We show that deep ReLU neural network classifiers can see a low-dimensional Riemannian manifold structure on data. Such structure comes via the local data matrix, a variation of the Fisher infor-mation 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 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, L; Fioresi, R. - In: SIAM JOURNAL ON IMAGING SCIENCES. - ISSN 1936-4954. - STAMPA. - 15:3(2022), pp. 1140-1156. [10.1137/21M1437056]
Model-Centric Data Manifold: The Data Through the Eyes of the Model
Fioresi, R
Co-primo
Membro del Collaboration Group
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 local data matrix, a variation of the Fisher infor-mation 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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.