The jamming transition in high dimension: an analytical study of the TAP equations and the e ective thermodynamic potential, Journal of Statistical Mechanics: Theory and Experiment, vol.2016, issue.9, p.93301, 2016. ,
An introduction to random matrices, vol.118, 2010. ,
Higher-order corrections to the e ective potential close to the jamming transition in the perceptron model, Physical Review E, vol.97, issue.1, p.12103, 2018. ,
Equilibrium Fluctuations in Maximally Noisy Extended Quantum Systems, SciPost Phys, vol.6, p.45, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02367770
Optimal errors and phase transitions in high-dimensional generalized linear models, Proceedings of the National Academy of Sciences, p.201802705, 2019. ,
Role of the interaction matrix in mean-eld spin glass models, Physical Review E, vol.67, issue.4, p.46112, 2003. ,
Convergent dynamics for solving the tap equations of ising models with arbitrary rotation invariant coupling matrices, 2019. ,
Self-averaging expectation propagation, 2016. ,
Integration with respect to the Haar measure on unitary, orthogonal and symplectic group, Communications in Mathematical Physics, vol.264, issue.3, pp.773-795, 2006. ,
New scaling of Itzykson-Zuber integrals, Annales de l'IHP Probabilités et statistiques, vol.43, pp.139-146, 2007. ,
S-amp: Approximate message passing for general matrix ensembles, IEEE Information Theory Workshop (ITW 2014), pp.192-196, 2014. ,
Stability of the sherrington-kirkpatrick solution of a spin glass model, Journal of Physics A: Mathematical and General, vol.11, issue.5, p.983, 1978. ,
Message-passing algorithms for compressed sensing, Proceedings of the National Academy of Sciences, vol.106, issue.45, pp.18914-18919, 2009. ,
Compressed sensing, IEEE Transactions on information theory, vol.52, issue.4, pp.1289-1306, 2006. ,
Phase retrieval algorithms: a comparison, Applied optics, vol.21, issue.15, pp.2758-2769, 1982. ,
A Fourier view on the R-transform and related asymptotics of spherical integrals, Journal of functional analysis, vol.222, issue.2, pp.435-490, 2005. ,
How to expand around mean-eld theory using hightemperature expansions, Journal of Physics A: Mathematical and General, vol.24, issue.9, p.2173, 1991. ,
Di erential operators on a semisimple lie algebra, American Journal of Mathematics, pp.87-120, 1957. ,
Adaptive Thouless-Anderson-Palmer approach to inverse Ising problems with quenched random elds, Physical Review E, vol.87, issue.6, p.62129, 2013. ,
Neural networks and physical systems with emergent collective computational abilities, Proceedings of the national academy of sciences, vol.79, pp.2554-2558, 1982. ,
The planar approximation. II, Journal of Mathematical Physics, vol.21, issue.3, pp.411-421, 1980. ,
Resummed mean-eld inference for strongly coupled data, Physical Review E, vol.94, issue.4, p.42118, 2016. ,
Inference from correlated patterns: a uni ed theory for perceptron learning and linear vector channels, Journal of Physics: Conference Series, vol.95, p.12001, 2008. ,
An integral formula for large random rectangular matrices and its application to analysis of linear vector channels, 6th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks and Workshops, pp.620-624, 2008. ,
Probabilistic reconstruction in compressed sensing: algorithms, phase diagrams, and threshold achieving matrices, Journal of Statistical Mechanics: Theory and Experiment, vol.2012, issue.08, p.8009, 2012. ,
Variational free energies for compressed sensing, 2014 IEEE International Symposium on Information Theory, pp.1499-1503, 2014. ,
Spherical model of a spin-glass, Physical Review Letters, vol.36, issue.20, p.1217, 1976. ,
Deep learning. nature, vol.521, p.436, 2015. ,
Generalized linear models. Routledge, 2018. ,
Random matrices, vol.142, 2004. ,
Mean-eld message-passing equations in the Hop eld model and its generalizations, Physical Review E, vol.95, issue.2, p.22117, 2017. ,
Expectation propagation for approximate Bayesian inference, Proceedings of the Seventeenth conference on Uncertainty in arti cial intelligence, pp.362-369, 2001. ,
Information, physics, and computation, 2009. ,
Distribution of eigenvalues for some sets of random matrices, Matematicheskii Sbornik, vol.114, issue.4, pp.507-536, 1967. ,
, Orthogonal amp. IEEE Access, vol.5, pp.2020-2033, 2017.
Replica eld theory for deterministic models: I. binary sequences with low autocorrelation, Journal of Physics A: Mathematical and General, vol.27, issue.23, p.7615, 1994. ,
Replica eld theory for deterministic models. II. a non-random spin glass with glassy behaviour, Journal of Physics A: Mathematical and General, vol.27, issue.23, p.7647, 1994. ,
Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications, World Scienti c Publishing Company, vol.9, 1987. ,
Mean-eld theory for a spin-glass model of neural networks: TAP free energy and the paramagnetic to spin-glass transition, Journal of Physics A: Mathematical and General, vol.30, issue.23, p.8085, 1997. ,
Generalized linear models, Journal of the Royal Statistical Society: Series A (General), vol.135, issue.3, pp.370-384, 1972. ,
A theory of solving TAP equations for Ising models with general invariant random matrices, Journal of Physics A: Mathematical and Theoretical, vol.49, issue.11, p.114002, 2016. ,
Advanced mean eld methods: Theory and practice, 2001. ,
Adaptive and self-averaging Thouless-Anderson-Palmer meaneld theory for probabilistic modeling, Physical Review E, vol.64, issue.5, p.56131, 2001. ,
Tractable approximations for probabilistic models: The adaptive Thouless-Anderson-Palmer mean eld approach, Physical Review Letters, vol.86, issue.17, p.3695, 2001. ,
Expectation consistent approximate inference, Journal of Machine Learning Research, vol.6, pp.2177-2204, 2005. ,
Expectation consistent free energies for approximate inference, Advances in Neural Information Processing Systems, pp.1001-1008, 2005. ,
Convergence condition of the TAP equation for the in nite-ranged Ising spin glass model, Journal of Physics A: Mathematical and general, vol.15, issue.6, p.1971, 1982. ,
Mean-eld equations for spin models with orthogonal interaction matrices, Journal of Physics A: Mathematical and General, vol.28, issue.18, p.5267, 1995. ,
Generalized approximate message passing for estimation with random linear mixing, 2011 IEEE International Symposium on Information Theory Proceedings, pp.2168-2172, 2011. ,
Vector approximate message passing, 2017 IEEE International Symposium on Information Theory (ISIT), pp.1588-1592, 2017. ,
Perceptron capacity revisited: classi cation ability for correlated patterns, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.32, p.324013, 2008. ,
Vector approximate message passing for the generalized linear model, 50th Asilomar Conference on Signals, Systems and Computers, pp.1525-1529, 2016. ,
Solution of'solvable model of a spin glass, Philosophical Magazine, vol.35, issue.3, pp.593-601, 1977. ,
Deterministic and generalized framework for unsupervised learning with restricted boltzmann machines, Physical Review X, vol.8, issue.4, p.41006, 2018. ,
Random matrix theory and wireless communications. Foundations and Trends® in Communications and Information Theory, vol.1, pp.1-182, 2004. ,
Graphical models, exponential families, and variational inference. Foundations and Trends® in Machine Learning, vol.1, pp.1-305, 2008. ,
Understanding belief propagation and its generalizations, vol.8, pp.236-239, 2003. ,
Statistical physics of inference: Thresholds and algorithms, Advances in Physics, vol.65, issue.5, pp.453-552, 2016. ,