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07/03/2023
Fitting an ellipsoid to a quadratic number of random points
We consider the problem (P) of fitting n standard Gaussian random vector...
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02/27/2023
Injectivity of ReLU networks: perspectives from statistical physics
When can the input of a ReLU neural network be inferred from its output?...
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09/05/2022
On free energy barriers in Gaussian priors and failure of MCMC for high-dimensional unimodal distributions
We exhibit examples of high-dimensional unimodal posterior distributions...
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06/17/2022
A remark on Kashin's discrepancy argument and partial coloring in the Komlós conjecture
In this expository note, we discuss an early partial coloring result of ...
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03/15/2022
Optimal denoising of rotationally invariant rectangular matrices
In this manuscript we consider denoising of large rectangular matrices: ...
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10/17/2021
Perturbative construction of mean-field equations in extensive-rank matrix factorization and denoising
Factorization of matrices where the rank of the two factors diverges lin...
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12/08/2020
Construction of optimal spectral methods in phase retrieval
We consider the phase retrieval problem, in which the observer wishes to...
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08/21/2020
Large Deviations of Extreme Eigenvalues of Generalized Sample Covariance Matrices
Very rare events in which the largest eigenvalue of a random matrix is a...
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06/09/2020
Phase retrieval in high dimensions: Statistical and computational phase transitions
We consider the phase retrieval problem of reconstructing a n-dimensiona...
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12/04/2019
Landscape Complexity for the Empirical Risk of Generalized Linear Models
We present a method to obtain the average and the typical value of the n...
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06/20/2019
High-temperature Expansions and Message Passing Algorithms
Improved mean-field technics are a central theme of statistical physics ...
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05/29/2019
The spiked matrix model with generative priors
Using a low-dimensional parametrization of signals is a generic and powe...
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06/14/2018
The committee machine: Computational to statistical gaps in learning a two-layers neural network
Heuristic tools from statistical physics have been used in the past to l...
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02/25/2018