Reconstructing Spiking Neural Networks Using a Single Neuron with Autapses

Wuque Cai; Hongze Sun; Quan Tang; Shifeng Mao; Zhenxing Wang; Jiayi He; Duo Chen; Dezhong Yao

cs.NEMar 25, 2026

Reconstructing Spiking Neural Networks Using a Single Neuron with Autapses

Authors: Wuque Cai, Hongze Sun, Quan Tang, Shifeng Mao, Zhenxing Wang, Jiayi He, Duo Chen, Dezhong Yao,

Organizations: Brain-Apparatus Communication Institute, University of Electronic Science and Technology of China, Chengdu, China · School of Artificial Intelligence, Chongqing University of Education, Chongqing, China

Abstract

Spiking neural networks (SNNs) are promising for neuromorphic computing, but high-performing models still rely on dense multilayer architectures with substantial communication and state-storage costs. Inspired by autapses, we propose time-delayed autapse SNN (TDA-SNN), a framework that reconstructs SNNs with a single leaky integrate-and-fire neuron and a prototype-learning-based training strategy. By reorganizing internal temporal states, TDA-SNN can realize reservoir, multilayer perceptron, and convolution-like spiking architectures within a unified framework. Experiments on sequential, event-based, and image benchmarks show competitive performance in reservoir and MLP settings, while convolutional results reveal a clear space--time trade-off. Compared with standard SNNs, TDA-SNN greatly reduces neuron count and state memory while increasing per-neuron information capacity, at the cost of additional temporal latency in extreme single-neuron settings. These findings highlight the potential of temporally multiplexed single-neuron models as compact computational units for brain-inspired computing.

Figures & tables

Dataset	Delay	1	2	4	8	16	32	64
DEAP	MC	83.52 $\pm$ 0.52	83.10 $\pm$ 1.10	83.63 $\pm$ 0.73	83.91 $\pm$ 1.14	83.85 $\pm$ 0.59	84.66 $\pm$ 0.62	84.47 $\pm$ 0.99
DEAP	RD	83.62 $\pm$ 1.12	83.34 $\pm$ 1.14	83.48 $\pm$ 0.64	83.73 $\pm$ 1.02	83.63 $\pm$ 0.76	83.98 $\pm$ 0.81	84.47 $\pm$ 0.99
SHD	MC	78.35 $\pm$ 0.61	72.09 $\pm$ 1.17	73.59 $\pm$ 0.67	74.69 $\pm$ 1.28	77.07 $\pm$ 0.48	79.36 $\pm$ 0.31	80.42 $\pm$ 0.39
SHD	RD	78.55 $\pm$ 0.68	78.62 $\pm$ 0.46	77.60 $\pm$ 2.49	78.58 $\pm$ 0.25	77.63 $\pm$ 1.87	79.26 $\pm$ 1.21	80.42 $\pm$ 0.39
MNIST	MC	33.53 $\pm$ 3.51	94.44 $\pm$ 0.10	94.39 $\pm$ 0.16	94.33 $\pm$ 0.13	94.37 $\pm$ 0.15	94.42 $\pm$ 0.20	94.38 $\pm$ 0.12
	RD	84.03 $\pm$ 19.14	93.32 $\pm$ 1.19	94.82 $\pm$ 0.15	95.11 $\pm$ 0.21	95.63 $\pm$ 0.14	95.98 $\pm$ 0.11	96.42 $\pm$ 0.09

Table 1: Experimental Results of Autaptic Selection Strategies Across Different Datasets

Model	Arch.	FLOPs	Params.	$N_{\text{Neu.}}$	Speed	$\mathbf{S}$
Model	Arch.	FLOPs	Params.	$N_{\text{Neu.}}$	(s/epoch)	(bit)
STD-SNN	RC	$N^{2}T$	$N^{2}$	$N$	22.57	489.91
	MLP	$N_{\text{in}}N_{\text{out}}T$	$N_{\text{in}}N_{\text{out}}$	$N_{\text{out}}$	8.36	3113.89
	Conv.	$2C_{\text{in}}C_{\text{out}}k^{2}WHT$	$C_{\text{in}}C_{\text{out}}k^{2}$	$C_{out}WH$	17.21	5.48
TDA-SNN	RC	$\sum_{d}\left(N-d\right)T$	$\sum_{d}\left(N-d\right)$	$1$	21.14	32096.37
	MLP	$\sum_{d}N_{d}T$	$\sum_{d}N_{d}$	$1$	90.91	199237.63

Table 2: Per-layer computational complexity, parameter count, neuron count, speed, and per-neuron information content across different models.

Figure 9: RC architecture of the TDA-SNN model. (a) Overall RC architecture constructed from the TDA-SNN model. (b) Autaptic weight matrix corresponding to the RC framework.

Figure 10: MLP architecture of the TDA-SNN model. (a) Overall MLP architecture constructed from the TDA-SNN model. (b) Autaptic weight matrix corresponding to the MLP framework.

Dataset	bs	lr	$T$	$\text{d}t$	$v_{\text{th}}$	$\tau$
DEAP	200	0.002	6	100	1.0	0.5
SHD	512	0.01	100	14	0.3	0.3
MNIST	512	0.002	4	-	0.3	0.5
fMNIST	512	0.002	4	-	0.3	0.5
DVS Gesture	128	0.002	8	125	1.1	0.67
CIFAR10	200	0.002	4	-	1.0	0.5

Table 3: The hyperparameters for different datasets.

Figure 11: Evolution of connection weights in the RC architecture. (a) Random delay strategy. (b) Low-node configuration. (c) Maximum connection strategy.

Figure 12: Evolution of connection weights in the MLP architecture. (a) Random delay strategy. (b) Low-node configuration. (c) Maximum connection strategy.

Dataset	Delay	1	2	4	8	16	32	64
DEAP	MC-RD	0.79	0.66	0.65	0.73	0.51	0.05	1.0
SHD	MC-RD	0.53				0.40	0.81	1.0
MNIST	MC-RD
	MC-T Inv.		0.06		0.65	0.97	0.95
	RD-T Inv.	0.35	0.88
fMNIST	MC-RD			0.59

Table 4: Paired t-tests of Autaptic Selection Strategies Across Different Delays. * denotes

p<0.05

Figure 13: Extending TDA-SNN to multi-layer deep models under the MLP architecture.

Figure 14: Learning rate sensitivity study for the MLP architecture on MNIST.

Figure 15: Number of nodes ablation on CIFAR100 for STD-SNN and TDA-SNN.

Figure 16: Training (a) and inference (b) time ratios of TDA-SNN relative to STD-SNN on CIFAR10. The yellow marker denotes STD-SNN (ratio = 1.0). The x-axis is logarithmic.

Spiking Neural Networks

Spiking neural networks process information through discrete, time-dependent neural events, aiming for efficient computation and biologically inspired learning.

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Scalable Training of Continuous-Time Spiking Neural Networks with Differentiable Spike-Time Discretization

Yusuke Sakemi, Tomoya Takeuchi, Takeo Hosomi, Kazuyuki Aihara

Research Center for Mathematical Engineering, Chiba Institute of Technology, Narashino, Japan · International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo, Tokyo, Japan · NEC Corporation, Kawasaki, Japan

Spiking Neural Networks LIF Neurons

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Continuous-time spiking neural networks (SNNs) provide an event-driven framework for temporal computation, computational neuroscience, and neuromorphic hardware. However, training deep continuous-time SNNs is severely constrained by the memory required for exact spike-time computation, which evaluates and retains candidate firing times over intervals determined by presynaptic spike ordering. Here we introduce a memory-efficient training framework based on differentiable spike-time discretization (DSTD) for leaky integrate-and-fire neurons with general membrane and synaptic time constants. DSTD maps irregular presynaptic spikes onto differentiable weighted events at fixed time points, replacing the input-dependent candidate dimension with

M

fixed time intervals while accurately approximating continuous-time membrane-potential dynamics. This reduces candidate-related activation memory from

O(N_{\mathrm{out}}N_{\mathrm{in}})

O(N_{\mathrm{out}}M)

in the case of time-to-first-spike (TTFS) coding, where

N_{\mathrm{in}}

and

N_{\mathrm{out}}

denote the numbers of presynaptic and postsynaptic neurons, respectively. We further introduce synfire-chain-inspired temporal regularization that organizes layer-wise firing windows, mitigates dead-neuron failures, and enables pipeline-like processing. In dense LIF layers, DSTD reduced peak memory consumption by up to approximately 100-fold and training time by up to approximately 20-fold compared with exact spike-time computation. Together, these methods allowed us to train 9-layer convolutional SNNs on CIFAR-10 and 20-layer convolutional SNNs on Fashion-MNIST on a single GPU.

Abstract

Spiking Neural Networks

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