证明了脉冲神经网络能高效表示简单时序函数
On the Universal Representation Property of Spiking Neural Networks
- 将脉冲网络视为输入输出脉冲序列的转换器
- 理论证明其可精确表示特定脉冲函数，参数量近最优
- 适合处理低维、短时序或复合型任务，对深度脉冲网络设计有指导意义
受生物启发，脉冲神经网络（SNNs）通过离散脉冲在时间上处理信息，是经典计算范式和人工神经网络（ANNs）的一种节能替代方案。本文将SNNs视为脉冲序列的序列到序列处理器，即把输入脉冲流转化为输出脉冲流的系统，分析其表征能力。我们为一类自然的脉冲序列函数建立了通用表征性质。结果是完全定量的、可构造的，并在所需权重和神经元数量上接近最优。分析表明，SNNs特别适合表示输入少、时间复杂度低或此类函数的复合形式。后者尤为重要，表明深度SNN可通过模块化设计高效捕捉复合函数。作为应用，我们讨论了脉冲序列分类问题。总体而言，这些结果为理解基于脉冲的类脑系统的能力与局限提供了严格的理论基础。
原文摘要 · Abstract (English)
Inspired by biology, spiking neural networks (SNNs) process information via discrete spikes over time, offering an energy-efficient alternative to the classical computing paradigm and classical artificial neural networks (ANNs). In this work, we analyze the representational power of SNNs by viewing them as sequence-to-sequence processors of spikes, i.e., systems that transform a stream of input spikes into a stream of output spikes. We establish the universal representation property for a natural class of spike train functions. Our results are fully quantitative, constructive, and near-optimal in the number of required weights and neurons. The analysis reveals that SNNs are particularly well-suited to represent functions with few inputs, low temporal complexity, or compositions of such functions. The latter is of particular interest, as it indicates that deep SNNs can efficiently capture composite functions via a modular design. As an application of our results, we discuss spike train classification. Overall, these results contribute to a rigorous foundation for understanding the capabilities and limitations of spike-based neuromorphic systems.
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