Model-centric Data Manifold: the Data Through the Eyes of the Model
Machine Learning
2021-04-28 v1 Optimization and Control
Machine Learning
Abstract
We discover 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 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 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.
Cite
@article{arxiv.2104.13289,
title = {Model-centric Data Manifold: the Data Through the Eyes of the Model},
author = {Luca Grementieri and Rita Fioresi},
journal= {arXiv preprint arXiv:2104.13289},
year = {2021}
}