Fetching the paper…
Reading the bibliography…
Factorization of matrices where the rank of the two factors diverges linearly with their sizes has many applications in diverse areas such as unsupervised representation learning, dictionary learning or sparse coding.
Vereinfachte numerische integration
Werner Romberg · 1955
Earlier work this paper cites.
Differential operators on a semisimple Lie algebra
Harish-Chandra · 1957
Earlier work this paper cites.
Distribution of eigenvalues for some sets of random matrices
Vladimir Alexandrovich Marchenko and Leonid Andreevich Pastur · 1967
Earlier work this paper cites.
Solvable model of a spin-glass
David Sherrington and Scott Kirkpatrick · 1975
Earlier work this paper cites.
Solution of ’solvable model of a spin glass’
David J Thouless, Philip W Anderson, and Robert G Palmer · 1977
Earlier work this paper cites.
The planar approximation. II
Claude Itzykson and J-B Zuber · 1980
Earlier work this paper cites.
Convergence condition of the TAP equation for the infinite-ranged ising spin glass model
Timm Plefka · 1982
Earlier work this paper cites.
Integral equations
Francesco Giacomo Tricomi · 1985
Earlier work this paper cites.
SK model: The replica solution without replicas
M Mézard, G Parisi, and M. A Virasoro · 1986
Earlier work this paper cites.
Addition of certain non-commuting random variables
Dan Voiculescu · 1986
Earlier work this paper cites.
Spin glass theory and beyond: An Introduction to the Replica Method and its Applications
Marc Mézard, Giorgio Parisi, and Miguel Virasoro · 1987
Earlier work this paper cites.
The space of interactions in neural networks: Gardner’s computation with the cavity method
Marc Mézard · 1989
Earlier work this paper cites.
How to expand around mean-field theory using high-temperature expansions
Antoine Georges and Jonathan S Yedidia · 1991
Earlier work this paper cites.
On the large-N limit of the Itzykson-Zuber integral
A Matytsin · 1994
Earlier work this paper cites.
Emergence of simple-cell receptive field properties by learning a sparse code for natural images
Bruno A Olshausen and David J Field · 1996
Earlier work this paper cites.
A blind source separation technique using second-order statistics
Adel Belouchrani, Karim Abed-Meraim, J-F Cardoso, and Eric Moulines · 1997
Earlier work this paper cites.
Sparse coding with an overcomplete basis set: A strategy employed by V1?
Bruno A Olshausen and David J Field · 1997
Earlier work this paper cites.
Expectation propagation for approximate Bayesian inference
Thomas P Minka · 2001
Earlier work this paper cites.
Statistical physics of spin glasses and information processing: an introduction
Hidetoshi Nishimori · 2001
Earlier work this paper cites.
Adaptive and self-averaging Thouless-Anderson-Palmer mean-field theory for probabilistic modeling
Manfred Opper and Ole Winther · 2001
Earlier work this paper cites.
Tractable approximations for probabilistic models: The adaptive Thouless-Anderson-Palmer mean field approach
Manfred Opper and Ole Winther · 2001
Earlier work this paper cites.
Large deviations asymptotics for spherical integrals
Alice Guionnet and Ofer Zeitouni · 2002
Earlier work this paper cites.
Dictionary learning algorithms for sparse representation
Kenneth Kreutz-Delgado, Joseph F Murray, Bhaskar D Rao, Kjersti Engan, Te-Won Lee, and Terrence J Sejnowski · 2003
Earlier work this paper cites.
First order asymptotics of matrix integrals; a rigorous approach towards the understanding of matrix models
Alice Guionnet · 2004
Earlier work this paper cites.
Large deviations and stochastic calculus for large random matrices
Alice Guionnet · 2004
Earlier work this paper cites.
Random matrices
Madan Lal Mehta · 2004
Earlier work this paper cites.
Lecture notes 4 for 247A
Terence Tao · 2004
Cited alongside, same era.
Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
Jinho Baik, Gérard Ben Arous, and Sandrine Péché · 2005
Cited alongside, same era.
Mutual information and minimum mean-square error in Gaussian channels
Dongning Guo, Shlomo Shamai, and Sergio Verdú · 2005
Cited alongside, same era.
Expectation consistent approximate inference
Manfred Opper and Ole Winther · 2005
Cited alongside, same era.
Sparse principal component analysis
Hui Zou, Trevor Hastie, and Robert Tibshirani · 2006
Cited alongside, same era.
Exact matrix completion via convex optimization
Emmanuel J Candès and Benjamin Recht · 2009
Cited alongside, same era.
Rotational invariant estimator for general noisy matrices
Joël Bun, Romain Allez, Jean-Philippe Bouchaud, and Marc Potters · 2016
Later among the works it cites.
Hydrodynamical spectral evolution for random matrices
Peter J Forrester and Jacek Grela · 2016
Later among the works it cites.
Phase transitions and sample complexity in Bayes-optimal matrix factorization
Yoshiyuki Kabashima, Florent Krzakala, Marc Mézard, Ayaka Sakata, and Lenka Zdeborová · 2016
Later among the works it cites.
A theory of solving TAP equations for Ising models with general invariant random matrices
Manfred Opper, Burak Cakmak, and Ole Winther · 2016
Later among the works it cites.
Vector approximate message passing for the generalized linear model
Philip Schniter, Sundeep Rangan, and Alyson K Fletcher · 2016
Later among the works it cites.
Statistical physics of inference: Thresholds and algorithms
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Online dictionary learning for sparse coding
Julien Mairal, Francis Bach, Jean Ponce, and Guillermo Sapiro · 2009
Cited alongside, same era.
Information, physics, and computation
Marc Mézard and Andrea Montanari · 2009
Cited alongside, same era.
An introduction to random matrices
Greg W Anderson, Alice Guionnet, and Ofer Zeitouni · 2010
Cited alongside, same era.
The power of convex relaxation: Near-optimal matrix completion
Emmanuel J Candès and Terence Tao · 2010
Cited alongside, same era.
Rectangular R-transform as the limit of rectangular spherical integrals
Florent Benaych-Georges · 2011
Cited alongside, same era.
The dynamics of message passing on dense graphs, with applications to compressed sensing
Mohsen Bayati and Andrea Montanari · 2011
Cited alongside, same era.
Lenka Zdeborová and Florent Krzakala · 2016
Later among the works it cites.
Cleaning large correlation matrices: tools from random matrix theory
Joël Bun, Jean-Philippe Bouchaud, and Marc Potters · 2017
Later among the works it cites.
Constrained low-rank matrix estimation: Phase transitions, approximate message passing and applications
Thibault Lesieur, Florent Krzakala, and Lenka Zdeborová · 2017
Later among the works it cites.
Statistical and computational phase transitions in spiked tensor estimation
Thibault Lesieur, Léo Miolane, Marc Lelarge, Florent Krzakala, and Lenka Zdeborová · 2017
Later among the works it cites.
The complex Burgers’ equation, the HCIZ integral and the Calogero-Moser system
Govind Menon · 2017
Later among the works it cites.
Nonlinear random matrix theory for deep learning
Jeffrey Pennington and Pratik Worah · 2017
Later among the works it cites.
Vector approximate message passing
Sundeep Rangan, Philip Schniter, and Alyson K Fletcher · 2017
Later among the works it cites.
Optimal shrinkage of eigenvalues in the spiked covariance model
David L Donoho, Matan Gavish, and Iain M Johnstone · 2018
Later among the works it cites.
Estimation in the spiked Wigner model: A short proof of the replica formula
Ahmed El Alaoui and Florent Krzakala · 2018
Later among the works it cites.
A random matrix approach to neural networks
Cosme Louart, Zhenyu Liao, and Romain Couillet · 2018
Later among the works it cites.
Introduction to random matrices: theory and practice
Giacomo Livan, Marcel Novaes, and Pierpaolo Vivo · 2018
Later among the works it cites.
Statistical Physics of Sparse and Dense Models in Optimization and Inference
Hinnerk Christian Schmidt · 2018
Later among the works it cites.
Optimal errors and phase transitions in high-dimensional generalized linear models
Jean Barbier, Florent Krzakala, Nicolas Macris, Léo Miolane, and Lenka Zdeborová · 2019
Later among the works it cites.
High-temperature expansions and message-passing algorithms
Antoine Maillard, Laura Foini, Alejandro Lage Castellanos, Florent Krzakala, Marc Mézard, and Lenka Zdeborová · 2019
Later among the works it cites.
Statistical limits of dictionary learning: random matrix theory and the spectral replica method
Jean Barbier and Nicolas Macris · 2021
Closest in time.
Graph-based approximate message passing iterations
Cédric Gerbelot and Raphaël Berthier · 2021
Closest in time.
Large Deviations Asymptotics of Rectangular Spherical Integral
Alice Guionnet and Jiaoyang Huang · 2021
Closest in time.
Deep learning via message passing algorithms based on belief propagation
Carlo Lucibello, Fabrizio Pittorino, Gabriele Perugini, and Riccardo Zecchina · 2021
Closest in time.
Multi-layer bilinear generalized approximate message passing
Qiuyun Zou, Haochuan Zhang, and Hongwen Yang · 2021
Closest in time.
Numerical code used to produce the figures
Antoine Maillard, Florent Krzakala, Marc Mézard, and Lenka Zdeborová · 2022
Closest in time.