6 papers
Dynamical Learning in Deep Asymmetric Recurrent Neural Networks
Davide Badalotti, Carlo Baldassi, Marc Mézard +2
We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to th…
Overlap Gap and Computational Thresholds in the Square Wave Perceptron
Marco Benedetti, Andrej Bogdanov, Enrico M. Malatesta +5
Square Wave Perceptrons (SWPs) form a class of neural network models with oscillating activation function that exhibit intriguing ``hardness'' properties in the high-dimensional li…
Are Neural Networks Collision Resistant?
Marco Benedetti, Andrej Bogdanov, Enrico M. Malatesta +5
When neural networks are trained to classify a dataset, one finds a set of weights from which the network produces a label for each data point. We study the algorithmic complexity…
Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training
Tony Bonnaire, Raphaël Urfin, Giulio Biroli +1
Diffusion models have achieved remarkable success across a wide range of generative tasks. A key challenge is understanding the mechanisms that prevent their memorization of traini…
Memorization and Generalization in Generative Diffusion under the Manifold Hypothesis
Beatrice Achilli, Luca Ambrogioni, Carlo Lucibello +2
We study the memorization and generalization capabilities of Diffusion Models (DMs) when data lies on a structured latent manifold. Specifically, we consider a set of data poin…
The Capacity of Modern Hopfield Networks under the Data Manifold Hypothesis
Beatrice Achilli, Luca Ambrogioni, Carlo Lucibello +2
We generalize the computation of the capacity of exponential Hopfield model from Lucibello and Mézard (2024) to more generic pattern ensembles, including binary patterns and patte…