arXiv AI By Dominik Dold, Philipp Christian Petersen

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

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The paper demonstrates that for a broad class of spiking neuron models, including the leaky integrate‑and‑fire with subtractive reset, any approximation bound proven for multi‑spike networks can be translated to an equivalent single‑spike network with only a linear change in neuron count, and vice versa. This establishes that single‑spike and multi‑spike neural networks possess identical approximation capabilities for general machine learning tasks. Consequently, existing approximation results for single‑spike networks automatically extend to the multi‑spike case.

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arXiv AI
Oct 12

Convex Optimization of Spiking Neural Networks with Global and Approximation Guarantees

The paper presents a convex formulation for training spiking neural networks (SNNs), showing that the weight‑decay‑regularized training problem for a class of threshold RNNs—including leaky integrate‑and‑fire SNNs—has zero duality gap and matches a convex program’s optimal value. To handle the exponential size of the resulting convex programs, the authors introduce a randomized surrogate with a high‑probability approximation guarantee. Empirical results demonstrate that the convex variant outperforms surrogate‑gradient training on addition and first‑last‑XOR tasks, matches performance on sequential MNIST, and falls slightly behind a reservoir baseline on base‑3 and base‑5 addition.

By Himanshu Udupi, Calvin Ang, Sungyoon Kim, Xiaocong Yang, ChengXiang Zhai