6 papers
Percolation and clustering in ecological communities: A dynamical theory
Dario Sergo, Cédric Koller, Vittorio Erba +1
Ecological communities with structured interactions exhibit collective phenomena such as percolation and clustering of occupied sites. While these effects have been documented in e…
The Rules-and-Facts Model for Simultaneous Generalization and Memorization in Neural Networks
Gabriele Farné, Fabrizio Boncoraglio, Lenka Zdeborová
A key capability of modern neural networks is their capacity to simultaneously learn underlying rules and memorize specific facts or exceptions. Yet, theoretical understanding of t…
Rigorous Asymptotics for First-Order Algorithms Through the Dynamical Cavity Method
Yatin Dandi, David Gamarnik, Francisco Pernice +1
Dynamical Mean Field Theory (DMFT) provides an asymptotic description of the dynamics of macroscopic observables in certain disordered systems. Originally pioneered in the context…
A solvable high-dimensional model where nonlinear autoencoders learn structure invisible to PCA while test loss misaligns with generalization
Vicente Conde Mendes, Lorenzo Bardone, Cédric Koller +6
Many real-world datasets contain hidden structure that cannot be detected by simple linear correlations between input features. For example, latent factors may influence the data i…
Minority Takeover in Majority Dynamics: Searching for Rare Initializations via the History Passing Algorithm
Marek Jankola, Freya Behrens, Cédric Koller +3
We investigate how much bias in the initial configuration is required to drive global agreement in synchronous, deterministic majority dynamics on large random -regular graphs.…
Spectral Thresholds in Correlated Spiked Models and Fundamental Limits of Partial Least Squares
Pierre Mergny, Lenka Zdeborová
We provide a rigorous random matrix theory analysis of spiked cross-covariance models where the signals across two high-dimensional data channels are partially aligned. These model…