Search Results for author: Umberto M. Tomasini

Found 3 papers, 2 papers with code

How Deep Neural Networks Learn Compositional Data: The Random Hierarchy Model

1 code implementation5 Jul 2023 Francesco Cagnetta, Leonardo Petrini, Umberto M. Tomasini, Alessandro Favero, Matthieu Wyart

The model is a classification task where each class corresponds to a group of high-level features, chosen among several equivalent groups associated with the same class.

How deep convolutional neural networks lose spatial information with training

1 code implementation4 Oct 2022 Umberto M. Tomasini, Leonardo Petrini, Francesco Cagnetta, Matthieu Wyart

Here, we (i) show empirically for various architectures that stability to image diffeomorphisms is achieved by both spatial and channel pooling, (ii) introduce a model scale-detection task which reproduces our empirical observations on spatial pooling and (iii) compute analitically how the sensitivity to diffeomorphisms and noise scales with depth due to spatial pooling.

Failure and success of the spectral bias prediction for Kernel Ridge Regression: the case of low-dimensional data

no code implementations7 Feb 2022 Umberto M. Tomasini, Antonio Sclocchi, Matthieu Wyart

Recently, several theories including the replica method made predictions for the generalization error of Kernel Ridge Regression.

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