Metric Space Magnitude and Generalisation in Neural Networks

• URL: http://arxiv.org/abs/2305.05611v1
• Date: Tue, 9 May 2023 17:04:50 GMT
• Title: Metric Space Magnitude and Generalisation in Neural Networks
• Authors: Rayna Andreeva and Katharina Limbeck and Bastian Rieck and Rik Sarkar
• Abstract summary: This work is to quantify the learning process of deep neural networks through the lens of a novel topological invariant called magnitude. We use magnitude to study the internal representations of neural networks and propose a new method for determining their generalisation capabilities.
• Score: 12.110483221042903
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deep learning models have seen significant successes in numerous applications, but their inner workings remain elusive. The purpose of this work is to quantify the learning process of deep neural networks through the lens of a novel topological invariant called magnitude. Magnitude is an isometry invariant; its properties are an active area of research as it encodes many known invariants of a metric space. We use magnitude to study the internal representations of neural networks and propose a new method for determining their generalisation capabilities. Moreover, we theoretically connect magnitude dimension and the generalisation error, and demonstrate experimentally that the proposed framework can be a good indicator of the latter.

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