We show that deep ReLU neural network classifiers can see a low-dimensional Riemannian manifold structure on data. Such structure comes via the \sl local data matrix, a variation of the Fisher information matrix, where the role of the model parameters is taken by the data variables. We obtain a foliation of the data domain, and we show that the dataset on which the model is trained lies on a leaf, the \sl data leaf, whose dimension is bounded by the number of classification labels. We validate our results with some experiments with the MNIST dataset: paths on the data leaf connect valid images, while other leaves cover noisy images.

Model-Centric Data Manifold: The Data Through the Eyes of the Model / Grementieri, Luca; Fioresi, Rita. - In: SIAM JOURNAL ON IMAGING SCIENCES. - ISSN 1936-4954. - ELETTRONICO. - 15:3(2022), pp. 1140-1156. [10.1137/21M1437056]

Model-Centric Data Manifold: The Data Through the Eyes of the Model

Fioresi, Rita
2022

Abstract

We show that deep ReLU neural network classifiers can see a low-dimensional Riemannian manifold structure on data. Such structure comes via the \sl local data matrix, a variation of the Fisher information matrix, where the role of the model parameters is taken by the data variables. We obtain a foliation of the data domain, and we show that the dataset on which the model is trained lies on a leaf, the \sl data leaf, whose dimension is bounded by the number of classification labels. We validate our results with some experiments with the MNIST dataset: paths on the data leaf connect valid images, while other leaves cover noisy images.
2022
Model-Centric Data Manifold: The Data Through the Eyes of the Model / Grementieri, Luca; Fioresi, Rita. - In: SIAM JOURNAL ON IMAGING SCIENCES. - ISSN 1936-4954. - ELETTRONICO. - 15:3(2022), pp. 1140-1156. [10.1137/21M1437056]
Grementieri, Luca; Fioresi, Rita
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/897624
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