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Andreeva, R.* ; Limbeck, K. ; Rieck, B. ; Sarkar, R.*

Metric Space Magnitude and Generalisation in Neural Networks.

In: (Proceedings of Machine Learning Research). 2023. 242-253 (Proceedings of Machine Learning Research ; 221)
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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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Publication type Article: Conference contribution
Corresponding Author
Conference Title Proceedings of Machine Learning Research
Quellenangaben Volume: 221, Issue: , Pages: 242-253 Article Number: , Supplement: ,
Non-patent literature Publications
Institute(s) Helmholtz Artifical Intelligence Cooperation Unit (HAICU)
Institute of AI for Health (AIH)