\mathcal{L}$ is the loss function, $\\mathbf{v}^{\\ell}[t]$ is the membrane potential, $\\mathbf{s}^{\\ell}[t]$ is the spike output at layer $\\ell$, and $\\mathbf{h}^{\\ell}[t]$ is the hidden state at layer $\\ell$ at time $t$. The decay factor $\\beta$ controls the leakiness of the neuron, and $\\vartheta$ is the threshold for spiking. \n\nProven by Appendix D of the original manuscript, the temporal ERF is the temporal effective receptive field decays exponentially with time delay $\\tau$, and the decay rate is primarily determined by the membrane potential decay constant $\\beta$, i.e., $\\underset{\\mathcal{T}}{\\mathrm{ERF}}(\\cdot,\\tau) \\propto \\beta^{\\tau}$. The four experiments used decay factors of 2.0, 1.33, 1.2, and 1.14, respectively, which may not be the commonly-said decay factors in many essays. Some amount of works define the LIF model as\n\n$\\mathbf{h}^{\\ell}[t]=(1-\\frac{1}{\\tau})\\mathbf{v}^{\\ell}[t]- \\vartheta \\mathbf{s}^{\\ell}[t], \\text{soft reset}$\n\nwhere $\\tau$ is the decay factor. However, in our theoretical framework, we use $\\beta=1-\\frac{1}{\\tau}$ for convenience while ensuring consistent monotonicity between $\\beta$ and $\\tau$\n\nThe shaded regions represent the $\\mathrm{mean \\pm std}$ deviation across 20 independent experimental trials. The solid lines represent the mean value points of the original data  connected, while the dashed lines represent curves fitted using $y=a \\beta^x + b$. Throughout the experiments, we observed that the fitted curves closely followed the trends of the original data, validating our theoretical framework. \n\nA3.2: In the analysis of Temporal ERF, it is essential to ensure that the network avoids vanishing or exploding gradients during backpropagation. Therefore, we meticulously controlled the surrogate gradient functions of neurons, the network’s parameter settings, and the value ranges of input tensors in our implementation to ensure stable capture of Temporal ERF characteristics during backpropagation. Detailed parameter configurations can be found in Appendix E. At the same time, we used PyTorch's automatic differentiation to compute gradients. Due to the inherent limitations of floating-point arithmetic (IEEE 754 standard), numerical errors may occur during computation, leading to jagged fluctuations in the Temporal ERF curve. This phenomenon is common in deep learning, especially when processing high-dimensional data or complex models."}, {"review_id": "1o4ivMyL7k", "reviewer": "Reviewer_Yc3k", "summary": "This paper introduces the Spatio-Temporal Effective Receptive Field (ST-ERF), a novel framework for analyzing learning behaviors in Spiking Neural Networks (SNNs). Extending traditional receptive field analysis to account for SNNs’ temporal dynamics, the authors establish two fundamental properties of ST-ERF: **Spatial Gaussianity**: ST-ERF exhibits Gaussian-like distributions in the spatial domain. **Temporal Power-law Attenuation**: Influence decays following a power-law pattern over time, driven by neuronal dynamics. Applying ST-ERF to analyze Transformer-based SNNs, the paper reveals that current architectures suffer from limited global receptive fields, impairing performance on visual long-sequence tasks. Crucially, the authors identify the channel-mixer design as the primary bottleneck. By proposing two novel block design: **MLPixer** and **SR block**, these designs significantly improve spatial ERF coverage in early network stages, enabling state-of-the-art performance on COCO and ADE20K benchmarks. The work bridges theoretical understanding (ST-ERF properties) and practical advancements (new architectures) for SNNs in complex vision tasks.", "questions": "1. Is there any further connections between ST-ERF and other biological theories of neural dynamics? The paper mentions that ST-ERF is a theoretical framework, but it does not discuss how it relates to existing biological theories of neural dynamics. Are there any connections between ST-ERF and other theories, such as the theory of synaptic plasticity or the theory of neural oscillations?\n2. Proposition 1 correlates spatial ERF with ANN-like behavior under the condition of \"pure instantaneous response\". However, many SNNs use time-coding (e.g., delayed coding), which defeats this premise. How is the ST-ERF compatible with the scheme of encoding information in pulse timing?", "limitations": "Yes. As discussed in the appendix, the authors transparently acknowledge the technical constraints (e.g., unexplored neurodynamics influences on ST-ERF, narrow experimental validation, and its connection with scalability). The authors also provide a clear roadmap for future work: exploring ST-ERF in more complex conditions.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n1. The paper provides convincing proofs on one proposition and two properties of ST-ERF, establishing a solid theoretical basis for understanding SNN learning dynamics and representing the first formal adaptation of ERF theory to SNN spatiotemporal dynamics.\n\n2. The proposed MLPixer/SR Blocks demonstrate consistent performance gains across all metrics, with improvements up to +3.6 mIoU, providing solid validation of the theoretical insights.\n\n3. Intuitive visualizations including ERF heatmaps (Figures 2, 4, 6) and decay curves (Figure 5) effectively illustrate spatial-temporal properties and make complex concepts tangible.\n\n4. Original analysis revealing channel-mixer design as the global ERF bottleneck, with the SR Block's MLP-convolution hybrid offering a novel solution for SNN receptive field enhancement.\n\n5. Thoughtful adaptation of architectural advances (Metaformer/MLPixer) to overcome SNN limitations, demonstrating how cross-paradigm synthesis can drive meaningful progress in the field.\n\n**Weaknesses:**\n1. Some figures contain ambiguities, such as Figure 3 where the second block design appears to lack residual connections, requiring verification and clearer explanations.\n\n2. Figure 5(b) legend lacks clear explanation of which experiments (a)-(d) each element represents, hindering interpretation.\n\n3. The paper primarily focuses on visual long-sequence tasks, which may limit the generalizability of findings to other domains and applications, suggesting need for broader task validation to demonstrate framework versatility.", "was_revised": true, "final_justification": "This paper introduces a solid theoretical framework (ST-ERF) for understanding SNN spatiotemporal dynamics, addressing an important research gap. The mathematical foundations are sound, and the identification of receptive field limitations in existing architectures leads to practical improvements with demonstrated performance gains.\n\nWhile the evaluation scope could be broader, the work makes meaningful contributions to both SNN theory and practice. The technical quality is adequate and the proposed methods are well-validated. Overall, the strengths outweigh the weaknesses.", "rebuttal": "> Q1: Corrigendum in Figure 3 where the second block design appears to lack residual connections.\n\nA1: We sincerely appreciate your meticulous review and valuable feedback. You rightly identified the missing residual connection in Figure 3, which was indeed an oversight in our original manuscript. We sincerely apologize for this error.\n\nWe have carefully revised Figure 3 in the updated manuscript—the residual pathway is now explicitly illustrated in the MLPixer block (black solid arrows). Furthermore, our actual implementation (Code in supplementary materials: `erf_compute/spatial_Erf/erf_sdt/models/sdtv3.py`, Lines 357 & 395) and mathematical formulations in the original manuscript (Eq. (12) & (13): $\\mathbf{X}''= \\mathbf{X}'+\\mathrm{Mixer}_{ch}(\\mathbf{X}')$) confirm that the residual connection was consistently incorporated in the design. \n\n> Q2: Figure 5(b) legend lacks clear explanation of which experiments (a)-(d) each element represents, hindering interpretation.\n\nA2: We apologize for the lack of clarity in the legend of Figure 5(b). In Figure 5(b), we aimed to illustrate the temporal ERF patterns of Spiking CNNs with different spike activations. We employ a 20-layer deep SCNN network to derive temporal ERFs across four distinct surrogate functions. From subfigures (a) to (d), the surrogate functions are as follows: (a): $\\mathrm{arctan(\\cdot)}$, (b): $\\mathrm{Sigmoid}(\\cdot)$, (c): $\\mathrm{Rect(\\cdot)}$, (d): $\\mathrm{Poly(\\cdot)}$. \n\nIn each subfigure, we visualize the temporal ERF patterns at different decay factors. Considering that the spike activations are achieved by LIF neurons, we can describe the forward process as follows:\n$$\n\\begin{aligned}\n    \\mathbf{v}^{\\ell}[t]&=\\mathbf{h}^{\\ell}[t-1]+f({\\mathbf{w}^{\\ell}},\\mathbf{x}^{\\ell-1}[t-1]), &\\text{(Charging function)} \\\\\n    \\mathbf{s}^{\\ell}[t]&=\\mathbf{\\Theta}(\\mathbf{v}^{\\ell}[t]-\\vartheta), &\\text{(Firing function)}\\\\\n    \\mathbf{h}^{\\ell}[t]&= \n        \\beta\\mathbf{v}^{\\ell}[t]- \\vartheta \\mathbf{s}^{\\ell}[t], &\\text{soft reset}\n    \\end{aligned}\n$$\n\nSome amount of works define the LIF model as\n\n$$\n\\begin{aligned}\n    \\mathbf{h}^{\\ell}[t]&=\n        (1-\\frac{1}{\\tau})\\mathbf{v}^{\\ell}[t]- \\vartheta \\mathbf{s}^{\\ell}[t], &\\text{soft reset} \n    \\end{aligned}\n$$\nwhere $\\tau$ is the decay factor. However, in our theoretical framework, we use $\\beta=1-\\frac{1}{\\tau}$ for convenience while ensuring consistent monotonicity between $\\beta$ and $\\tau$\n\nProven by Appendix D of the original manuscript, the temporal ERF is the temporal effective receptive field decays exponentially with time delay $\\tau$, and the decay rate is primarily determined by the membrane potential decay constant $\\beta$, i.e., $\\underset{\\mathcal{T}}{\\mathrm{ERF}}(\\cdot,\\tau) \\propto \\beta^{\\tau}$. The four experiments used decay factors of 2.0, 1.33, 1.2, and 1.14, respectively, which may not be the commonly-said decay factors in many essays. Throughout the experiments, we observed that the fitted curves closely followed the trends of the original data, validating our theoretical framework.\n\n> Q3: Broader task validation to demonstrate framework versatility.\n\nA3: We appreciate your suggestion to validate our framework across a broader range of tasks. In response, we have conducted additional experiments on **(a): DVS data classification tasks** using DVS128Gesture, and **(b): event-based tracking tasks** using the FE108 and VisEvent datasets. \n\n**(a): DVS data classification tasks.** The baseline network is QKFormer-PE1(4-layer-res)-S1-PE2(2-layer-res)-S2, containing two stages of Q-K attention (S1 & S2) and the corresponding positional encoding blocks(PE1 & PE2). We apply the block design of MLPixer and SR block on the PEs. Note that because the original QKFormer has residual paths in PEs, we also added the block design of MLPixer and SR block on the residual paths to see their performance. The results are summarized in the following table:\n| Architecture                          |Step | Param (M) | DVS128Ges. Acc. (%) |\n|--------------------------------------|----|----|-----|\n| **QKFormer-PE1-S1-PE2-S2**           |$16$|1.99|97.9|\n| ✓ ***+PE1-MLPixer ($\\epsilon=2$)***  |$16$|1.91|97.9|\n| ✓ ***+PE1res-MLPixer***              |$16$|1.91|97.2|\n| ♠ ***+PE1-MLPixer ($\\epsilon=3$)***  |$16$|1.93|98.3|\n| ♠ ***+PE1res-MLPixer***              |$16$|1.93|97.2|\n| ► ***+PE1-SR ($\\epsilon=2$)***       |$16$|1.92|98.3|\n| ► ***+PE1res-MLPixer***              |$16$|1.92|98.6|\n| ✓ ***+PE2-MLPixer ($\\epsilon=2$)***  |$16$|1.21|97.6|\n| ✓ ***+PE2res-MLPixer***              |$16$|1.21|98.3|\n| ♠ ***+PE2-MLPixer ($\\epsilon=3$)***  |$16$|1.26|97.9|\n| ♠ ***+PE2res-MLPixer***              |$16$|1.26|98.3|\n| ► ***+PE2-SR ($\\epsilon=2$)***       |$16$|1.48|98.3|\n| ► ***+PE2res-MLPixer***              |$16$|1.48|98.6|\n\n**(b): Event-based tracking tasks.** Our experimental setup employed the SD-Track architecture as the baseline, which integrates event-based feature extraction specifically designed for processing event streams. We systematically replaced the core processing blocks with our proposed MLPixer and SR block variants while maintaining identical experiment setups. The results are summarized in the following tables:\n| Model         |#T|#P| FE108 Tracking (AUC/PR) | VisEvent Tracking (AUC/PR) |\n|:--------------|--|--|:-------------------------|:---------------------------|\n| ODTrack       |1*1|92.83|43.2/69.7|24.7/34.7|\n| HIPTrack     |1*1|120.51|50.8/81.0|32.1/45.2|  \n| SD-Track(Tiny)|4*1|19.61|56.7/89.1|35.4/48.7|\n| SD-Track(Tiny)|1*4|19.61|59.0/91.3|35.6/49.2|\n| SD-Track(Tiny)-MLPixer ($\\epsilon=4$)|1*4|20.21|57.1/89.2|33.7/47.3|\n| SD-Track(Tiny)-MLPixer ($\\epsilon=6$)|1*4|22.99|57.9/90.1|34.5/48.9|\n| SD-Track(Tiny)-SR ($\\epsilon=4$)|1*4|21.43|58.2/88.5|33.8/48.0|\n\nThe results demonstrate that our architectural modifications not only preserve but in some cases improve tracking performance across both precision (PR) and area-under-curve (AUC) metrics. Notably, MLPixer with $\\epsilon=6$ and SR blocks show consistent improvements, validating that our ERF-guided architectural choices are effective across diverse temporal processing tasks beyond static image classification. \n\n> Q4: Further connections between ST-ERF and other biological theories of neural dynamics?\n\nA4.1 **Connections with neural oscillation theory:** While the current ST-ERF framework focuses on temporal-domain assessment of dynamic feature variations, its natural extension to frequency-domain analysis would unveil neuronal response mechanisms across spectral bands. Such a multidimensional spatiotemporal-frequency analytical approach would: (i) deepen understanding of feature extraction processes in biological neural populations, and (ii) advance bio-plausible computational models for next-generation neuromorphic chips (e.g., Loihi), particularly in cognitive tasks demanding sophisticated time-frequency processing (e.g., working memory and spatial navigation). This proposed expansion aligns with the emerging paradigm of hybrid time-frequency analysis in computational neuroscience. \n\nA4.2 **Connections with synaptic plasticity theories:**  Although the current ST-ERF framework is based on gradients, a simple yet potential method to incorporate STDP into the proposed ST-ERF framework to the analysis of synaptic weights can be modifying the core definition in the original manuscript Eq.(3) with an STDP window function $g(\\Delta t)$, where $\\Delta t = t_{\\text{post}} - t_{\\text{pre}} $ captures pre-/post-synaptic timing relationships. This allows explicit modeling of how synaptic efficacy modulates input-output sensitivity. The spatial (Eq.(4)) and temporal (Eq.(5)) decompositions of ST-ERF further benefit from STDP-aware formulations: Spatial ERFs should weight contributions by STDP-driven synaptic updates $w(t,\\tau) \\propto \\eta \\sum_{\\Delta t} g(\\Delta t) I_{\\text{pre}}(t - \\tau) I_{\\text{post}}(t)$, while temporal ERFs can directly adopt the bi-exponential form to reflect STDP’s asymmetric time constants. This unified perspective may reveal how STDP dynamically sculpts spatiotemporal processing, which can be a critical insight bridging synaptic mechanisms with system-level information encoding.\n\n> Q5: How is the ST-ERF compatible with the scheme of encoding information in pulse timing?\n\nA5: Our framework employs **dynamic firing threshold (DFT)-based neurons**, which process input spikes in two stages:\n1. **Membrane potential accumulation**:$$V_j^l(t) = \\sum w_{ij}^l \\cdot \\mathrm{ReL}(I_i^{l-1}(t))$$\n2. **Dynamic Spike firing (DFT mechanism)**:The firing time $ t_j^l $ is determined by direct/standard firing or no firing based on a dynamic threshold $\\theta^l[t]$\nNote that the spatial ERF is similar to the original formulation. The temporal ERF captures how the timing of input spikes influences the output spike timing. \nAs the spike time-to-first-arrival (TFA) is a primary parameter to describe the output spikes, we rewrite the temporal ERF in the manuscript Eq.(7) as:\n$$\\mathrm{ERF}_\\mathcal{T}(s^{\\ell}, \\tau) =\\sum\\frac{\\partial \\mathcal{L}}{\\partial s^{\\ell}[T]} \\cdot \\frac{\\partial s^{\\ell}[T]}{\\partial (T-\\tau)^{\\ell}}$$\n$$\\frac{\\partial s^{\\ell}[t]}{\\partial t^{\\ell}}=\\frac{\\partial s^l[t]}{\\partial \\Theta_j^l[t]} \\cdot \\frac{\\partial \\Theta_j^l[t]}{\\partial V_j^{l}[t]} \\cdot \\frac{\\partial V_j^{l}[t]}{\\partial t^{l}} - \\frac{\\partial s^l[t]}{\\partial \\Theta_j^l[t]} \\cdot \\frac{\\partial \\Theta_j^l[t]}{\\partial \\theta^l[t]} \\cdot \\frac{\\partial \\theta^l[t]}{\\partial t^{l}}$$\n\nBy setting the gradient stimuli $\\frac{\\partial \\mathcal{L}}{\\partial s_{(i,j)}^{\\ell}[T]}$ to 1, we can compute the temporal ERF using Pytorch's autograd functionality. This allows us to analyze how the timing of input spikes influences the output spike timing, thus providing insights into how information is encoded in the timing of spikes."}, {"review_id": "nFEYOQax1X", "reviewer": "Reviewer_oAHP", "summary": "This paper introduces the Spatio-Temporal Effective Receptive Field (ST-ERF), an extension of the traditional Effective Receptive Field concept from ANNs to SNNs that considers both spatial and temporal dynamics, and shows that ST-ERFs are Gaussian distributed in space and decay over time according to a power law. Based on ST-ERF, this paper also reveals that existing transformer-based SNNs suffer from overly localized receptive fields that hinder long-sequence modeling. The authors attribute this issue to the design of channel mixers and propose two novel modules, MLPixer and Splash-and-Reconstruct Block, to enhance early global receptive fields. Experiments confirm the effectiveness of these modules. In summary, this paper defines ST-ERF for SNNs, identifies a key limitation in transformer-based architectures, and offers effective mixer designs to address it.", "questions": "1. In Figure 6, the receptive field of SR-SDT is mainly concentrated in the lower-left region. What causes this localization?\n\n2. More experiments should conducted to compare to SOTA  methods?\n\n3. The authors have conducted comprehensively analysis about ERF in SNNs,  how can we adapt these conclusions to practical applications?", "limitations": "Yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1.This work introduces the concept of the Effective Receptive Field to the SNN community, filling a critical gap and uncovering the key properties of ST-ERF.\n\n2.By analyzing the spatio-temporal effective receptive field (ST-ERF) of transformer-based SNNs, this paper identifies their limitations and proposes novel modules to address them. The proposed modules are well motivated.\n\nWeaknesses:\n\n1.In the Verification of Gaussian-like distribution of ERF, the paper should also include the ERF of the more commonly used LIF model to check if it likewise follows a Gaussian distribution.\n\n2.There is no comparison with other state-of-the-art methods.", "was_revised": true, "final_justification": "The weaknesses and questions I mentioned have been well addressed by the author.", "rebuttal": "> Q1: ST-ERF in commonly used LIF model :\n\nA1: We apologize for the oversight in not including the ST-ERF visualization for the commonly used LIF model in our original submission. We have now finished this visualization. The detailed explanation of the ST-ERF for the LIF model is shown below the table since the rebuttal contents are not allowed to contain image links. We will include this visualization in the appendix to provide a more comprehensive understanding of the ST-ERF in commonly used LIF models. (**SG**: surrogate gradient function)\n\n\n| Model         | Spatial ERF Pattern |horizontal $\\sigma^2$|vertical $\\sigma^2$|\n|---------------|---------------------|-----|----------|\n| I-LIF         | 2D Gaussian-like    | 4.1 | 4.1 |\n| NI-LIF        | 2D Gaussian-like    | 3.8 | 3.8 |\n| **LIF(SG=$\\mathbf{arctan(\\alpha=2)}$)**| 2D Gaussian-like    | 1.3 | 1.3 |\n| **LIF(SG=$\\mathbf{arctan(\\alpha=4)}$)**| 2D Gaussian-like    | 1.3 | 1.3 |\n| **LIF(SG=$\\mathbf{arctan(\\alpha=8)}$)**| 2D Gaussian-like    | 1.3 | 1.3 |\n| **LIF(SG=$\\mathbf{Sigmoid(\\alpha=2)}$)**| 2D Gaussian-like    | 1.6 | 1.6 |\n| **LIF(SG=$\\mathbf{Sigmoid(\\alpha=4)}$)**| 2D Gaussian-like    | 1.6 | 1.6 |\n| **LIF(SG=$\\mathbf{Sigmoid(\\alpha=8)}$)**| 2D Gaussian-like    | 1.6 | 1.6 |\n\nExperiment Setting:\n| **Hyperparameter**        | **Value**   |\n|-------------------------  |-------------|\n| `arch.`                   | Spiking-CNN |\n| `layers`                  | 20          |\n| `trials of running`       | 50          |\n\nThe LIF-based ST-ERF visualization results show that the ST-ERF distribution follows the 2D Gaussian-like pattern, which is consistent with the findings in our paper. The horizontal and vertical $\\sigma^2$ values are smaller than those of the I-LIF and NI-LIF models, indicating a more localized receptive field distribution.\n\n> Q2: More comparison to SOTA models on various tasks:\n\nA2: We appreciate your suggestion. We have conducted additional experiments on event-based tracking tasks using the FE108 and VisEvent datasets to compare with SOTA models.\n\n**Event-based Tracking Experiments**: To comprehensively evaluate our ERF-guided architectural improvements across different temporal processing domains, we extended our evaluation to event-based object tracking tasks. Event-based tracking presents unique challenges as it requires processing asynchronous, sparse event streams with high temporal resolution while maintaining spatial consistency across time. Unlike traditional RGB tracking, event cameras capture brightness changes asynchronously, producing sparse event streams that require specialized temporal aggregation and spatial attention mechanisms.\n\nOur experimental setup employed the SD-Track architecture as the baseline, which integrates event-based feature extraction specifically designed for processing event streams. We systematically replaced the core processing blocks with our proposed MLPixer and SR block variants while maintaining identical experiment setups. The FE108 dataset provides high-speed tracking scenarios with rapid object motion, while VisEvent offers more diverse tracking conditions with varying lighting and occlusion patterns. The results are summarized in the following tables:\n\n| Model         |#T|#P| FE108 Tracking (AUC/PR) | VisEvent Tracking (AUC/PR) |\n|:--------------|--|--|:-------------------------|:---------------------------|\n| ODTrack       |1*1|92.83|43.2/69.7|24.7/34.7|\n| HIPTrack     |1*1|120.51|50.8/81.0|32.1/45.2|  \n| SD-Track(Tiny)|4*1|19.61|56.7/89.1|35.4/48.7|\n| SD-Track(Tiny)|1*4|19.61|59.0/91.3|35.6/49.2|\n| SD-Track(Tiny)-MLPixer ($\\epsilon=4$)|1*4|20.21|57.1/89.2|33.7/47.3|\n| SD-Track(Tiny)-MLPixer ($\\epsilon=6$)|1*4|22.99|57.9/90.1|34.5/48.9|\n| SD-Track(Tiny)-SR ($\\epsilon=4$)|1*4|21.43|58.2/88.5|33.8/48.0|\n\nThe results demonstrate that our architectural modifications not only preserve but in some cases improve tracking performance across both precision (PR) and area-under-curve (AUC) metrics. Notably, MLPixer with $\\epsilon=6$ and SR blocks show consistent improvements, validating that our ERF-guided architectural choices are effective across diverse temporal processing tasks beyond static image classification. \n\n> Q3: In Figure 6, the receptive field of SR-SDT is mainly concentrated in the lower-left region. What causes this localization?\n\nA3: The localization of the receptive field in the lower-left region of Figure 6 is primarily due to the model's learning selectivity. This phenomenon occurs because the analysis framework is based on the propagation of gradients, which can lead to a shift in the effective receptive field when the gradient stimuli backwards towards the whole network. The input data also plays a role in this localization effect, as it influences how the model learns to focus on specific regions of the input space. \n\nTo verify whether the Spatial ERF is pixel-wise invariant, we can conduct experiments by shifting the input gradient stimuli and observing the corresponding changes in the spatial ERF pattern. If we use a stimuli that simply shifts the focus by a certain amount, we would see a totally different receptive field distribution. This result demonstrates that in a properly-trained network, every single pixel has its own unique ERF pattern. To verify whether the training data is responsible for this effect, we can conduct ablation studies by sampling a subset of the original training data and observing the changes in the spatial ERF given the same gradient stimuli. We will include the visualization explanation in the updated manuscript to clarify this point further. The comparison is below the table since the rebuttal contents are not allowed to contain image links.\n\n|Model|Gradient Stimuli|Spatial ERF Pattern in Stage 3|\n|------------|--------|--------------|\n| SDT-v3-Tiny|Centered|Conv-like Gaussian facula|\n| SDT-v3-Tiny|Shifted $(+5)_{vertical}$ pixels|Conv-like Gaussian facula (shifted $(+5)_{vertical}$)|\n| SDT-v3-Tiny|Shifted $(+5)_{horizontal}$ pixels|Conv-like Gaussian facula (shifted $(+5)_{horizontal}$)|\n| SDT-v3-Tiny-MLPixer($\\epsilon=4$)|Centered|Patchy distribution with regional selectivity|\n| SDT-v3-Tiny-MLPixer($\\epsilon=4$)|Shifted $(+5)_{vertical}$ pixels|Patchy distribution with regional selectivity (totally different from original)|\n| SDT-v3-Tiny-MLPixer($\\epsilon=4$)|Shifted $(+5)_{horizontal}$ pixels|Patchy distribution with regional selectivity (totally different from original)|\n| SDT-v3-Tiny-SR($\\epsilon=4$)|Centered|Patchy distribution with regional selectivity|\n| SDT-v3-Tiny-SR($\\epsilon=4$)|Shifted $(+5)_{vertical}$ pixels|Patchy distribution with regional selectivity (totally different from original)|\n| SDT-v3-Tiny-SR($\\epsilon=4$)|Shifted $(+5)_{horizontal}$ pixels|Patchy distribution with regional selectivity (totally different from original)|\n\nThe exploration of the spatial ERF in S-ViTs, particularly in the context of MLPixer and SR blocks, reveals that the design of these architectures plays a crucial role in introducing a disaggregated-then-reintegrated receptive field structure. This finding highlights the importance of architectural choices in shaping the effective receptive fields and their localization properties.\n\n> Q4: How to adapt ERF-based conclusions in SNNs to practical applications?\n\nA4: Through the comprehensive ST-ERF analytical framework, we demonstrate that SNN blocks with specialized designs (including but not limited to task-specific convolutional operators, adaptive/windmill convolutions, or attention-enhanced mechanisms such as self-attention/SE modules) exhibit distinct input feature preferences. These spatially modulated preferences facilitate the interpretability of block-level behaviors across different tasks, thereby providing principled guidance for: (1) designing more powerful and computationally efficient task-specific architectures, or (2) formulating constraints for Neural Architecture Search (NAS) to discover optimal topologies.\n\nTemporally, our analysis reveals dynamic preference variations across timesteps in SNN implementations (under current LIF/I-LIF activation paradigms). The intrinsic membrane potential updating mechanism inherently strengthens responses to recent inputs while attenuating distant temporal information—a property we term temporal locality bias. This finding motivates further investigation via the ST-ERF framework to quantify how neuronal dynamics parameters govern spatiotemporal receptive fields in more biologically plausible SNNs. Such exploration could yield fundamental insights into the shared principles and divergences between brain-inspired networks and biological neural systems."}, {"review_id": "7dizT2TXd2", "reviewer": "Reviewer_X2Er", "summary": "This paper introduces the Spatio-Temporal Effective Receptive Field (ST-ERF), a gradient-based metric for analyzing how spiking neural networks (SNNs) process spatial and temporal information. Using ST-ERF, the authors evaluate several existing Spiking Vision Transformer (S-ViT) models and identify a limitation in their global receptive field coverage. To address this, they propose two new channel-mixer designs—MLPixer and Splash-and-Reconstruct (SR) Block—which aim to enhance global spatial ERF in early stages. The proposed methods are evaluated on COCO 2017 and ADE20K, showing improvements in detection and segmentation tasks.", "questions": "See Weaknesses", "limitations": "N/A", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1. The paper proposes ST-ERF, a well-motivated and theoretically grounded framework to understand the spatial and temporal behavior of SNNs.\n2. The diagnostic application of ST-ERF to Transformer-based SNNs is insightful and helps identify architectural bottlenecks related to global receptive field coverage.\n3. The proposed MLPixer and SR Block modules are lightweight and show performance improvements on standard vision benchmarks.\nWeaknesses:\n1.  The comparison between ViT-B (a lightweight, pure Transformer) and S-ViTs (which include heavy neuromorphic modules like SPS blocks) is not well controlled. Differences in ERF may arise from structural depth and convolutional paths rather than the spiking mechanism itself.\n2. ERF distributions can vary with activation types. No comparisons are made with ReLU/GELU or quantized ViT variants.  Modern ViT variants (e.g., Swin-T, PVT) are excluded, weakening claims about S-ViT inferiority in global modeling.\n3. The paper does not isolate the effects of MLPixer and SR Block via controlled replacements or report their individual contributions. Though the method is motivated by temporal modeling, only static image datasets (COCO, ADE20K) are used. No temporal benchmarks are evaluated.\n4. The path from ERF diagnosis to MLPixer/SR block design lacks clarity. More intuition, derivation, or visualization is needed to justify the structural choices.", "was_revised": true, "final_justification": "The authors have addressed my concerns clearly and conducted extensive additional experiments to support their claims. I appreciate the clarification of the architectural comparisons, the added analysis of spatial ERFs across various ViT variants, and the new temporal benchmark results. The connection between ERF diagnosis and the proposed module designs is now better explained. Overall, the rebuttal strengthens the paper, and I have decided to raise my score.", "rebuttal": "> Q1: Concerns about the comparison between ViT-B and S-ViTs:\n\nA1: We sincerely appreciate your attention to the clarity of Figure 2 and the ensuing concerns it raised regarding the rigor of our experimental controls. We understand your concerns and would like to clarify the original intent behind Figure 2 and its key findings.\n\nThe primary purpose of Figure 2 was to: provide a visualization and comparison of the Spatial Effective Receptive Fields (*Spatial ERFs*) for comparable ANN- and SNN-based Transformer models. This approach was designed to profoundly reveal the underlying learning mechanisms and behavioral patterns. Our experimental design rigorously controlled for architectural consistency:\n1.  **ViT-like Architecture Comparison Group**: The Vanilla ViT (ANN) and Spikformer/SDT-V1 (SNN) exhibit identical module structure, with the core difference residing solely in the activation function (ANN: ReLU; SNN: Spiking).\n2.  **Metaformer Architecture Comparison Group**: The CAFormer-s18 (ANN, Metaformer paradigm) and its counterpart Meta-SDT-S (SNN) are precisely matched in critical design elements such as convolutional pathways and mixed hierarchical block design.\n\nThe experimental results clearly demonstrate that, under strict control of architectural variables, the ANN and SNN models exhibit strikingly similar Spatial ERF distribution characteristics:\n*   ViT-like architecture's ERF manifests a `checkerboard pattern`, which is highly similar to the ERF patterns observed in both Spikformer (8-512) and SDT-V1.\n*   Similarly, the ERF of both CAFormer-s18 (ANN) and Meta-SDT-S (SNN) display a highly `localized pattern`, remarkably analogous to that of traditional CNN networks. This indicates the model's focus is primarily concentrated on local regions, with relatively limited interaction occurring with other image patches.\n\nTherefore, the consistent ANN/SNN ERF patterns presented in Figure 2 precisely serve as compelling evidence for the effectiveness of our experimental design and the rigor of our variable control (particularly concerning architecture). This observed consistency directly captures the key phenomenon we aimed to introduced: Different architectures influence the learning behavior of ANN vs. SNN models, which is the foundation of our investigation on the limitation in spatial ERF distribution in current S-ViT models.\n\nTo present the aforementioned experimental design and core findings more clearly, we will undertake a comprehensive reorganization of Figure 2:\n*   ANN models will be presented side-by-side with their structurally identical SNN counterparts.\n*   Move QKFormer (10-384) visualization to Appendix, as its architecture is not quite comparable to the other models.\n\n> Q2: More Spatial ERF visualizations for other ViT models:\n\nWe have supplemented the following ViT variants to provide a more comprehensive presentation of the Spatial ERF characteristics across different ViT models.\nSince the rebuttal contents are not allowed to contain image links, we will give an overall comparison in the following table:\n\n| Model                     |ImageNet Acc-1(%)  | Spatial ERF Pattern       | Interaction Intensity with other patches |\n|---------------            |---------------    |---------------------      |--------------------|\n| Meta-SDT-S(SNN)           | 75.3              | Conv-like Gaussian facula              | +            |\n| ViT-Tiny (ReLU) (ANN)            | 73.0              | Checkerboard              | ++            |\n| ViT-Tiny (GELU) (ANN)           | 75.4              | Checkerboard              | ++            |\n| Q-ViT DeiT-Tiny (4-bit) (ANN)   | 74.3              | Checkerboard              | ++           |\n| Swin-Tiny (ANN)                 | 80.9              | Hierarchical block        | +++           |\n| PVTv2-B0 (ANN)                  | 70.5              | Conv-like Periodic facula | ++            |\n\nNote that all the above ANN-based models exhibit a more global receptive field distribution compared to the S-ViT models, which is consistent with the findings in our paper. The interaction intensity with other patches in ANN-based models is also higher, indicating a more global receptive field distribution.\nWe will include these visual aids into the revised manuscript to facilitate a more comprehensive comparison of the Spatial ERF distributions across different ViT models.\n\n> Q3: Concerns about the controlled replacements of MLPixer and SR Block and unclear analysis path from spatial ERF to MLPixer/SR block design:\n\nA3.1: We thank the reviewer for raising this point. In our detection and segmentation experiments, all blocks in Stages 1 & 2 were systematically replaced with MLPixer or SR Block, ensuring that block type was the sole variable. This controlled setup allowed us to isolate the impact of architectural design on model performance.\n\nA3.2: We acknowledge that the connection between Spatial ERF analysis and our block design choices was not fully articulated. The key insight is that the Spatial ERF distribution of the S-ViTs, as visualized in Figure 2, reveals a more localized pattern: having a stronger focus on local features but limited global context. This suggests that current S-ViTs may not fully leverage the global receptive field capabilities of their ANN counterparts. Throughout the exploration, we observed that the MLPixer and SR Block designs, which are more suited for global feature extraction, align better with the Spatial ERF distribution of S-ViTs. This is why we chose to replace the original blocks with MLPixer and SR Block in our experiments. Our experiments demonstrated that these replacements led to improved performance in detection and segmentation tasks, further supporting the hypothesis that S-ViTs can benefit from architectural designs that enhance global context understanding.\n\n> Q4: Question on the benchmarking of S-ViTs: Provide more temporal benchmarks:\n\nWe appreciate your suggestion to provide more temporal benchmarks for S-ViTs. We have conducted additional experiments on the DVS128 Gesture datasets based on the QKFormer network, which are commonly used benchmarks for event-based vision classification tasks. \n\nThe baseline network is QKFormer-PE1(4-layer-res)-S1-PE2(2-layer-res)-S2, containing two stages of Q-K attention (S1 & S2) and the corresponding positional encoding blocks(PE1 & PE2). We apply the block design of MLPixer and SR block on the PEs. Note that because the original QKFormer has residual paths in PEs, we also added the block design of MLPixer and SR block on the residual paths to see their performance\n\nThe results are summarized in the following table:\n\n| Architecture                          |Step | Param (M) | DVS128Ges. Acc. (%) |\n|--------------------------------------|----|----|-----|\n| **QKFormer-PE1-S1-PE2-S2**           |$16$|1.99|97.9|\n| ✓ ***+PE1-MLPixer ($\\epsilon=2$)***  |$16$|1.91|97.9|\n| ✓ ***+PE1-respath-MLPixer***              |$16$|1.91|97.2|\n| ♠ ***+PE1-MLPixer ($\\epsilon=3$)***  |$16$|1.93|98.3|\n| ♠ ***+PE1-respath-MLPixer***              |$16$|1.93|97.2|\n| ► ***+PE1-SR ($\\epsilon=2$)***       |$16$|1.92|98.3|\n| ► ***+PE1-respath-MLPixer***              |$16$|1.92|98.6|\n| ✓ ***+PE2-MLPixer ($\\epsilon=2$)***  |$16$|1.21|97.6|\n| ✓ ***+PE2-respath-MLPixer***              |$16$|1.21|98.3|\n| ♠ ***+PE2-MLPixer ($\\epsilon=3$)***  |$16$|1.26|97.9|\n| ♠ ***+PE2-respath-MLPixer***              |$16$|1.26|98.3|\n| ► ***+PE2-SR ($\\epsilon=2$)***       |$16$|1.48|98.3|\n| ► ***+PE2-respath-MLPixer***              |$16$|1.48|98.6|\n\nExp Setting:\n| **Hyperparameter**        | **Settings for DVS128 Gesture**   |\n|-------------------------  |-------------|\n| `batch_size`              | 16          |\n| `T` (time steps)          | 16          |\n| `opt`                     | adamw       |\n| `opt_eps`                 | 1e-08       |\n| `weight_decay`            | 0.06        |\n| `momentum`                | 0.9         |\n| `sched` (scheduler)       | cosine      |\n| `lr`                      | 0.001       |\n| `warmup_lr`               | 1e-05       |\n| `min_lr`                  | 2e-05       |\n| `epochs`                  | 192         |\n| `decay_epochs`            | 20          |\n| `warmup_epochs`           | 10          |\n| `decay_rate`              | 0.1         |\n| `smoothing` (label smooth)| 0.1         |\n| `mixup`                   | 0.5         |\n| `cutmix`                  | 0.0         |\n| `cutmix_minmax`           | `None`      |\n| `mixup_prob`              | 0.5         |\n| `mixup_switch_prob`       | 0.5         |\n\nWe also have conducted additional experiments on the Event-based tracking tasks on FE108 dataset and VisEvent dataset. The results are summarized in the following tables:\n\n| Model         |#T|#P| FE108 Tracking (AUC/PR) | VisEvent Tracking (AUC/PR) |\n|:--------------|--|--|:-------------------------|:----------------------------|\n| SD-Track(Tiny)|4*1|19.61|56.7/89.1|35.4/48.7|\n| SD-Track(Tiny)|1*4|19.61|59.0/91.3|35.6/49.2|\n| SD-Track(Tiny)--MLPixer ($\\epsilon=4$)|1*4|20.21|57.1/89.2|33.7/47.3|\n| SD-Track(Tiny)--MLPixer ($\\epsilon=6$)|1*4|22.99|57.9/90.1|34.5/48.9|\n| SD-Track(Tiny)--SR ($\\epsilon=4$)|1*4|21.43|58.2/88.5|33.8/48.0|\n\nExp Setting:\n| **Hyperparameter**        | **Settings for FE108** | **Settings for VisEvent** |\n|-------------------------  |-------------|-------------|\n| `epochs`                  | 100         | 100         |\n| `opt`                     | adamw       | adamw       |\n| `sample number`           | 60000       | 30000       |\n| `lr`                      | 4e-4        | 4e-4        |\n| `decay_epochs`            | 80          | 80          |\n\nThese results confirm that the MLPixer and SR block designs preserve S-ViT performance. While current temporal benchmarks show promise, further improvement is possible. We appreciate your insightful suggestion, which has highlighted this important direction for exploration."}]

Author rebuttal:

Meta-review: This paper received four positive reviews, with all four reviewers converging to accept recommendations --- 2 Accept, 2 Borderline Accept. 

There was general appreciation for the importance of the problem considered here, the novelty of the solution and the analysis, the strength of the results and the overall presentation. 

While there were some concerns raised in the original reviews, they were adequately addressed during the author-reviewer discussion phase. As a result, an accept decision was reached.
Decision: Accept (poster)