Paper List

期刊: ArXiv Preprint
发布日期: 2026-03-13
Computational NeuroscienceMachine Learning Theory

Equivalence of approximation by networks of single- and multi-spike neurons

Faculty of Mathematics and Research Network DataScience @ Uni Vienna, University of Vienna

Dominik Dold, Philipp Petersen
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IN SHORT: This paper resolves the fundamental question of whether single-spike spiking neural networks (SNNs) are inherently less expressive than multi-spike SNNs, proving their theoretical equivalence in approximation capabilities.

核心创新

  • Theory Established a formal transference principle (Theorem 1) proving that approximation bounds for multi-spike SNNs directly translate to single-spike SNNs with at most N_s·n neurons, and vice versa.
  • Methodology Developed constructive proofs showing how to replace any multi-spike neuron with N_s single-spike neurons (by threshold adjustment) and any single-spike neuron with αN_s multi-spike neurons (via spike cancellation).
  • Theory Extended the equivalence to include lower bounds (Corollary 1) and common input encoders (Corollary 2), making existing theoretical results for one paradigm immediately applicable to the other.

主要结论

  • Single-spike and multi-spike SNNs are theoretically equivalent in approximation capabilities for a large class of neuron models including LIF with subtractive reset.
  • Any approximation bound for multi-spike SNNs with n neurons translates to single-spike SNNs with at most N_s·n neurons (linear scaling in maximum spike count).
  • The reverse direction holds with prefactor α ≤ min(1, 6/π² + 1/√N_s) for N_s ≥ 1, and α < 6/π² + 1/(2√N_s) for N_s ≥ 8.
研究空白： Previous approximation theory for SNNs was fragmented, with results derived separately for single-spike and multi-spike networks, creating uncertainty about whether single-spike networks were fundamentally limited in expressivity compared to their multi-spike counterparts.

摘要: 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.