单脉冲神经元与多脉冲神经元在函数逼近能力上等价。
Equivalence of approximation by networks of single- and multi-spike neurons
- 证明了单脉冲与多脉冲神经元在逼近能力上等价，仅需线性增加神经元数量。
- 针对漏电整合-放电模型等常见脉冲神经网络，该等价性成立。
- 为单脉冲神经网络的理论结果可推广至多脉冲场景提供依据。
在脉冲神经网络中，是否每个神经元最多只放电一次就足够？近期研究给出了脉冲神经网络对目标函数拟合能力的逼近界，但这些结果仅适用于最多放电一次的神经元，通常被认为存在强限制。本文证明，对于一大类脉冲神经元模型（包括常用的带减法重置的漏电整合-放电模型），任意适用于多脉冲神经网络的逼近界，均存在一个具有线性更多神经元（以最大放电次数为基准）的单脉冲神经网络集合，使得该界同样成立。反之亦然。因此，在一般机器学习任务的函数逼近能力上，单脉冲与多脉冲神经网络是等价的。这意味着文献中许多关于单脉冲神经网络的逼近结果也适用于多脉冲情况。
原文摘要 · Abstract (English)
In a spiking neural network, is it enough for each neuron to spike at most once? In recent work, approximation bounds for spiking neural networks have been derived, quantifying how well they can fit target functions. However, these results are only valid for neurons that spike at most once, which is commonly thought to be a strong limitation. Here, we show that the opposite is true for a large class of spiking neuron models, including the commonly used leaky integrate-and-fire model with subtractive reset: for every approximation bound that is valid for a set of multi-spike neural networks, there is an equivalent set of single-spike neural networks with only linearly more neurons (in the maximum number of spikes) for which the bound holds. The same is true for the reverse direction too, showing that regarding their approximation capabilities in general machine learning tasks, single-spike and multi-spike neural networks are equivalent. Consequently, many approximation results in the literature for single-spike neural networks also hold for the multi-spike case.
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