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This research establishes a theoretical equivalence between single-spike and multi-spike spiking neural networks regarding their function approximation capabilities. By proving that bounds valid for one model type apply to the other with only linear adjustments in neuron count, the study removes a perceived limitation of single-spike models like the leaky integrate-and-fire architecture. This finding simplifies theoretical analysis and suggests that constraints on spike frequency do not inherently reduce the expressive power of these networks for general machine learning tasks.
Equivalence of approximation by networks of single- and multi-spike neurons
arXiv:2603.13478v2 Announce Type: replace-cross Abstract: 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 (or less) 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.
Abstract: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 (or less) 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.
Neural and Evolutionary Computing (cs.NE); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Neurons and Cognition (q-bio.NC); Machine Learning (stat.ML)
arXiv:2603.13478 [cs.NE]
(or arXiv:2603.13478v2 [cs.NE] for this version)
https://doi.org/10.1007/978-3-032-38398-3_16 DOI(s) linking to related resources
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