Fractional-order Spiking Neural Network
Chengjie Ge, Yufeng Peng, Zihao Li, Qiyu Kang, Xueyang Fu, Xuhao Li, Qixin Zhang, Junhao Ren, Zheng-Jun Zha
TL;DR
This paper introduces fractional-order spiking neural networks (f-SNNs) that model long-range dependencies in neural dynamics, leading to improved accuracy and robustness while maintaining energy efficiency.
Contribution
The paper proposes a novel fractional-order SNN framework that generalizes traditional models to better capture long-term dependencies and demonstrates its effectiveness across various tasks.
Findings
f-SNNs achieve higher accuracy than traditional SNNs
f-SNNs maintain comparable energy efficiency
f-SNNs show increased robustness to noise
Abstract
Spiking Neural Networks (SNNs) draw inspiration from biological neurons to enable brain-like computation, demonstrating effectiveness in processing temporal information with energy efficiency and biological realism. Most existing SNNs are based on neural dynamics such as the (leaky) integrate-and-fire (IF/LIF) models, which are described by first-order ordinary differential equations (ODEs) with Markovian characteristics. This means the potential state at any time depends solely on its immediate past value, potentially limiting network expressiveness. Empirical studies of real neurons, however, reveal long-range correlations and fractal dendritic structures, suggesting non-Markovian behavior better modeled by fractional-order ODEs. Motivated by this, we propose a fractional-order spiking neural network (f-SNN) framework that strictly generalizes integer-order SNNs and captures long-term…
Peer Reviews
Decision·ICLR 2026 Poster
The paper is well-written, precise, and enjoyable to read. The definition of the continuous-time f-SNN and the derivation of the discrete-time counterpart are well-explained. Also, the experimental setup is clear and well-documented, and the results are consistent with the claims.
The paper contains some minor imprecision that can be easily fixed. For instance, in equation (1) line 126, there is an a which I suppose is meant to be a 0. Moreover, in line 172, the authors mentioned "learnable synaptic weights" that are not introduced since in line 170, only the input current is mentioned $I_{in, k}$. The caption of Figure 4, page. 7, could be a little bit extended by explaining how to interpret Figure 4 (at least to me, it is not straightforward). I would appreciate seein
1. The proposed fractional-order spiking neural network (f-SNN) framework effectively captures long-term dependencies in membrane potential and spike trains via fractional dynamics, addressing the limitation of traditional integer-order SNNs (based on IF/LIF models) that only rely on immediate past states. 2. The f-SNN demonstrates superior performance in multiple aspects: it achieves higher accuracy than conventional SNNs on neuromorphic vision
1. The concept of fractional-order has already been proposed by others; the authors seem to have only put forward a framework and tested it on different datasets, which is more like an engineering problem. 2. The datasets used are limited, and results on widely tested datasets such as CIFAR-10, CIFAR-100, and ImageNet are missing.
1. The introduction of fractional dynamics into SNNs is novel and biologically inspired. It directly addresses the Markovian limitation of conventional LIF/IF neurons, linking to real neuronal behaviors and fractal dendritic structures. 2. The derivation from Caputo derivatives to the discrete f-LIF formulation is rigorous. Theorem 1 and the comparison of exponential vs. power-law decay are clearly presented and intuitive. 3. The f-SNN framework is a strict superset of conventional SNNs (α =
1. The theory mainly discusses long-term dependence qualitatively via the Mittag–Leffler function; deeper analyses such as stability, gradient dynamics, or expressive power would strengthen the theoretical contribution. 2. Although the paper mentions O(NlogN) and truncated-memory approximations, there is no clear empirical benchmark on training/inference speed or memory consumption compared to standard SNNs. 3. Lack of ablation on fractional order $\alpha$. While $\alpha$ is a key hyperparamet
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Taxonomy
TopicsNeural Networks and Applications · Fractional Differential Equations Solutions