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06/07/2023
Bayesian Extensive-Rank Matrix Factorization with Rotational Invariant Priors
We consider a statistical model for matrix factorization in a regime whe...
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06/02/2023
Matrix Inference in Growing Rank Regimes
The inference of a large symmetric signal-matrix 𝐒∈ℝ^N× N corrupted by a...
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04/24/2023
Rectangular Rotational Invariant Estimator for General Additive Noise Matrices
We propose a rectangular rotational invariant estimator to recover a rea...
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03/16/2023
Gradient flow on extensive-rank positive semi-definite matrix denoising
In this work, we present a new approach to analyze the gradient flow for...
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12/13/2022
Gradient flow in the gaussian covariate model: exact solution of learning curves and multiple descent structures
A recent line of work has shown remarkable behaviors of the generalizati...
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10/22/2021
Model, sample, and epoch-wise descents: exact solution of gradient flow in the random feature model
Recent evidence has shown the existence of a so-called double-descent an...
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09/14/2021
Statistical limits of dictionary learning: random matrix theory and the spectral replica method
We consider increasingly complex models of matrix denoising and dictiona...
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07/19/2021
Mismatched Estimation of rank-one symmetric matrices under Gaussian noise
We consider the estimation of an n-dimensional vector s from the noisy e...
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05/25/2021
Rank-one matrix estimation: analytic time evolution of gradient descent dynamics
We consider a rank-one symmetric matrix corrupted by additive noise. The...
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12/09/2020
Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes
Non-linear partial differential Kolmogorov equations are successfully us...
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06/26/2020
Tensor estimation with structured priors
We consider rank-one symmetric tensor estimation when the tensor is corr...
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06/19/2020
Information theoretic limits of learning a sparse rule
We consider generalized linear models in regimes where the number of non...
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06/14/2020
All-or-nothing statistical and computational phase transitions in sparse spiked matrix estimation
We determine statistical and computational limits for estimation of a ra...
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04/15/2020
High-dimensional rank-one nonsymmetric matrix decomposition: the spherical case
We consider the problem of estimating a rank-one nonsymmetric matrix und...
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12/12/2019
Bell Diagonal and Werner state generation: entanglement, non-locality, steering and discord on the IBM quantum computer
We shortly review Bell-diagonal and Werner states of two quantum bits an...
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11/12/2019
0-1 phase transitions in sparse spiked matrix estimation
We consider statistical models of estimation of a rank-one matrix (the s...
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04/09/2019
Mutual Information for Low-Rank Even-Order Symmetric Tensor Factorization
We consider a statistical model for finite-rank symmetric tensor factori...
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02/19/2019
Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method
We rigorously derive a single-letter variational expression for the mutu...
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01/19/2019
The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models
In this contribution we give a pedagogic introduction to the newly intro...
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12/06/2018
Rank-one matrix estimation: analysis of algorithmic and information theoretic limits by the spatial coupling method
Factorizing low-rank matrices is a problem with many applications in mac...
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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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06/13/2018
Adaptive Path Interpolation for Sparse Systems: Application to a Simple Censored Block Model
A new adaptive path interpolation method has been recently developed as ...
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05/24/2018
Entropy and mutual information in models of deep neural networks
We examine a class of deep learning models with a tractable method to co...
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02/25/2018
The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices
There has been definite progress recently in proving the variational sin...
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08/10/2017