Model-Centric Data Manifold: The Data Through the Eyes of the Model
| Autor: | Luca Grementieri, Rita Fioresi |
|---|---|
| Přispěvatelé: | Grementieri, Luca, Fioresi, Rita |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Deep Learning Statistics - Machine Learning Optimization and Control (math.OC) Applied Mathematics General Mathematics FOS: Mathematics Machine Learning (stat.ML) Mathematics - Optimization and Control Machine Learning (cs.LG) |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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