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arXiv · 2007.02777

Parametric machines: a fresh approach to architecture search

Pietro Vertechi·Mattia G. Bergomi
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Abstract

Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how simple machines can be combined into more complex ones. We explore finite- and infinite-depth machines, which generalize neural networks and neural ordinary differential equations. Borrowing ideas from functional analysis and kernel methods, we build complete, normed, infinite-dimensional spaces of machines, and we discuss how to find optimal architectures and parameters -- within those spaces -- to solve a given computational problem. In our numerical experiments, these kernel-inspired networks can outperform classical neural networks when the training dataset is small.

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Pietro Vertechi, Mattia G. Bergomi. 2020-07-06. Parametric machines: a fresh approach to architecture search. https://arxiv.org/abs/2007.02777

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