用因果片段分析脉冲神经网络，揭示其性能与结构的关系。
Causal pieces: analysing and improving spiking neural networks piece by piece
- 将输入空间分解为因果片段，衡量SNN的表达能力。
- 训练成功与初始参数对应的因果片段数量正相关。
- 正权重前馈SNN片段多，性能媲美主流模型。
我们提出一种针对脉冲神经网络（SNNs）的新概念——'因果片段'，源自用于分析人工神经网络（ANNs）表达能力的'线性片段'思想。我们证明，SNN的输入域可分解为多个因果区域，在这些区域内，输出脉冲时间对输入脉冲时间及网络参数呈局部Lipschitz连续。因果片段的数量反映了SNN的近似能力。模拟结果显示，训练集上初始参数产生的因果片段数越高，SNN训练成功率越高。此外，仅含正权重的前馈SNN展现出惊人的高因果片段数，可在基准任务上达到竞争性表现。我们认为因果片段不仅是改进SNN的强大而严谨工具，未来或可用于比较SNN与ANN的新方式。
原文摘要 · Abstract (English)
We introduce a novel concept for spiking neural networks (SNNs) derived from the idea of "linear pieces" used to analyse the expressiveness and trainability of artificial neural networks (ANNs). We prove that the input domain of SNNs decomposes into distinct causal regions where its output spike times are locally Lipschitz continuous with respect to the input spike times and network parameters. The number of such regions - which we call "causal pieces" - is a measure of the approximation capabilities of SNNs. In particular, we demonstrate in simulation that parameter initialisations which yield a high number of causal pieces on the training set strongly correlate with SNN training success. Moreover, we find that feedforward SNNs with purely positive weights exhibit a surprisingly high number of causal pieces, allowing them to achieve competitive performance levels on benchmark tasks. We believe that causal pieces are not only a powerful and principled tool for improving SNNs, but might also open up new ways of comparing SNNs and ANNs in the future.
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