Cannistraci-Hebb Training on Ultra-Sparse Spiking Neural Networks
Authors: Yuan Hua
Jilin Zhang
Yingtao Zhang
Leyi You
Baobo Xiong
Carlo Vittorio Cannistraci
Hong Chen
Venue: ICLR 2026 Poster (2026)
Keywords: Sparse Spiking Neural Network
Dynamic Sparse Training
Pruning and Regrowth
Primary area: applications to neuroscience & cognitive science

Abstract: Inspired by the brain's spike-based computation, spiking neural networks (SNNs) inherently possess temporal activation sparsity. However, when it comes to the sparse training of SNNs in the structural connection domain, existing methods fail to achieve ultra-sparse network structures without significant performance loss, thereby hindering progress in energy-efficient neuromorphic computing. This limitation presents a critical challenge: how to achieve high levels of structural connection sparsity while maintaining performance comparable to fully connected networks. To address this challenge, we propose the Cannistraci-Hebb Spiking Neural Network (CH-SNN), a novel and generalizable dynamic sparse training framework for SNNs consisting of four stages. First, we propose a sparse spike correlated topological initialization (SSCTI) method to initialize a sparse network based on node correlations. Second, temporal activation sparsity and structural connection sparsity are integrated via a proposed sparse spike weight initialization (SSWI) method. Third, a hybrid link removal score (LRS) is applied to prune redundant weights and inactive neurons, improving information flow. Finally, the CH3-L3 network automaton framework inspired by Cannistraci-Hebb learning theory is incorporated to perform link prediction for potential synaptic regrowth. These mechanisms enable CH-SNN to achieve sparsification across all linear layers. We have conducted extensive experiments on six datasets including CIFAR-10 and CIFAR-100, evaluating various network architectures such as spiking convolutional neural networks and Spikformer. The proposed method achieves a maximum sparsity of 97.75% and outperforms the fully connected (FC) network by 0.16% in accuracy. Furthermore, we apply CH-SNN within an SNN training algorithm deployed on an edge neuromorphic processor. The experimental results demonstrate that, compared to the FC baseline without CH-SNN, the sparse CH-SNN architecture achieves up to 98.84% sparsity, an accuracy improvement of 2.27%, and a 97.5$\times$ reduction in synaptic operations, and the energy consumption is reduced by an average of 55$\times$ across four datasets. Our code is available at https://github.com/HuaGuaiGuai/CH-SNN.

Published as a conference paper at ICLR 2026
CANNISTRACI-HEBB TRAINING ON ULTRA-SPARSE SPIKING NEURAL NETWORKS
Yuan Hua Jilin Zhangl i, Yingtao Zhang*.3 Leyi You', Baobo Xiong', Carlo Vittorio Cannistraci 3, Hong Chen
I School of Integrated Circuits, Tsinghua University, Beijing China
2 Center for Complex Network Intelligence the Tsinghua Laboratory of Brain and Intelligence,
Department of Psychological and Cognitive Sciences
3 Department of Computer Science and Technology, Tsinghua University, Beijing, China
4 Department of Physics, Tsinghua University, Beijing, China
5 Zhili College, Tsinghua University, Beijing. China
6 School of Biomedical Engineering, Tsinghua University, Beijing, China
Corresponding authors
Equal contribution
ka kalokagathos.c aaooagaathoo...onmmmlllaa agon@gmail com, hongchen@tsingguu..o edu.
ABSTRACT
Inspired by the brain's 's spike-basee computation, spiking neural networks (SNNs) inherently possess temporal activation sparsity. However, when it comes the sparse training of SNNs in the structural connection domain, existing methods fail achieve ultra-sparse network structures without significant performance loss, thereby hindering progress in energy-efficient neuromorphic computing. This lim- itation presents a critical challenge: how to achieve high levels of structural con- nection sparsity while maintaining performance comparable to fully connected networks. To address this challenge, we propose the Cannistraci Hebb Spiking Neural Network (CH-SNN), novel and generalizable dynamic sparse training framework for SNNs consisting of four stages. First, we propose a sparse spike correlated topological initialization (SSCTT) method to initialize a sparse network based on node correlations. Second, temporal activation sparsity and structural connection sparsity are integrated via a proposed sparse spike weight initializa- tion (SSWI) method. Third, a hybrid link removal score (LRS) is applied to prune redundant weights and inactive neurons, improving information flow. Fi- nally, the CH3-L3 network automaton framework inspired by Cannistraci- Hebb learning theory is incorporated to perform link prediction for potential synaptic regrowth. These mechanisms enable CH-SNN to achieve sparsification across all linear layers. We have conducted extensive experiments on six datasets including CIFAR-10 and CIFAR- 100, evaluating various network architectures such spik- ing convolutional neural networks and Spikformer. The proposed method achieves maximum sparsity of 97.75% and outperforms the fully connected (FC) network by 0.16% in accuracy. Furthermore, we apply CH-SNN within an SNN training algorithm deployed an edge neuromorphic processor. The experimental results demonstrate that, compared to the FC baseline without CH-SNN, the sparse CH- SNN architecture achieves up to 98 88.84% sparsity, an accuracy improvement of 2.27%, and a 97.5% x reduction in synaptic operations, and the energy consumption is reduced by an average of 55x across four datasets. Our code available htnps//ggthhb.comm/uuuuuuuuuaulu
INTRODUCTION
The increasing computational demands and energy consumption of deep neural networks have spurred the exploration of energy-efficient alternatives. Inspired by the event-driven processing mechanism of the human brain, spiking neural networks (SNNs) have emerged as a promising solu- tion due to their inherent temporal activation sparsity (Liett 2024 Roy al. 2019). The temporal

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Published as a conference paper at ICLR 2026
activation sparsity of SNNs stems from their spiking characteristics necrros nnerons only fire spikes when the membrane potential reaches the threshold, remaining in resting state for most of the time (Wu et al. 2023). Compared to artificial neural networks (ANNs), SNNs demonstrate significant advan- tages in energy efficiency, making them well-suited for a variety of edge-side applications such as
gas detection (Huo al. 2025), sEMG-based gesture recognition (Zhang al. 2024a) and real-time
multi-object recognition (Merolla et al. 2014).
Despite the inherent advantages in temporal activation sparsity, SNNs often suffer from a fixed ar- chitecture that lacks flexibility and structural plasticity, which limits the learning capability of SNNs and their application in resource- resource-lmmited neuromorphic hardware (Davies al.) 2018). To address this problem, previous works introduce structural connection sparsity through network pruning and regrowth (Bennett et al. 2018). Although sparse training has proven effective reducing parameter counts and improving computational efficiency in ANNs (Mocanu et al., 2018 Evei et al. 2019] Yuan et al.] [ Zhang et al.] 2022). its application in SNNs remains challenging. This due to the spike-based computation and the non-differentiable nature of the spiking activation function of optimization. Consequently, most sparse training meth- ods for ANNs that rely gradient information cannot be directly applied to SNNs.
SNNs, which hinder direct gradient-
Specifically, current research in sparse SNNs training methods faces a significant challenge in achieving high levels of structural connection sparsity while maintaining performance compara- ble to that of their fully connected counterpart. For instance, the adaptive structural development of SNN (SD-SNN) model (Han et al., 2025a), incorporates multiple brain-inspired developmental mechanisms, including synaptic elimination, neuronal pruning and synaptic regeneration. Besides, it also uses adaptive pruning and regrowth rates, which led to the structural stability. As result, SD-SNN achieves 98.56% accuracy with 1.45% improvement on DVS-Gesture dataset, but only reaches a maximum sparsity of 61.10%. Similarly, [Shen al. (025) propose two-stage dynamic structure learning method, effectively addressing the limitations of fixed pruning ratios and static sparse training methods prevalent existing models. Nonetheless, their approach attains an average structural connection sparsity of around 70%. Some studies directly apply ANN-based sparse train- ing methods to SNNs, Gradient Rewiring (Shen et al. 2025) method achieves up to 90% sparsity. However, it exhibits accuracy degradation of 3.55% compared to its fully connected counterpart.
To address this challenge, we propose the Cannistraci- novel and generalizable dynamic sparse training framework for SNNs, which achieves high levels of structural connection sparsity and maintaining performance comparable to that of its fully connected (FC) counterpart. The main contributions of this work are summarized follows:
Spiking Neural Network (CH-SNN), a
Introducing a novel sparse training framework. We propose a four-stage dynamic sparse training framework (CH-SNN) consisting of sparse topology initialization, sparse weight initialization, network pruming and network regrowth. CH-SNN attains 99% structural con- nection sparsity in all linear layers and shows better performance than FC networks on the CIFAR-100, MNIST, N-MNIST, CIFARIO-DVS and DVS-Gesture datasets respectively.
Proposing efficient initialization methods. We propose two initialization methods, one is Sparse Spike Correlated Topological Initialization (SSCTT) which initializes ultra- sparse network structure by leveraging correlations among input nodes, another is Sparse Spike Weight Initialization (SSWI) which incorporates temporal activation sparsity and structural connection sparsity of SNNs to initialize weights. SSCTI and SSWI enhance the performance of the link predictor and facilitate faster training from the initial phases.
Demonstrating superior performance across architectures and datasets. We have con- ducted extensive experiments, the experimental results demonstrate that CH-SNN outper- forms existing sparse SNN training methods across six datasets (CIFAR10-DVS, CIFAR- 10, CIFAR- 100, MNIST, N-MNIST and DVS-Gesture) and three network structures. No- tably, it attains a O. 0.16% accuracy improvement over the FC network at sparsity of 97.75% We apply CH-SNN to a hardware- -frinrddrrreyyyy algorithm S-TP, which has been implemented neuromorphic processor for edge-side Al applications. Experimental results show that CH-SNN significantly improve energy efficiency, achieving an average improvement of 55x across four datasets.
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2
RELATED WORKS
2.1 SPARSE SPIKING NEURAL NETWORKS
Structural connection sparsification is one of the key technologies for enhancing SNNs energy ef- ficiency. By reducing redundant links and neurons within the model, it can significantly reduce computational and storage overhead. Existing sparse SNNs training methods can be categorized into pruning and sparse training.
Pruning. Pruning methods initialize fully connected network structure and gradually remove in- significant links during training. Current SNNs pruning approaches can be divided into the two types: (1) Biological plasticity pruning. This approach draws inspiration from the developmen- tal mechanisms of the brain, leveraging biological synaptic plasticity to accomplish the pruning of SNNs. Han et al. 2025b a) propose the developmental plasticity-inspire adaptive pruning method, which takes into account multiple biologically realistic mechanisms, so that the network structure can be dynamically optimized. |athi et al. (2019) present a sparse SNN training method where pruning is based on the spike timing dependent plasticity model (STDP). Links between pre-neuron and post-neuron with low correlation or uncorrelated spiking activity are pruned. Liu et al. (2022) propose a dynamic pruning framework (named DynSNN) for SNNs, enabling dynamic optimization of the network topology. (2) Transfer ANNs pruning method to SNNs. These methods adapt prun- ing techniques from ANNs. For instance. [hen al. (2022) use different functions describing the growing threshold of state transition to regulate the pruning speed, avoiding disastrous performance
degradation at the final stage of training. Deng et al. (023) formulate the link pruning problem as a constrained optimization problem, which is addressed by integrating spatiotemporal backpropaga- tion (STBP) with the alternating direction method of multipliers (ADMMs). Backpropagation with sparsity regularization (BPSR) (Yan et al.] 2022) incorporates an LI regularization term into the loss function to drive the weights toward zero, followed by a static threshold-based pruning method, thereby achieving network structural connection sparsification.
Sparse training. In contrast to pruning methods, sparse training begins with a sparsely connected network and dynamically alternates between pruning less important connections and growing new ones during learning. It maintains sparsity in both the forward and backward propagation during the training process, resulting in lower hardware requirements. For example, the Deep Rewiring (Deep R) (Bellec et al. (2018) method prunes links when their value changes sign during updates, and randomly regenerate an equivalent number of links. This process is repeated over multiple rounds. Based on Deep R. Chen et al. (202T) introduce a Gradient Rewiring (Grad R) approach to further modify the gradient values of the links, enabling previously pruned links to regenerate. Furthermore. Shen et al. (2025) propose a two-stage dynamic structure learning method for deep SNNs, the first stage evaluates the network's s compressibility based on the PQ index (Diao et al.) 2023) and adaptively determines the regrowth ratio, and the second stage performs pruning and regrowth according to this ratio. Qi et al. (2018) propose a spiking neural network with connection gates (SNN-CG) to jointly learn the topology and the weights in SNN. The connection structures and the weights are learned alternately until a termination condition is satisfied. Neurogenesis dynamics- inspired spiking neural network (NDSNN) training method (Huang al. 2023) trains model from scratch using dynamic sparsity. NDSNN creates a trop-and-grov strategy to promote link reduction. Based on Rigl. (Evei al. 2019) Lasby et al. (2024) propose a sparse-to-spen to-saars dynamic sparse training method named Structured (SRigl,, which learns sparse neural network with constant fan-in fine-grained structured sparsity while maintaining generalization comparable with RigL.
2.2 CANNISTRACI--ERR THEORY AND NETWORK TOPOLOGY INTELLIGENCE
Inspired by the dynamic sparse connectivity characteristics of the brain, the Cannistraci Hebb (CH) theory (Cannistraci et al., 2013 Daminelli et al. 2015; Cannistraci] 2018a| Muscoloni et al. 2018 Zhao et al. 2025) is a general theoretical framework developed in the hield of network science to pre- dict the non-observed dynamic connectivity of complex networks, using the mere knowledge of the network topology. CH theory is also recently introduced (Zhao et al. 2025 Zhang et al. 2024b) for dynamic sparse training for deep AI, demonstrating gradient-free link regrowth mechanism that re- lies solely topological information. For example, Cannistraci- -ebttrarc---hbbbbb Training (CHT) (Zhang et al.) 2024d) is applied to ANNs, utilizing the CH3-L3 network automaton for link prediction. CH3-L3 is one of the highest-performing and most robust network automata under the Cannistraci-Hebb the-
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2025). It can automatically evolve the network topology of a given structure by ory (Zhao et al. identifying node pairs with the fewest externa connections within the local community structure, thereby guiding link regrowth. For multiple tasks, CHT achieves better performance surpassing than fully connected networks with only 1% connections, demonstrating the ultra-sparse advantage. Im- portantly, CHT is shown to induce during training also node sparsification process (called network node percolation), which at the end of the training compressed the node size of certain networks to around the 30 percent of the initial size, preserving or improving task performance. Further- more, Zhang et al. (002c) put forward a Cannistraci- Hebb Training soft rule (CHTss which prob- abilistically removes network links based on a removal fraction and regrows new links according to CH3-L3 prediction scores, overcoming CHT's tendency to fall into epitopological local minima during the early stages of training when topological noise significant.
3 METHODS
3.1 SPIKING NEURAL NETWORK
Fundamentals. Unlike artificial neural networks, SNNs use sparse spike signals to transmit infor- mation. The spike signals enable SNNs avoid Multiply-Accumulate (MAC) operations. Thereby reducing energy consumption and computational load (Rueckauer et al. 2017). In this paper, we adopt the leaky integrate-and-fire (LIF) neuron (Abbott T999) process spike signals, shown in Equation II.
(1 (1-
+ E Wi +1),
- =(()=0(;;00) -)
(1)
where t denotes the time step, v-) represents the membrane potential of the neuron j. a is the membrane potential decay constant, Way denotes the synaptic weight, xx()) is the input spike, and U is the step function. When the membrane potential accumulates and exceeds the firing threshold 0, the neuron emits an output spike, denoted by 2-(-) = 1. Otherwise, the neuron remains silent, i... 2-(-) 0. After firing spike, the membrane potential is reset to zero
Training method. It is challenging to apply standard gradient descent to SNNs. The step function in Equation ① results in a derivative that is zero almost everywhere and undefined the threshold point. This makes the direct calculation of partial derivatives duz(] impossible using conventional calculus, which prevents the application of the backpropagation algorithm. Thus we use the surro- gate gradient method (Wu et al. 2018) to update the weights of SNNs.
dz;(1
Sparse Target Propagation. Sparse Target Propagation (S-TP) (Zhang et al. 2024a) adopts a hardware-friendly surrogate gradient method. S-TP randomly selects target windows in the learning process, reducing over 90% of the spike number in the learning process without noticeable accuracy degradation. S-TP has been implemented in low-power neuromorphic processor, which proves its notable wrrdware-freendliness..
3.2 CANNISTRACI-HERB SPIKING NEURON NETWORK
In this paper, we propose the four-stage dynamic sparse training method for SNNs, named Cannistraci-Hebb Spike Neuron Network (CH-SNN). It is general sparse training framework ca- pable of sparsifying all linear layers in SNNs. The framework of CH-SNN is illustrated in Fig- [ The first stage is sparse topology initialization. We propose a sparse topology initialization method named Sparse Spike Correlated Topological Initialization (SSCTI) based on Pearson's phi coefficient to initialize an ultra-sparse network. The second stage is sparse weight initialization. We introduce the Sparse Spike Weight Initialization (SSWI) method, which incorporates the tem- poral activation sparsity, structural connection sparsity and neuronal threshold information of SNNs into the weight initialization process to perform weight initialization. The third stage is network pruning. We use a probability-basee links pruning strategy to remove links according to dynamic ratio Ç. Subsequently, inactive neurons are identified and removed, according to the CHT network percolation procedure (Zhang al. 2024d). The fourth stage is network regrowth. Here, the regrowth score of potential links is computed using CH3-L3. According to this score, links are regenerated with the same ratio applied in the network pruning stage, thereby maintaining the pre-
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CH-SNN
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Figure 1: The framework of Cannistraci-Hebb Spiking Neural Network (CH-SNN).
defined structural connection sparsity. Links with higher regrowth scores are proportionally sampled according to the CHT's methodology (Zhang et al. 2024c).
3.2.1 SPARSE TOPOLOGY INITIALIZATION
As know, the topology of network should reflect the relationships between node features within some latent geometric space (Cannistraci Muscoloni 2020). The correlations between input fea- tures directly define the geometric relationships among nodes in this latent feature space. Therefore, by computing the correlations between nodes in the input layer, we preserve connections between highly correlated nodes according the predefined sparsity. Thus, we propose the Sparse Spike Correlated Topological Initialization (SSCTI) method, as shown in Figure [ Stage 1. Since the in- put of SNNs are discrete binary spike trains, we measure the correlation between input nodes using Pearson's 's phi coefficient (Pearson) 2015), which measures the strength and direction of association between two binary variables. We take each dimension of the input data z; and each time step as variable and independent sample, respectively. Thus, the total number of samples is N x T. The Pearson's 's phi coefficient is described in Equation (
Σ ExT(, - E + NT +MT - E
1 = 2NT
(2)
2NT
where dij represents the Pearson's phi coefficient between input data o; and Vj. M denotes the dimension of the input data, T' is total time step, N stands for the number of samples, X2 represents the Chi-square statistic, and E. is the mean value of rG, From Equation (2). we obtain the correlation matrix Φ E M M we keep the top (1 S,) proportion of links of the SNN with the strongest correlations and remove other links in SNN, where S, stands for the structural connection sparsity, thereby completing the initialization of the network structure. The dimensionality of the hidden layer is determined by an expansion factor 3 2 1, 3 E Z, such that the dimension of the hidden layer equals the input dimension multiplied by This allows the hidden layer dimensionality to be flexibly adjusted, as shown in Figure [ Stage 1. However, when CH-SNN is used to sparsify inter- mediate layers, such as linear layers within spiking convolutional neural networks (Lv et al. 2024)
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Spikformer (Zhou al. 2022). the input distribution may be altered by preceding convolutional layers or attention layers. This makes difficult for SSCTI to accurately capture feature correla- tions between nodes. To address this issue, adopt a uniform random initialization strategy. which ensures that each node retains an equal number of connections. See more details in Appendix A.4
3.2.2 SPARSE SPIKE WEIGHT INITIALIZATION
For ANNs, weight initialization strategies such Kaiming initialization (He 2015) are widely adopted. Most of these methods assume that weights follow a zero-mean Gaussian distribution, and determine the variance of this distribution under the principle of maintaining consistent variance of input data across layers. However, such approaches cannot be directly applied to the weight initial- ization structural sparse networks. Although methods like SWI (Zhang et al., (024d) have been proposed for sparse artificial neural networks, they are unsuitable for SNNs owing to their inabil- ity to incorporate temporal activation sparsity and the unique activation function of LIF neurons. To address this problem, put forward the Sparse Spike Weight Initialization (SSWI) method, which incorporates the temporal activation sparsity (St), structural connection sparsity (S,) and the neuronal threshold information (0) of SNNs into the weight initialization process. The detailed derivation is provided Appendix A.1 The SSWI method is presented Equation
St
(1=1)
n11 S.)
8 8/
(SWI(W))~NOO.. ~ -²=
(1<l<L)
(3)
V2e 1/2 - (S))'
8² TT
(1= L)
/2e- 1/2n
where St denotes the temporal activation sparsity of the input data in SNNs. S, represents the structural connection sparsity, / is the index of the layer (with a total of L layers), n indicates the input feature dimension of the layer, and denotes the spike threshold in the LIF neuron. SSWI enhances training efficiency, leading to faster convergence from the initial phases.
3.2.3 NETWORK PRUNING
Link Removal. We propose a hybrid strategy to calculate the link removal score (LRS) that com- bines relative importance (RI) and weight magnitude (WM). The approach not only accelerates network sparsification but also promotes the activation more neurons during training. The LRS defined as follows:
W
LRS
(4)
1+ Σ. 11
1 E, (
f. E, W represents the sum of the magnitude of all weights connected to the input neuron i, and E, ( denotes the sum of the magnitude of all weights connected the output neuron Instead of using the magnitude of the LRS as the direct criterion for link removal, we sample from a multi-nomial distribution based on the LRS value determine whether link should be removed. See more details in Appendix [... AA.3
where !RS!] denotes the link removal score the weight (!())
Chain Removal. After link removal, neurons that are unilaterally or bilaterally disconnected (i.c., without any incoming or outgoing links) are regarded as inactive neurons. Since these inactive neurons lose the ability to transmit information, they may hinder information flow throughout the network. Because of the mechanism of CH3-L3, such inactive neurons are unable to regrow new links during the network regrowth stage. Therefore, during the chain removal step, we permanently remove them from the network. As illustrated in Figure Stage 3, this process enhances overall information propagation.
3.2.4 NETWORK REGROWTH
We employ CH3-L3 to compute the link regrowth score for potential links, as CH3-L3 is recognized the most robust and stable link predictor within the Cannistraci-Hoes Hebb theory (Zhang et al. 2024b

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Zhao et al.
2025). To mitigate the risk of falling into epitopological local minima due to structural noise in the network, we sample from a binomial distribution based on the regrowth score to stochastically determine whether link should be regenerated, instead of using the regrowth score directly as the criterion for link regrowth (Zhang et al. 2024c). The formula for calculating the link regrowth score is as follows:
2025| Zhang et al.,
(u,-
E 21
(5)
v(1 + des,) x (1 + d
where and are two nodes that may potentially form link, and 21, 22 denote two intermediate nodes along a path of length 3 between u and v-also referred to as common neighbor nodes of and v. The terms de and dez, represent the external local community connectivity degrees of nodes 21 and 22, respectively. A detailed description of the CH3-L3 is provided in Appendix [A.2
4 EXPERIMENTS
4.1 COMPREHENSIVE PERFORMANCE COMPARISON WITH OTHER METHODS
We compare our CH-SNN with existing sparse SNNs training methods including Grad R (Chen) et al. 202I). SD-SNN (Han et al. 2025a) and DPAP (Han et al. 2025b), using the same net- work architectures for fair comparison. In addition,
have conducted experiments on the Spik- former (Zhou et al.] 2022) architecture to further verify our methods. is worth noting that none of the compared methods have been evaluated on the Spikformer. Detailed experimental settings are provided in Appendix A.5 and reproducibility statement is provided in Appendix A. The experimental results are summarized in Table and Figure _
Performance on Non-Spiking Datasets. On the MNIST dataset with the two-layer fully connected (2FC) architecture, CH-SNN attains a 97.75% sparsity while improving accuracy by 0.16% over the FC baseline. Compared to the state-of-the-art method DPAP, CH-SNN not only increases spar- sity by approximately 20% but also achieves performance gain of 0.23%. With the 2CONV2FC architecture, CH-SNN realizes 93.91% sparsity with 0.16% improvement in accuracy. These re- sults demonstrate that CH-SNN delivers both the highest level of sparsity and the most significant performance gains among all compared methods. Furthermore, when applied to the Spikformer ar- chitecture, CH-SNN achieves an 81. 11.72% sparsity with a slight performance improvement of 0.02%. On the CIFAR- 10 dataset, CH-SNN again achieves the highest level of sparsity-74,66 only a minimal accuracy drop of O. 14%. Similarly, when applied to Spikformer, it maintains spar- sity of 82.21% % with negligible performance degradation of 0.10%. On the CIFAR- 100 dataset, although the performance improvement of CH-SNN is marginally lower than that of SD-SNN, it in- creases sparsity by nearly 38% Additionally, with the Spikformer architecture, CH-SNN provides a 0.75% performance improvement at 82. 11% sparsity.
Performance comparison on MNIST with 2CONV structure
Performance comparison on N-MNIST
Performance comparison on CIFAR-10 dataset with 6CONV 2FCstrec
dataset with 2CONV 2FC structure
Annuary
Imprwemennt
Improveentt
Seruturra Sporityy
79%
80%
SMN
DPAP
0.09%
-0.1%
Stalk
00.5%%
0.4%%
-0.2%
-0.7%%
D00P
50%
85%
90% 1065,
70%
800
90%
Accrray
Sparsty
Strucuraa Spursity
Inpersmmet
Figure 2: Performance comparison of different methods on MNIST, N-MNIST and CIFAR-10. We plot the performance of different sparse SNN training methods with structural sparsity on the x-axis and accuracy improvement on the y-axis. The plot clearly shows that CH-SNN achieves the highest level of sparsity alongside the greatest improvement accuracy.
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Table 1: Performance comparison of different methods CIFAR-IO, CIFAR-100, MNIST, N- MNIST. CIFARIO-DVS and DVS-Gesture datasets. The gray section indicates the performance of CH-SNN. For each dataset, we have bolded the method with the highest accuracy improvement and the one with the highest sparsity. We exclude Spikformer from our comparison here.
Accuracy improvement
Dataset
Method
Network
Link sparsity
Acc.
Grad R
6Conv 2FC
71.59%
92.54%
-0.30%
DPAP
6Conv 2FC
50.80%
93.83%
%
CIFAR-10
SD-SNN
6conv 2FC
35.57%
94.59%
-0.15%
CH-SNN
6Conv 2FC
74.62%
94.60%
-0.14%
CH-SNN
Spikformer
82.21 %
94.26%
-0.10%
SD-SNN
6Conv 2FC
36.94%
75.33%
+3.27%
CIFAR-100
CH-SNN
6Conv 2FC
74.45%
75.22%
+3.16%
CH-SNN
Spikformer
82.11%
76.23%
+0.75%
Grad R
2FC
74.29%
98.59%
-0.33%
DPAP
2FC
77.36%
98.74%
-0.07%
SD-SNN
2FC
45.86%
98.90%
+0.09%
CH-SNN
2FC
97.75% %
98.97%
+0.16%
MNIST
Grad R
2Conv 2FC
49.16%
99.37%
+0.02%
DPAP
2Conv 2FC
61.25%
99.59%
+0.13%
SD-SNN
2Conv 2FC
49.83%
99.51%
+0.14%
CH-SNN
2Conv 2FC
93.91
99.53%
+0.16%
CH-SNN
Spikformer
81.72%
99.73%
+0.02%
Grad R
2Conv 2FC
75.00%
98.56%
-0.27%
DPAP
2Conv 2FC
63.95%
99.59%
+0.06%
N-MNIST
SD-SNN 2Conv 2FC
58.62%
98.78%
-0.29%
CH-SNN 2Conv 2FC
94.73%
99.15%
+0.08%
CH-SNN Spikformer
85.74%
99.45%
+0.10%
CIFARTO-DVS
CH-SNN 6Conv 2FC
84.34%
72.00%
+1.50%
CH-SNN Spikformer
85.37%
70.60%
+0.40%
Deep R
2Conv 2FC
75.00%
81.23%
-2.99%
Grad R
2Conv 2FC
75.00%
91.95%
+7.83%
DVS-Gesture
SD-SNN
2Conv 2FC
61.10%
96.21%
+1.14%
CH-SNN
2Conv 2FC
94.73%
95.45%
+0.38%
CH-SNN
Spikformer
82.25%
93.56%
+1.14%
Performance on Spiking Datasets. On the N-MNIST dataset, CH-SNN attains 0.08% perfor- mance improvement at 94.73% sparsity, outperforming the FC network. On the DVS-Gesture dataset, although CH-SNN's accuracy gain is lower than those of SD-SNN and Grad R, it still demonstrates 95.45% accuracy with 0.38% improvement compared to the FC baseline and reaches significantly higher sparsity level (94.73%) than all other compared methods. On the CIFAR 1--DS dataset, CH-SNN exhibits an accuracy improvement SNN framework removes inactive neurons, the sparse network with CH-SNN achieves higher node sparsity compared to other methods. Detailed results are provided in Table 9 of the appendix A.8
1.50% at 84.34% sparsity. Since the CH-
4.2 EXPERIMENTS ON HARDWARE-FRIENDI ALGORITHMS S-TP
Hardware-friendll algorithm S-TP has been realized chip ANP-I (Zhang al. 2024a), which low-power neuromorphic processor for edge-side AI applications. To verify methods, apply CH-SNN to S-TP. Detailed experimental configurations and network architectures are provided in Appendix A.5 We have conducted comprehensive experiments to evaluate the performance of CH- SNN in terms of accuracy and energy efficiency. The results are shown in Table 2 and Figure
Accuracy Analysis. At average sparsity of 96.4%, the sparse network with CH-SNN achieves the comparable accuracy of the FC network without CH-SNN on all four datasets. Notably, on the DVS- OVS-Gesture dataset, sparse network attains 2.27% improvement in accuracy at 98. 98.84% sparsity.
8

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Published as a conference paper at ICLR 2026
For the N-MNIST dataset, although the accuracy of the sparse network is slightly lower than that of the FC network, it successfully prunes nearly half of the nodes (41.90% node sparsity) with only a minimal accuracy drop of 0.18%.
Table 2: Performance and energy consumption of CH-SNN on MNIST, and CIFAR-IO 10 datasets (S-TP). For each dataset, the first row shows the performance of the fully connected network, and the second row shows that of the sparse network with CH-SNN. A 3FC ar- chitecture is consistently employed across all experiments, with details provided in the appendix A.5
N-MNIST
Spike
Firing rate
Link sparsity
Node
Dataset
SOPs
Acc.
Energy
count
sparsity
6.1 x 10a
6.3 10
31.22%
0% 94.59%
0%
97.29%
948mJ
MNIST
3.3 108
3.2 x 1020
16.83% %
23.47%
97.56%
48mJ
DVS-
2.2 x 107
5.2 1030
4.02%
0%
0%
89.02%
78mJ
Gesture
1.3 x 107
5.0 x 10
2.45%
98.84 %
12.30 %
91.29% %
0.8mJ
2.5 x 10
1.4 10"
10.42%
0%
0%
96.38%
216mJ
N-MNIST
1.2 x 10
2.9 x 10
4.72 %
98.46 %
41.90% %
96.20%
4.4mJ
6.3 x 107
2.8 x 1000
30.70%
0%
0%
80.67%
41mJ
CIFAR-10
1.9 107
4.8 x 10
9.28%
93.78% %
0%
82.84%
0.7m.J
Energy Analysis. We evaluate the energy efficiency in terms of the average firing rate, total spike count, and the number of Synaptic Operations (SOPs). The measured energy consumption of ANP- I chip is 1.5 pJ/SOP (Zhang et al.) 2024a), which is regarded energy consumption by multiplying this baseline by the total SOPs. As illustrated in Figure on the DVS-Gesture dataset, the CH-SNN with sparse connectivity consumes 97.5 times less energy than its fully connected counterpart. Furthermore, it yields an average reduction in energy consumption of 55 times and a 10.77% decrease in the average firing rate across the four datasets.
baseline. We calculate the total
Firing Rate across Datasets
Accuracy Different Sparsity
Energy Consumption Different Datasets
PC Network
K-MNIST DVS-Greeture
PC Network
Sparse Yetwork
Accuracy
NNIST
CIFAR-10
Intua[Enengy/u
Sparaa Network
100%
3.00
30%
1430%
96
0.00
22.5
10%
Up 60.3/4 h.5
5%
82%
00:078
0.75
CIFAR:
Gesture
DVS
N-NISST MNIST
Dutaset
Sparsity
CIFAR-10
Gesture
DV5
N-MNIST
Figure 3: Experimental results of CH-SNN on hardware-friendly algorithm S-TP. A comparison of firing rates between the sparse network with CH-SNN and the FC network across four datasets is presented in the left plot. The middle plot provides an accuracy comparison among the FC network and sparse networks at sparsity levels of 80%, 95%, and 99%. The right plot displays the energy consumption comparison, with the vertical axis on a base-100 logarithmic scale. A scale difference of 0.99 signifies that the energy consumption of the FC network 97.5 (1000.99) times greater than that of the sparse network.
Supplementary Experiments. We perform ablation studies to verify the SSCTI and SSWI methods, with results in Appendix [A Besides, sensitivity analyses are conducted on critical hyperparam-
eters viers-including learning rate, batch size and pruning ratio also conducted a robustness analysis and details are provided in Appendix A.9 Details of large language model usage in the writing process can be found in the Appendix A.13
summarized in Appendix A.7 We

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Published as a conference paper at ICLR 2026
5 CONCLUSION
To address the challenge in achieving high levels of structural connection sparsity while maintain- ing performance comparable that of fully connected networks, this paper presents CH-SNN, four-stage dynamic sparse training framework for learning ultra-sparse spiking neural networks. The framework comprises: (1) sparse topology initialization, leveraging input correlation initial-
ize the network structure; (2) sparse weight initialization, which incorporates temporal activation sparsity, structural connection sparsity and neuronal threshold information of SNNs initialize the weights of SNNs within a sparse network structure. (3) network pruning based on removal score, combined with the removal of inactive neurons to improve information flow, and (4) network regrowth using the CH3-L3 score with probabilistic strategy. These stages enable CH-SNN to achieve sparsification across all linear layers and enables effective training at ultra-high levels of sparsity conditions. Experimental results demonstrate that CH-SNN outperforms existing sparse SNNs training methods, achieving 97.75% sparsity on MNIST with a 0.16% accuracy improvement over the FC baseline. In addition, realizes 98. 98.84% sparsity with a 2.27% performance gain over the FC network while improving energy efficiency by approximately 97.5x. In summary, CH-SNN achieves performance comparable to FC networks even ultra-high levels of sparsity, offering promising solution for implementing edge AI on neuromorphic hardware.
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A APPENDIX
A.I SPARSE SPIKE WEIGHT INITIALIZATION
For the sparse spiking neural network, we first introduce the sparse connection matrix C' {0, 1)mx,, where represents a connection exists and represents no connection exists. For a sparse network, we have:
(6) where @ represents the Hadamard product, ( E R= is the weight matrix, x E Rxx denotes the input vector, D(9) E TR is the bias vector, ( E RR=x1 stands for the output vector, and represents the layer index. Next we assume that bias 0 and the number of network layers is L, For the i element ( the output vector y we discuss its variance:
=0==00 @ (( + b(l)
Varly = Var ar
Σ j=1
C. W and æ are independent of each other, All elements in the matrices W,C. W.C.a x are independently and identically distributed, and the three matrices have different distributions. Then the variance of V can be expressed as follows:
Varlu [ = n1((V [[(Var(Ciy) + r2) (Var(W))))) (V 22)
PE H
(8)
where y is the mean. For the elements of the sparse connection matrix C, we assume that it follows the Bernoulli distribution, then we have:
1, 1-1-
Cs
=c=1- Sa, Var[Cyy] = S, - S.)
0, p p=
where S, is the structural connection sparsity. Based on previous work (He et al. 2015). similarly
define Wij to follow a zero-mean Gaussian distribution, which means μы = 0. The Equation ( can be changed to:
Varly.")
[9] = n01 - S.)(V or (W)))( m2)
(10)
We expect maintain the same variance of the input feature across layers, which means Varly (0
V Var(u!--1), For the input layer = 1). it can be expressed as Varly!" = V Var[z,), because there no activation function applied to the input feature. The input of the spiking neural network I or
0, therefore, we can assume that æ; follows the Bernoulli distribution with parameter p S.. We can get the variance of the Way as follows:
Var (1)
S
(11)
r2l ((1-S.) S.)
where S, is the temporal activation sparsity, and is the dimension of the input. For the rest of sparsely connected layers, yi follows a distribution with zero mean and symmetric about zero, since Wi()) follows zero-mean Gaussian distribution and the input of every layer is zero one, which will not affect the symmetry of w((). To simplify the analysis, assume that ( also follows zero-mean Gaussian distribution. In the spiking neural network, the activation function is not ReLU, but rather the step function, which can be expressed as:
[1,
y (1-1) + Vmmn 2 0
x = U(y) (1-) + Vmme - 0) {
(12)
y (1-1) + Vmmm < 0
14

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Published as a conference paper at ICLR 2026
(1-1)
Where 0 is the threshold of the spiking neural network. We approximate that Vinem and Di follow the same distribution. Therefore, Equation (12 can be expressed as follows:
1, g(-1) 2 8/2
U22y 1111) 0)
(13)
0, y( < <0/2
We expect to find relationship between Varlz) (1) + u and Varly, that will simplify Equa- tion 10). Based on Equation (13. we have:
Varlz (1)
I J012
1
/2Vorl 1)
dr 4(0/2) Varly, (14)
22 111111
where ((-)) is the cumulative distribution function of the standard normal distribution. We expand
Equation 14 in a Taylor series around f/2 with Varly) [1 as the variable and discard the higher-
order terms:
1/2
Varla, + = -1))
e 1) (Varly, (11) 1
Varly Varly--1 1
(15)
V2
4
VTQ22
Next, we substitute Equation
15) into Equation
(T). obtaining the following result:
0 V
Var War
V2e-1/2 - S.) (1<l<L)
(16)
Finally, we assume that the output layer is fully connected, which means S. = so we can obtain the following result:
Var Var(W ( )
(17)
/2e-1/24
In summary, we can summarize the Sparse Spike Weight Magnitude Initialization (SSWI) fol- lows:
S. (1=1)
n11
S.)'
8² 8T
(SW[WW))N(00d6 d²=
(1<l<L)
(18)
V2e 1/2n(11 - -S,)²
02 VT
-2e-1/2p (1=
A.2 EXPLANATION OF CH3-L3
To illustrate the application of CH3-L3 for link prediction, consider hypothetical network contain- ing nodes and that are not directly connected. The CH3-L3 method evaluates potential links by analyzing all length-3 paths between u and e and incorporating the local community connectivity of intermediate nodes.
Common Neighbors
External Nodes
Seed Nodes
?
eLCL
u
V
iLCL
Figure 4: Example of link prediction using CH3-L3.
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We provide an illustrative example in Figure 4 Red nodes represent seed nodes between which no direct connection is currently observed, but which have the potential to regenerate a link. Green nodes denote common neighbors-noot connections between common neighbors, referred to as internal Local Community Links (iLCL.. Blue nodes represent external nodes outside the set of seed nodes and their common neighbors. Blue edges correspond to connections between common neighbors and these external nodes, termed external Local Community Links (eLCL). The calculation process of CH3-L3 as follows:
directly connected to both seed nodes. Red edges indicate
CH
E (1 v(1 + des,) (1 de
(19)
where u and u denote two seed nodes, and 21, 22 represent two common neighbor nodes along path of length between and The terms de,, and dez, correspond to the number of eLCL associated with node 21 and 22, respectively. The CH3-L3 score is computed by summing the contributions from all length-3 paths between and v. Here, adding to de,, and de,, prevents division by zero and ensures numerical stability when no external links are present.
A.2.1 GUARANTEEING TRAINING STABILITY VIA THE CH3-L3
The CH3-L3 regrowth score is derived from the Cannistraci- Hebb theory of local-community orga- nization (Cannistraci 201 8b Zhang et al. 2024d Zhao et al., (025). The term des in Equation [9 (the external degree of common neighbor 2) acts penalty term. It inherently discourages the formation new links that would connect to nodes that are already highly connected outside their immediate local community. This design naturally prevents the mechanism from getting stuck in redundant loops of adding and removing the same connections. It preferentially strengthens con- nections within structurally isolated communities, which stable, self-reinforcing process. is gradient-free, topology-driven predictive network automata (Zhang et al.) [0255] (Zhao et al., 2025)
that guides the network towards a sparse, hub-and-communn structure (Zhang al. 2024dd
While CH3-L3 is inherently stable, we proactively introduced an early-stop mechanism in the CH- SNN framework to explicitly monitor and halt any potential redundancy. We track the overlap rate between the set of links removed and the set of links regrown in each topological update cycle. Once this overlap rate exceeds a high threshold (e.g.. 95%), it signals that the network topology has stabilized. At this point, we permanently stop the topological evolution (pruning and regrowth) for that layer and focus solely on weight update.
Furthermore, our framework includes chain removal, as shown in section 3.2.3 that permanently removes inactive neurons. Since these neurons cannot attract new connections via CH3-L3, their removal prevents structural dead-ends and further contributes to overall training stability and effi- ciency.
Our extensive experiments across multiple datasets and architectures, where CH-SNN consistently converges and outperforms baselines, serve as empirical validation of this stable behavior. Finally, the previous studies dynamic sparse training (DST) never raised concern of stable convergence or meaningful structure learning because the DST methodology selects which link should be re- moved during the training by using the weight update, this ensures convergence of the model towards meaningful structures (Zhang et al.) [2024d] Evci et al. 2019 Zhang et al. 2024c) even with a random predictor such as SET (Mocanu et al. 2018).
A.2.2 BIOLOGICAL INTERPRETABILLN OF CH3-L3
The CH3-I33 mechanism operationalizes Hebbian principles at a network-structural level, embody- ing the concept that "neurons that fire together wire together" (Hebb) 1949). Specifically, it identifies pairs of neurons that exhibit structural correlations, such as sharing common neighbors or belonging to the same local community, and predicts the formation of new links between them. This process mirrors synaptic turnover and rewiring observed in biological neural circuits, where connections are dynamically formed strengthened based on functional relatedness.
Although CH3-L3 does not explicitly model precise spike timing, it captures the topological out- comes of STDP-like plasticity. CH3-L3 leverages these structural signatures, derived from local
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community detection, guide link regrowth, effectively simulating topology form of plas- ticity. This approach is analogous to how STDP reinforces connections within functionally related neuronal assemblies, promoting sparse yet efficient network dynamics. In dynamic sparse networks, such regrowth ensures adaptability while maintaining biological realism, as it avoids random recon- nections and prioritizes structurally plausible ones.
In summary, while CH3-L3 not a direct biophysical simulation STDP, provides a functionally equivalent and biologically interpretable mechanism for synaptic rewiring, enhancing the model's relevance to neuroscience applications.
A.3 DETAILS OF NETWORK PRUNING AND NETWORK REGROWTH
During dynamic sparse training, we generate sparse connectivity matrix C, where Cj in- dicates the presence of a link between nodes i and j. and C₁ 0 indicates no link between the nodes. After each training epoch, a process of network pruning and network regrowth is performed. Correspondingly, the sparse connectivity matrix C' is updated.
A.3.1 LINK REMOVAL
During the link removal phase, we calculate the Link Removal Score (IRR) for the existing links (where Ci = 1). The I,S,; is computed as shown Equation (20
LRS., = ( W Σ, Wil
W Wgl 1 Σ, Way
(20)
The parameter 8 controls the sampling distribution. When ö = 0, it means the LRS is identical for all links. In this scenario, the corresponding sampling method random sampling, where links are randomly selected and removed. When 8 = 1, the sampling becomes deterministic, and links are removed directly based on their LRS values. When 0.5, it means sampling from a multinomial distribution based on the LRS values. In this situation, calculate the link removal probability (remonal) using the LRS.j. as shown Equation 21:
Pij
Pij.
(removal)
LRS Eig LRS;j
i,j E (a,b] Cab = 1}
(21)
Subsequently, based on the link removal probabilities, we remove a certain proportion (() of links as specified Equation (22). completing the link removal process.
{
fremoval) (removal)
Cij
Pij
i E ba Cas = 1}
(22)
0
Pij
A.3.2 LINK REGROWTH
During link regrowth, we compute the link regrowth score (CH3-L3(1u, v)) for nonexistent links (where Cuv 0), formulated in Equation (2)).
CH3-L3 (u,
Σ
(23)
(1 v(I dez,) x (1 de
Consistent with the link removal, the parameter 8 controls the sampling distribution. represents random sampling, 8 indicates that links will be directly regrown based on the CH3-L3(u, v), and
0.5 signifies sampling from multinomial distribution based the
(regrouth) as shown in Equa- CH3-L3(u, (u, v). Similarly, we compute the link regrowth probability pue
tion 24
CH3-L33 v)
(regrowth)
u. E {a. 1666., Cab = 0}
(24)
Σ
CH3-L3(u,
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Following the regrowth probabilities, the regrowth of links can be completed as shown in Equation
25 The number of regrowth links remains consistent with the number of pruned links, thereby maintanning the pre-defined overall network sparsity.
(regrowth)
Cue
1
Puv
u fa, Cab = 0}
(25)
(regrowth) Puc
O
1
To evaluate the impact of different regrowth sampling distributions on model accuracy, we conducted comprehensive experiments. As shown in Table 3 Consequently, for all experimental results reported this paper, we set & 0.5, which means we sample regrowth links from multinomial distribution.
the highest accuracy is achieved when ó 0.5.
Table 3: Sensitivity experiment ó.
Dataset
5 = 1
8 = 0.5
8 = O
N-MNIST
96.30%
97.21%
96.63%
89.02%
91.29%
90.53%
MNIST
98.28%
98.40%
98.30%
CIFAR-10
78.87%
82.84%
77.68%
A.4 DETAILS OF SPARSE SPIKE CORRELATED TOPOLOGICAL INITIALIZATION
To enhance the performance of the link predictor, we propose the Sparse Spike Correlated Topolog- ical Initialization (SSCTI), a method for initializing the topology of layers that interact directly with input features.
Assuming we have N samples with input features and a timestep of T, the SSCTI procedure consists of the following four steps, illustrated in Figure 5 (1) Temporal Unfolding and Stack- ing. We treat each timestep as an independent sample and stack them along the feature dimension, resulting in data matrix of TR MNT for subsequent processing. culation. Based on the R MNT matrix, we compute the Pearson's phi coefficient between every pair of features, constructing feature correlation matrix of M (3) Top-K Sparsification and Adjacency Matrix Construction. We retain only the top-(1 S,) values in the correlation matrix (where S. denotes the structural connection sparsity) and set them I, forming an adjacency matrix of IR X that defines the initial topological structure of the layer. When the hidden layer dimension matches the input dimension (M), connections exist only where the adjacency matrix contains 1. the hidden layer is larger (e.g., 2MM), the adjacency matrix is tiled or repeated accordingly (e.g.. to R XxMM ), allowing flexible scaling of hidden dimensions. The same process is applied initial- ize topological structures between hidden layers. (4) Sparse Topological Initialization. Finally, we initialize the network topology based on the adjacency matrix, preserving only the connections indicated by I's in the matrix.
(2) Feature Correlation Cal-
Sparse Spike Correlated Topological Inttializaation
Possible Link Sparsely Connected
Existiig
Time Step
Time
Time
Fully
Stop
Stop
Stop
Connected
d
Nontre 2
Keep Sparsity Step
100
Remover
Node
Samples
Sumple
2amptr
Sumple
2M-OUT
Figure 5: An example of how to construct the SSCTI the N-MNIST dataset
A.5 EXPERIMENTAL SETUP
To evaluate the performance of CH-SNN, conduct extensive experiments multiple datasets, including MNIST (Deng 2012), CIFARIO (Krizhessky) 2009). CIFAR100 KKrizhessky,20de N-
MNIST (Orchard et al.] 2015), CIFARIO-DVS (Li al. 2017) and DVS-Gesture (Amir et al.
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2017). Both the MNIST and N-MNIST datasets contain 10 classes of handwritten numbers (0-9), each consisting of 60,000 training samples and 10,000 test samples. types of gestures captured using event-based camera. For these three datasets, adopt the following network architecture: Input - 15 (Channel Count)Cony (Layer x Size) AvgPool2x2 - 433 AvgPool2 - Flatten - 300 Classes. For MNIST, a layer fully connected network is used: 784 + 1568 - 10. Since CIFARIO and CIFAR 100 share similar data format, we employ the same network structure for both: Input - [128Conv3 x3]x2 MaxPool2 - 512Conv3 x3 Flatten - 512x 8x + 512 + 10. All networks are configured with a time step of 8. Non-Spiking datasets (CIFARIO, CIFAR 100, MNIST) are encoded using direct encoding. For all experiments, we adopt the standard Spikformer architecture (Zhou et al. 2022), configured with encoder layers, hidden dimension of 512, 8 attention heads, and timestep of 4. A uniform sparsity of 99% is applied to all linear layers (except for the output layer). Weight updates are performed via surrogate gradient methods. Within each epoch, after completing weight training. CH-SNN performs pruning and regeneration according to the pruning ratio Ç followed by testing. The value of Ç decays cosine- aaiine-annealinlly to zero the course of training, which can be expressed as follows:
comprises
+ MaxPool2 x2 - [256Conv3x3]-)
< < (1 cos( total epochs ))
epoch
(26)
For the S-TP algorithm, we perform experiments on the CIFAR-10, MNIST, N-MNIST and DVS- Gesture datasets using a network structure defined as input-XXnnu-->xlnnutttCCa Classsssss with input sizes of 578 for N-MNIST, 784 for MNIST, 512 for CIFAR-10, and 2048 for DVS-Gesture. Throughout training, we set the learning rate to 0.0001, the dynamic pruning ratio Ç 0.35, the batch size to 100, the target window size to 4, the number of epochs to 100, and the neuronal firing threshold
A.6 ABLATION EXPERIMENT
We have conducted ablation studies validate the effectiveness of our proposed SSCTI and SSWI. The results are summarized in Table When both SSCTI and SSWI are removed, the model fails converge in most of performance degradation. Notably, with a high level of sparsity of 99%, the model becomes unstable and fails to train when SSWI is ablated. These ablation results demonstrate the critical importance and effectiveness of both SSCTI and SSWI in maintaining network performance under extreme sparsity.
Removing either SSCTI SSWI individually leads varying degrees
Table 4: Ablation Study SSCTI and SSWI (When SSCTT ablated, we employ random structural initialization: when SSWI is removed, we use Kaiming initialization).
99%
95%
80 %
70%
Dataset
SSCTI
SSWI
Sparsity
Sparsity
Sparsity
Sparsity
9.80%
9.80%
9.80%
91.99%
9.80%
88.82%
96.95%
97.12%
N-MNIST
89.61% %
94.74%
96.53%
96.87%
96.20%
97.21 %
97.29%
97.22%
9.80%
9.80%
97.23%
97.78%
70.41% %
96.57%
97.57%
97.57%
MNIST
78.09%
96.81%
97.88%
97.91%
96.88 %
97.56% %
98.11% %
98.00%
9.09%
9.09%
9.09%
9.09%
9.09%
9.09%
78.79%
86.74%
DVS-Gesture
76.52%
87.12%
87.50%
86.74%
91.29%
91.29%
88.64%
89.02%
10.00%
57.35%
78.89%
77.95%
34.55%
76.83%
80.01%
78.19%
CIFAR-10
77.40%
81.62%
80.62%
80.65%
78.94%
82.84%
81.73%
81.42%
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A.7 SENSITIVITY TEST
We have conducted a sensitivity analysis of the hyperparameters in CH-SNN, focusing primarily on the learning rate, batch size, dynamic pruning ratio, and static sparsity rate, evaluate the model's performance under variations in these parameters.
Learning Rate (LR). We train CH-SNN using different learning rates (0.01, 0.005, 0.001, 0.0005, 0,0001) and record its performance, as summarized in Table The results indicate that as the learn- ing rate increases, the model exhibits noticeable decline in performance. Through further analysis, we conclude that this performance degradation stems from the S-TP algorithm: during weight up- dates, an excessively large learning rate leads oversized training steps, preventing convergence to an optimal solution. This is validated by conducting learning rate sensitivity experiment on fully connected network, where a similar performance drop is observed, as shown in Table
Table 5: Learning rate sensitivity experiment.
Dataset
1r-0.01
Ir-0.005
Ir-0.001
1r-0.0005
1r-0.0001
N-MNIST
83.08%
85.59%
95.84%
96.87%
96.91%
DVS- Gesture
65.91%
75.76%
89.77%
89.77%
89.77%
MNIST
67.18%
85.83%
94.98%
96.19%
97.98%
CIFAR-10 10
78.74%
79.96%
82.84%
82.73%
82.54%
N-MNIST(FC)
69.65%
80.90%
88.16%
96.31%
96.38%
DVS- DVS-Gesture(FC)
68.56%
68.18%
85.98%
88.64%
89.02%
MNIST(FC) 79.90%
84.58%
92.43%
94.12%
97.29%
CIFAR-10(FC) 59.86%
55.49%
80.14%
81.92%
80.67%
Batch Size (BS). We employ different batch sizes to train CH-SNN, and the experimental results presented in Table 6 show that variations in batch size did not cause significant changes in its per- formance.
Table 6: Batch size sensitivity experiment.
Dataset
BS-16
BS-32
BS-50
BS-64
BS-100
N-MNIST
96.88%
96.86%
96.85%
97.00%
96.91%
DVS-Gesture
89.77%
89.39%
89.02%
89.39%
89.77%
MNIST
98.08%
98.09%
98.11%
98.07%
97.98%
CIFAR-10
82.64%
81.95%
81.88%
81.74%
82.84%
Dynamic Pruning Ratio ((). To evaluate the impact of different pruning rate strategies model performance, we first test the dynamic pruning rate strategy as defined in Equation (26). We adjust various decay starting points (0.5, 0.4. 0.3, 0.2, 0.1). and the experimental results are shown in 'Table 7 It can be observed that CH-SNN exhibits negligible performance variation across different initial pruning rates, demonstrating strong stability response to changes in the pruning rate. The model consistently achieves strong performance under the predefined sparsity targets.
Table Dynamic removal rate sensitivity experiment.
Dataset (-0.5
(-0.4
(-0.3
(-0.2
Ç-0.1
N-MNIST 97.14%
96.91%
96.96%
97.04%
97.10%
DVS-Gea Gesture
89.39%
90.53%
89.02%
88.64%
89.39%
MNIST 97.98%
97.98%
97.98%
97.98%
97.98%
CIFAR-10
82.64%
82.24%
82.84%
83.03%
82.75%
Statie Pruning Ratio (C). Similarly, evaluate static pruning rate strategy. Unlike the dynamic approach, the static pruning rate remains constant at its initial value throughout training. We test multiple starting values for the static pruning rate, and the results are presented in Table CH-SNN
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shows minimal performance variation across different static pruning rates. It is worth noting that compared to the dynamic pruning strategy, the static approach generally leads to a slight decrease in overall accuracy.
Table 8: Static removal rate sensitivity experiment.
Dataset Ç-0.5
Ç-0.4
(-0.3
Ç-0.2
ç-0.1
N-MNIST 96.90%
96.87%
96.84%
96.81%
97.10%
DVS-Gesture
88.64%
89.39%
89.02%
89.02%
88.64%
MNIST 97.98%
97.98%
97.98%
97.98%
97.98%
CIFAR-10
82.24%
82.26%
82.53%
82.63%
82.25%
A.8 NODE SPARSITY
In the CH-SNN framework, neurons that are unilaterally bilaterally disconnected (i.e., without any incoming or outgoing links) are regarded as inactive neurons. Since these inactive neurons lose the ability transmit information, they may hinder information flow throughout the network. We assume that such inactive neurons are unable to regrow new links during the network regrowth stage. Therefore, during the chain removal step. we permanently remove them from the network. As illustrated in Figure [ Stage 3, this process enhances node sparsity. We compare CH-SNN with SD-SNN, an existing open-source method, as shown in Table
Table 9: Node sparsity of different methods on CIFAR-10, CIFAR-100, MNIST, N-MNIST and DVS-Gesture datasets.
Dataset
Method
Network
Node sparsity
SD-SNN
6conv 2FC
0.28%
CIFAR-10
CH-SNN
6Conv 2FC
1.21 %
SD-SNN
6Conv 2FC
0.46%
CIFAR-100
CH-SNN
6Cony 2FC
0.69 %
SD-SNN
2Conv 2FC
0.02%
CH-SNN
2Conv 2FC
0.04%
MNIST
SD-SNN
2FC
0.77%
CH-SNN
2FC
2.03 %
SD-SNN
2Conv 2FC
6.32%
N-MNIST
CH-SNN
2Conv 2FC
8.09 %
SD-SNN
2Conv 2FC
1.28%
DVS-Gesture
CH-SNN
2Cony 2FC
6.35 %
A.9 ROBUSTNESS ANALYSIS
We train ultra-sparse networks using CH-SNN. In comparison to fully-connected (FC) networks, increasing the structural sparsity leads to corresponding increase in temporal sparsity. This phe- nomenon reduces both the number of active spiking neurons and the total spike count. We hy- pothesize that this loss of information may adversely affect robustness. To test this and evaluate the robustness of CH-SNN, we conduct experiments where the models, trained on clean data, are exposed to corrupted inputs during testing. The corruption involves three noise types: (1) Bit-flip noise. This noise randomly flips Os to 1s and to Os. Its destructive nature stems from dual effect: it corrupts the input by both adding spurious spikes and removing authentic ones. (2) False-spike noise. This corruption randomly changes Os to 1s, which generates extrancous spikes. This directly compromises the timing precision fundamental to SNN operation. (3) Spike-dropout noise. This type randomly changes Is to Os, thereby dropping genuine spikes. designed to emulate spike loss in real neuromorphic hardware.
Our experimental investigation aimed to evaluate the noise robustness of the proposed CH-SNN. All models in this study were implemented as 3FC networks with 99% structural sparsity. The testing
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Table 10: Aceuracy the MNIST dataset with input noise, where denotes the noise ratio.
Dataset
Method
P = 0%
P 5%
P 10%
P 15%
P = 20%
FC
97.91%
97.64%
95.78%
83.19%
68.25%
Bit-flip
CH-SNN
98.21%
97.86%
94.75%
81.19%
65.03%
FC
97.91%
97.74%
96.50%
89.97%
78.39%
False-spike
CH-SNN
98.21%
97.73%
95.74%
86.72%
75.25%
FC 97.91%
97.25%
94.37%
87.25%
67.65%
Spike-dropout
CH-SNN
98.21%
97.48%
93.84%
83.81%
66.58%
protocol involved corrupting the input with three noise types across a range of intensities. The noise intensity was controlled by the noise ratio, defined as the proportion of timesteps in the input spike train that are altered. We report the classification accuracy on the MNIST, N-MNIST, CIFAR-I0. and DVS-Gesture datasets under these conditions, with the complete results presented in Tables T0
13
Table 11: Accuracy on the N-MNIST dataset with input noise, where P denotes the noise ratio.
Dataset
Method
P = 0%
P 1%
P = 2%
P = 3%
P = 4%
FC
95.82%
93.09%
83.76%
73.65%
62.35%
Bit-flip
CH-SNN
96.62%
94.00%
83.47%
74.97%
65.87%
FC
95.82%
93.19%
84.13%
74.03%
63.96%
False-spike
CH-SNN
96.62%
94.08%
83.89%
75.7%
67.32%
FC
95.82%
95.85%
95.77%
95.78%
95.78%
Spike-dropout
CH-SNN
96.62%
96.53%
96.43%
96.54%
96.47%
Table 12: Accuracy on the CIFAR-10 dataset with input noise, where P denotes the noise ratio.
Dataset
Method
P = 0%
P = 1%
P = 2%
P = 3%
P = 4%
FC
79.23%
65.55%
56.16%
48.15%
42.63%
Bit-flip
CH-SNN
79.27%
60.68%
49.42%
41.58%
35.17%
FC
79.23%
66.89%
57.31%
49.73%
43.28%
False-spike
CH-SNN
79.27%
60.76%
49.82%
41.22%
34.43%
FC
79.23%
79.19%
79.03%
78.85%
78.75%
Spike-dropout
CH-SNN
79.27%
79.14%
79.03%
78.88%
78.62%
Our results delineate a sharp contrast in robustness against different noise corruptions. Models demonstrate substantial tolerance to spike-dropout noise. With a dropout rate under 5%, accuracy remains largely stable, and we observe a slight performance enhancement on CIFAR-10 and DVS- Gesture. This robustness implies that the random omission of small number of spikes acts as mild form of regularization, which is insufficient to alter the overall network output. This finding holds for both sparse and dense networks.
Conversely, bit-flip and false-spike noise cause pronounced performance degradation. Their de- structive nature stems from the introduction of spurious spikes, which corrupts the inherent timing- dependent computation in SNNs. This forees neurons to fire at incorrect timesteps, thereby com- promising the integrity of the final decision and resulting in substantial accuracy loss, regardless of network sparsity.
The robustness of the model is quantified using the Relative Performance Degradation Rate (RPDR). The RPDR metric is formally defined as Equation 27]
RPDR ACCotean ACCnoiss
(27)
ACCalean
where ACCatean is the baseline accuracy on unperturbed data, and AC'Onois is the accuracy evalu- ated under specific noise corruption. This metric is interpreted follows: smaller RPDR denotes
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Table 13: Accuracy on the DVS-Gesture dataset with input noise, where P denotes the noise ratio.
Dataset
Method
P = 0%
P 1%
P = 2%
P = 3%
P = 4%
FC
87.12%
83.33%
79.32%
78.79%
57.58%
Bit-flip
CH-SNN
87.12%
84.85%
79.92%
75.38%
63.26%
FC
87.12%
84.47%
77.65%
69.32%
60.98%
False-spike
CH-SNN
87.12%
87.12%
79.55%
74.62%
64.02%
FC
87.12%
87.12%
87.12%
87.50%
87.50%
Spike-dropout
CH-SNN
87.12%
87.12%
87.50%
87.50%
87.50%
stronger robustness, as it reflects smaller relative drop in accuracy. Table 14 presents comprehen- sive summary, detailing the RPDR for each noise type alongside the mean RPDR aggregated over all noise conditions.
Table 14: The relative performance degradation rate of the model under the three types of noise.
Dataset
Method
Bit-flip
False-spike
Spike-dropout
Average
FC
11.95% %
7.41 %
11.52 %
10.29
MNIST
CH-SNN
13.75%
9.52%
13.01 %
12.09%
FC
18.38%
17.73%
0.03% %
12.05%
N-MNIST
CH-SNN
17.64%
16.95%
0.13%
11.57%
FC 32.95%
31.46%
0.35%
21.59%
CIFAR-10
CH-SNN
41.07%
41.27%
0.44%
27.59%
FC
14.19%
16.09%
-0.22%
10.02%
DVS-Gesture
CH-SNN
12.93%
12.39
-0.33%
8.33%
Analysis on non-spiking datasets (MNIST, CIFAR-10). On these converted datasets, where static images encoded into spike trains, the FC baseline exhibits greater robustness average com- pared to the CH-SNN. We postulate that the densely and uniformly distributed information static images aligns better with the FC network's inherent redundancy, granting it higher fault tolerance. The structural sparsity of CH-SNN, while beneficial in other contexts, leads to increased temporal sparsity that offers no robustness advantage here. Consequently, achieving robustness on such tasks would necessitate design with lower structural sparsity.
Analysis on native spiking datasets (DVS-Gesture, N-MNIST). The scenario reverses for native spiking data. When subjected to the most destructive noise types (bit-flip and false-spike), CH- SNN consistently shows lower performance degradation rate than its FC counterpart. This result underscores that CH-SNN sparse architecture effectively leverages the inherent sparsity of the data to filter out corrupting noise and protect crucial information, thus validating its stronger robustness for bestt-based computation.
A. REPRODUCIBILITY STATEMENT
Regarding the experimental results in Table 1 we provide the following two-part clarifications on reproducibility to ensure all comparisons are fair.
Comparison with other sparse training methods. For SD-SNN, whose code is publicly available, faithfully reproduced its sparse training procedure. Specifically, first trained dense neural network as the baseline. Under identical experimental conditions, we then applied both SD-SNN and CH-SNN obtain their respective sparse networks from this common baseline, guaranteeing fully fair comparison between the two methods.
For other sparse training methods (e.g., Grad), since their code is not open-source, did not attempt to reimplement them. Therefore, the results shown Table [ for these methods, along with their corresponding dense baseline performances, are directly quoted from their original publications.
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Published as a conference paper at ICLR 2026
Comparison between dense and sparse networks. When comparing the dense network with the sparse network trained via CH-SNN, we ensured strict fairness: all training settings and hyperpa- rameters are kept identical, with the only difference being the introduced sparsity.
A.11 PERFORMANCE DIFFERENT TIMESTEPS
The number of timesteps (T) is critical hyperparameter in SNNs, governing fundamental trade- between latency and aceuracy. A shorter 7 reduces latency by shortening spike trains but risks creating information bottleneck that degrades performance. Conversely, a longer 7 enhances temporal resolution and accuracy at the expense of increased latency. empirically analyze this trade-off in our CH-SNN framework, under identical settings while systematically varying T. The results shown in Table Table[33 clearly illus- trate this balance and identify T the optimal operating point, delivering strong performance with moderate latency.
conducted controlled study by training sparse networks
Table 15: Performance on different timesteps.
Dataset
Network
T= 2
T =
T [== 8
T = 16
N-MNIST
2CONV2FC
96.20%
98.32%
99.15%
99.20%
MNIST
2CONV2FC
98.55%
98.89%
99.53%
99.55%
DVS- DVS-Gesture
6CONV2FC
85.60%
90.63%
95.45%
95.45%
CIFAR-I0
6CONV2FC
75.33%
87.21%
94.60%
94.71%
CIFAR-100
6CONV2FC
72.04%
73.52%
75.22%
75.34%
A.12 EXTENSION EXPERIMENT
To validate our approach on more complex datasets and deeper network architectures, we evaluate our CH-SNN against DPAP (Han et al. 2025b), currently the leading sparse training method for SNNs, on the Tiny-Iman Imageee and ImageNet datasets using a ResNet-18 1---ased SNN architecture. To demonstrate the scalability of our approach, layer types. CH-CNN (Hanming et al. 2025) is used to sparsify the convolutional layers, while CH- SNN sparsifies the linear layers in the SNN architecture. The comparative top-1 accuracy results are summarized in the table I6 demonstrating the competitive performance and strong scalability of our method.
apply the same core methodology two distinct
Table 16: Performance on Tiny ImageNet and ImageNet.
Dataset
Method
Sparsity
ACC.(sparse)
ACC.(dense)
Ace loss
Tiny
CH-SNN
69.37%
44.97%
45.98%
1.01% %
ImageNet
CH-SNN
66.94%
62.77%
63.62%
0.85%
DPAP
51.71%
60.41%
65.74%
5.33%
ImageNet
DPAP
37.76%
63.35%
65.74%
2.39%
DPAP
22.69%
63.74%
65.74%
2.00%
On the are not available in the literature. Our CH-SNN model achieves an accuracy of 44.97% while main- taining a 69.37% sparsity rate, a performance level that comparable to the dense baseline.
dataset, we report the results for CH-SNN comparative results for DPAP
On the ImageNet dataset, We directly report the results for DPAP and its corresponding FC baseline from the original publication. This approach ensures a faithful comparison and avoids potential implementation discrepancies. For our CH-SNN, adopted the identical ResNet- 18 architecture used DPAP and conducted a fair comparison by training both a fully-commected (FC) model and sparse CH-SNN model under the same experimental protocol. The results demonstrate that CH- SNN achieves high structural sparsity of 66. 94% while attaining competitive performance, with only 0.85% accuracy drop compared to the FC baseline.
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Published as a conference paper at ICLR 2026
A.13 USAGE OF LARGE LANGUAGE MODELS
In the process of preparing this manuscript, we utilized the DeepSeek large language model to assist in polishing the English writing and refining the wording of the Abstract, Introduction and Conclusion sections. The core ideas, theoretical contributions, experimental design, data analysis, and results remain entirely the work of the authors. The authors take full responsibility for the entire content of this paper.
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Reviews:
[{"review_id": "RqvvH3oFPl", "reviewer": "Reviewer_iDtv", "summary": "This paper proposes CH-SNN, a dynamic sparse training framework for SNNs. The method sparsifies all linear layers in SNNs through four stages: (1) sparse topology initialization (SSCTI), (2) sparse weight initialization (SSWI), (3) hybrid pruning based on link removal scores (LRS), and (4) link regrowth using CH3-L3. Experiments shows that CH-SNN achieves ultra-high structural sparsity while maintaining accuracy. The authors also report significant energy savings when deploying CH-SNN on hardware-friendly algorithm S-TP.", "questions": "1. Section 3.2.1 states that for intermediate layers (e.g., after conv or attention), SSCTI is inapplicable and replaced by uniform random initialization. Does this mean the core topological initialization method is effectively limited to the first layer? How can CH-SNN ensure stable convergence or meaningful structure learning in deeper networks where feature correlations are nontrivial?\n\n2. On CIFAR-100, sparse models report large improvements over the baseline (Table 1). Can the authors explain why there are such large improvements? Intuitively, such a large gap strongly suggests the baseline FC models may not have been sufficiently tuned.\n\n3. Table 1 shows Grad R achieves 91.95% accuracy on DVS-Gesture with an accuracy improvement of +7.83%. However, CH-SNN reports 95.45% accuracy with only +0.38% improvement. Is there a reporting error in the accuracy or the improvement values?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. CH-SNN achieves ultra-high sparsity (>90% on some datasets) without performance degradation.\n\n2. The four-stage framework is well-structured and includes ablation studies showing the necessity of SSCTI and SSWI for stable training under extreme sparsity.", "weaknesses": "1. All experiments are conducted on relatively simple tasks using very shallow networks. The lack of evaluation on more complex datasets and deeper SNNs raises serious doubts about scalability. For example, the extremely high sparsity achieved on MNIST is likely attributable to the simplicity of the task, whereas the sparsity drops significantly on CIFAR. It can be inferred that on more challenging benchmarks like ImageNet, the claimed “ultra-sparse” may not be achievable. In contrast, works like SRigL (cited in Section 2.1) have been validated on ResNet-scale models. If the authors can provide relevant evidence, I am willing to increase my rating accordingly.\n\n2. The Spikformer results lack meaningful comparison. First, no other sparse training method is evaluated on Spikformer, making any performance comparison meaningless. Second, Transformers are typically designed for large-scale datasets, applying them to MNIST-level tasks offers little insight. Moreover, the paper never specifies the depth or width of the Spikformer used, making it impossible to assess the result’s significance.\n\n3. The paper repeatedly highlights marginal gains (e.g., outperforms FC network by 0.16% on MNIST) as evidence of superiority. However, MNIST is nearly saturated (~99% accuracy), and such a gain is statistically negligible. This risks overstating the method’s effectiveness.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "f5BE2kuWXw", "reviewer": "Reviewer_zWas", "summary": "This paper introduces Cannistraci-Hebb Spiking Neural Network (CH-SNN), a dynamic sparse training framework for ultra-sparse SNNs. Extensive experiments are conducted on six datasets, demonstrating that CH-SNN achieves high sparsity while retaining or improving accuracy over fully connected baselines.", "questions": "Can the authors clarify the multinomial sampling procedure in the pruning step, how exactly the link removal score (LRS) is converted into actual pruning decisions?\nHow accurate is the SSWI initialization method under varying degrees of input temporal sparsity, structural connection sparsity,and spike threshod？", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper presents an approach to ultra-sparse SNN training, integrating initialization, pruning methods, and Cannistraci-Hebb-inspired topological regrowth. \nExperiments were conducted on multiple datasets, and thorough ablation experiments and sensitivity analyses were carried out. \nThe framework is implemented on a hardware-friendly algorithm S-TP, achieving significant gains in energy efficiency.", "weaknesses": "Some key areas of the mathematical description, particularly around pruning and regrowth, lack sufficient clarity.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "QZnQOQ0GU4", "reviewer": "Reviewer_9DG8", "summary": "This paper presents CH-SNN, a novel four-stage dynamic sparse training framework for spiking neural networks (SNNs) that achieves ultra-high structural sparsity while maintaining/improving accuracy compared to baselines. Extensive experiments on six datasets and three architectures demonstrate consistent performance and energy advantages.", "questions": "1. Could the authors provide a theoretical argument or empirical evidence that the CH3-L3 regrowth mechanism guarantees stability or avoids redundant regrowth loops?\n2. How sensitive is CH-SNN to the hyperparameters controlling sparsity ratio, pruning frequency, and regrowth sampling distribution?\n3. The timestep of SNN is 8 according to this paper, could the authors explained the performance on different timesteps?\n4. Is the CH3-L3 topological regrowth biologically interpretable in terms of synaptic rewiring or STDP-like plasticity?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Strong novelty and cross-disciplinary contribution: bridges network science (Cannistraci-Hebb theory) with neuromorphic learning, introducing a biologically and topologically inspired sparse training approach.\n2. Comprehensive experimental validation: covers multiple datasets, architectures.\n3. Clear modular structure: the four-stage design (SSCTI, SSWI, LRS, CH3-L3) is intuitive and extensible to other SNNs, which provides a reasonable baseline for SNN training.", "weaknesses": "1. Theoretical insufficiency: The paper lacks formal analysis of the convergence and stability of the CH3-L3 regrowth dynamics.\n2. Scalability questions: Experiments are limited to medium-scale datasets. The framework’s behaviour on larger datasets (e.g., ImageNet or DVS-CIFAR100) remains untested.\n3. Biological claim ambiguity: The connection to Hebbian principles is mostly conceptual; empirical neuroscientific grounding is minimal.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "h2FnwTKMZ9", "reviewer": "Reviewer_nSp9", "summary": "This paper introduces CH-SNN (Cannistraci-Hebb Spiking Neural Network), which is a four-stage dynamic sparse training framework for ultra-sparse spiking neural networks (SNNs). Extensive experiments on six datasets show CH-SNN achieves performance comparable to FC networks even at ultra-high levels of sparsity", "questions": "(1) Temporal sparsity–accuracy trade-off: Have the authors analyzed the effect of increasing temporal sparsity on latency or robustness?\n(2) Reproducibility: Please clarify whether all baseline methods were reimplemented under identical training conditions or if their results were directly adopted from previous studies.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Originality\n(1) Integrates Cannistraci-Hebb theory, originally from complex network science, into SNN sparse training.\n(2) Introduces two novel initialization schemes (SSCTI, SSWI) specifically designed for spike-based learning.\n\nQuality\n(1) Extensive experiments across six datasets show robustness and generalizability.\n(2) Includes ablation, sensitivity, and hardware efficiency analyses, showing methodological thoroughness.\n\nClarity\nThe paper is clearly structured, with each stage of CH-SNN well explained. The biological and theoretical motivations are well linked to the computational framework.", "weaknesses": "(1) Insufficient analysis of temporal dynamics: \nThe paper emphasizes structural sparsity but offers limited insight into the temporal spike dynamics.\n(2) Clarity of comparison fairness:\nIt is not entirely clear whether all baseline methods were reimplemented under identical experimental conditions. The paper does not specify whether these results were reproduced using a unified experimental setup or directly taken from prior publications, which affects the transparency and comparability of the reported performance gains.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)