Nonsmooth Optimisation and neural networks

Vinesha Peiris; Nadezda Sukhorukova

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arXiv · 2503.01860

Nonsmooth Optimisation and neural networks

Vinesha Peiris·Nadezda Sukhorukova

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Abstract

In this paper, we study neural networks from the point of view of nonsmooth optimisation, namely, quasidifferential calculus. We restrict ourselves to the case of uniform approximation by a neural network without hidden layers, the activation functions are restricted to continuous strictly increasing functions. We develop an algorithm for computing the approximation with one hidden layer through a step-by-step procedure. The nonsmooth analysis techniques demonstrated their efficiency. In particular, they partially explain why the developed step-by-step procedure may run without any objective function improvement after just one step of the procedure.

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Vinesha Peiris, Nadezda Sukhorukova. 2025-02-24. Nonsmooth Optimisation and neural networks. https://arxiv.org/abs/2503.01860

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