A function space analysis of finite neural networks with insights from sampling theory

• URL: http://arxiv.org/abs/2004.06989v2
• Date: Fri, 25 Feb 2022 18:58:49 GMT
• Title: A function space analysis of finite neural networks with insights from sampling theory
• Authors: Raja Giryes
• Abstract summary: We show that the function space generated by multi-layer networks with non-expansive activation functions is smooth. Under the assumption that the input is band-limited, we provide novel error bounds. We analyze both deterministic uniform and random sampling showing the advantage of the former.
• Score: 41.07083436560303
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work suggests using sampling theory to analyze the function space represented by neural networks. First, it shows, under the assumption of a finite input domain, which is the common case in training neural networks, that the function space generated by multi-layer networks with non-expansive activation functions is smooth. This extends over previous works that show results for the case of infinite width ReLU networks. Then, under the assumption that the input is band-limited, we provide novel error bounds for univariate neural networks. We analyze both deterministic uniform and random sampling showing the advantage of the former.

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