On Transversality of Bent Hyperplane Arrangements and the Topological Expressiveness of ReLU Neural Networks

DOI10.1137/20M1368902MaRDI QIDQ5073711

Kathryn A. Lindsey, J. Elisenda Grigsby

Publication date: 3 May 2022

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.09052

zbMATH Keywords

polyhedral complexesReLU neural networkstopological expressiveness

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Critical points and critical submanifolds in differential topology (57R70) Polyhedral manifolds (52B70) PL-topology (57Q99)

Cites Work

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• Facing up to arrangements: face-count formulas for partitions of space by hyperplanes
• Lectures on Polytopes
• Convex Polytopes
• Reconciling modern machine-learning practice and the classical bias–variance trade-off
• Lower Bounds for Approximation by Nonlinear Manifolds
• Approximation by superpositions of a sigmoidal function
• On decision regions of narrow deep neural networks

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