22 citations · 59 across the 7 of their papers we have counts for
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Breaking the Curse of Dimensionality in Deep Neural Networks by Learning Invariant Representations
Leonardo Petrini
Artificial intelligence, particularly the subfield of machine learning, has seen a paradigm shift towards data-driven models that learn from and adapt to data. This has resulted in…
How Deep Neural Networks Learn Compositional Data: The Random Hierarchy Model
Francesco Cagnetta, Leonardo Petrini, Umberto M. Tomasini +2
Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabli…
How deep convolutional neural networks lose spatial information with training
Umberto M. Tomasini, Leonardo Petrini, Francesco Cagnetta +1
A central question of machine learning is how deep nets manage to learn tasks in high dimensions. An appealing hypothesis is that they achieve this feat by building a representatio…
Relative stability toward diffeomorphisms indicates performance in deep nets
Leonardo Petrini, Alessandro Favero, Mario Geiger +1
Understanding why deep nets can classify data in large dimensions remains a challenge. It has been proposed that they do so by becoming stable to diffeomorphisms, yet existing empi…
Perspective: A Phase Diagram for Deep Learning unifying Jamming, Feature Learning and Lazy Training
Mario Geiger, Leonardo Petrini, Matthieu Wyart
Deep learning algorithms are responsible for a technological revolution in a variety of tasks including image recognition or Go playing. Yet, why they work is not understood. Ultim…
Geometric compression of invariant manifolds in neural nets
Jonas Paccolat, Leonardo Petrini, Mario Geiger +2
We study how neural networks compress uninformative input space in models where data lie in dimensions, but whose label only vary within a linear manifold of dimension $d_\para…