Upper bounds on the number of causal pieces in spiking neural networks
The input space of single-spike neural networks decomposes into causal pieces, and the number of causal pieces has been shown to provide a lower bound on the approximation error for some spiking neural networks. While this decomposition is applicable to a wide range of spiking neuron models, the limits of how many causal pieces can be realised by spiking neural networks are still unknown. In this work, we derive two complementary upper bounds on the number of causal pieces in feedforward single-spike neural networks. First, we establish a combinatorial bound given by the poly-Bernoulli numbers, which applies to a broad class of spiking neuron models. The bound is of order $e^{2(L-1)N\log ...
| Authors | Dominik Dold, Dennis Elbrächter, Philipp Petersen |
|---|---|
| Primary category | cs.NE |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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