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

A new theoretical paper by researchers Dominik Dold and Philipp Christian Petersen challenges a long-held belief in neuromorphic computing and computational neuroscience. The work, titled 'Equivalence of approximation by networks of single- and multi-spike neurons,' demonstrates that for a broad class of spiking neuron models—including the widely used leaky integrate-and-fire model with subtractive reset—networks constrained to fire each neuron only once are fundamentally as powerful as networks where neurons can spike multiple times. This equivalence holds for general machine learning tasks, meaning the two architectures can approximate the same set of target functions.

The core technical result shows that for every approximation bound proven for a set of multi-spike networks, there exists an equivalent set of single-spike networks where the same bound holds, requiring only a linear increase in the number of neurons relative to the maximum spike count. Crucially, the reverse is also true, establishing a formal equivalence. This finding has immediate implications: it validates that many existing mathematical approximation theorems derived for the simpler, more analytically tractable single-spike models automatically extend to the more complex and biologically realistic multi-spike case.

This breakthrough simplifies the theoretical landscape for developing next-generation AI hardware. Neuromorphic engineers designing low-power, brain-inspired chips often grapple with the complexity of multi-spiking dynamics. This proof suggests that systems designed around simpler, single-spike neurons can achieve the same computational universality, potentially streamlining both hardware architecture and the mathematical frameworks used to understand them. It bridges a gap between theoretical computer science and practical neuromorphic engineering.