Finance and Stochastics Seminar – Tom Hadfield

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Speaker: Tom Hadfield Title: Patnaik-Pearson intrinsic dimension for internal representations of neural networks Abstract: We define a new measure of intrinsic dimension of a data manifold, which we call the Patnaik-Pearson dimension, and apply this to internal representations of neural networks, in particular transformers. The inspiration for this comes from the HTSR and SETOL work of Martin, Mahoney and Hinrichs, combined with the TwoNN intrinsic dimension estimator of Facco et al. We prove various properties of this intrinsic dimension estimator. Treating weight matrices of neural networks…