6 papers
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…
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…
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…
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 patter…
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…