📄 中文摘要
在脉冲神经网络中，是否每个神经元最多只需发射一次脉冲就足够？近期的研究为脉冲神经网络推导了近似界限，量化了它们拟合目标函数的能力。然而，这些结果仅适用于最多发射一次脉冲的神经元，这被普遍认为是一个严重的限制。研究表明，对于包括常用的带有减法重置的泄漏积分发射模型在内的大类脉冲神经元模型，适用于多脉冲神经网络的一组近似界限，存在一组等效的单脉冲神经网络，其中神经元数量仅比最大脉冲数线性增加，并且该界限依然成立。
单脉冲和多脉冲神经元网络的近似等价性
📄 English Summary
Equivalence of approximation by networks of single- and multi-spike neurons
In spiking neural networks, the question arises whether it is sufficient for each neuron to spike at most once. Recent works have derived approximation bounds for spiking neural networks, quantifying their ability to fit target functions. However, these results are limited to neurons that spike at most once, which is often considered a significant constraint. This study demonstrates that, for a broad class of spiking neuron models, including the widely used leaky integrate-and-fire model with subtractive reset, for every approximation bound valid for a set of multi-spike neural networks, there exists an equivalent set of single-spike neural networks with only linearly more neurons (in terms of the maximum number of spikes) for which the bound holds.