path: root/topology.bib

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 title = {Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2019},
 month = {January},
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 url = {http://dx.doi.org/10.1103/PhysRevE.99.010401},
 doi = {10.1103/physreve.99.010401},
 issn = {2470-0053}
}

@article{Annesi_2023_Star-shaped,
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 title = {Star-Shaped Space of Solutions of the Spherical Negative Perceptron},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2023},
 month = {11},
 number = {22},
 volume = {131},
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 issn = {1079-7114}
}

@article{Annibale_2003_Supersymmetric,
 author = {Annibale, Alessia and Cavagna, Andrea and Giardina, Irene and Parisi, Giorgio},
 title = {Supersymmetric complexity in the {Sherrington}-{Kirkpatrick} model},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
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}

@article{Annibale_2003_The,
 author = {Annibale, Alessia and Cavagna, Andrea and Giardina, Irene and Parisi, Giorgio and Trevigne, Elisa},
 title = {The role of the {Becchi--Rouet--Stora--Tyutin} supersymmetry in the calculation of the complexity for the {Sherrington--Kirkpatrick} model},
 journal = {Journal of Physics A: Mathematical and General},
 publisher = {IOP Publishing},
 year = {2003},
 month = {10},
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 doi = {10.1088/0305-4470/36/43/018}
}

@article{Annibale_2004_Coexistence,
 author = {Annibale, Alessia and Gualdi, Giulia and Cavagna, Andrea},
 title = {Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses},
 journal = {Journal of Physics A: Mathematical and General},
 publisher = {IOP Publishing},
 year = {2004},
 month = {11},
 number = {47},
 volume = {37},
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 url = {https://doi.org/10.1088%2F0305-4470%2F37%2F47%2F001},
 doi = {10.1088/0305-4470/37/47/001}
}

@book{Audin_2014_Morse,
 author = {Audin, Michèle and Damian, Mihai},
 title = {{Morse} theory and {Floer} homology},
 publisher = {Springer},
 year = {2014},
 address = {London},
 isbn = {9781447154952},
 series = {Universitext},
 translator = {Erné, Reinie}
}

@unpublished{Auffinger_2022_The,
 author = {Auffinger, Antonio and Zhou, Yuxin},
 title = {The Spherical $p+s$ Spin Glass At Zero Temperature},
 year = {2022},
 month = {9},
 url = {http://arxiv.org/abs/2209.03866},
 note = {arXiv preprint},
 date = {2022-09-08T15:08:26Z},
 eprint = {2209.03866},
 eprintclass = {math.PR},
 eprinttype = {arxiv}
}

@article{Baldassi_2016_Unreasonable,
 author = {Baldassi, Carlo and Borgs, Christian and Chayes, Jennifer T. and Ingrosso, Alessandro and Lucibello, Carlo and Saglietti, Luca and Zecchina, Riccardo},
 title = {Unreasonable effectiveness of learning neural networks: From accessible states and robust ensembles to basic algorithmic schemes},
 journal = {Proceedings of the National Academy of Sciences},
 publisher = {Proceedings of the National Academy of Sciences},
 year = {2016},
 month = {11},
 number = {48},
 volume = {113},
 pages = {E7655--E7662},
 url = {http://dx.doi.org/10.1073/pnas.1608103113},
 doi = {10.1073/pnas.1608103113},
 issn = {1091-6490}
}

@article{Baldassi_2019_Properties,
 author = {Baldassi, Carlo and Malatesta, Enrico M. and Zecchina, Riccardo},
 title = {Properties of the Geometry of Solutions and Capacity of Multilayer Neural Networks with Rectified Linear Unit Activations},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2019},
 month = {10},
 number = {17},
 volume = {123},
 pages = {170602},
 url = {https://doi.org/10.1103%2Fphysrevlett.123.170602},
 doi = {10.1103/physrevlett.123.170602}
}

@article{Baldassi_2023_Typical,
 author = {Baldassi, Carlo and Malatesta, Enrico M. and Perugini, Gabriele and Zecchina, Riccardo},
 title = {Typical and atypical solutions in nonconvex neural networks with discrete and continuous weights},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2023},
 month = {August},
 number = {2},
 volume = {108},
 pages = {024310},
 url = {http://dx.doi.org/10.1103/PhysRevE.108.024310},
 doi = {10.1103/physreve.108.024310},
 issn = {2470-0053}
}

@article{BenArous_2019_Geometry,
 author = {Ben Arous, Gérard and Subag, Eliran and Zeitouni, Ofer},
 title = {Geometry and Temperature Chaos in Mixed Spherical Spin Glasses at Low Temperature: The Perturbative Regime},
 journal = {Communications on Pure and Applied Mathematics},
 publisher = {Wiley},
 year = {2019},
 month = {11},
 number = {8},
 volume = {73},
 pages = {1732--1828},
 url = {https://doi.org/10.1002%2Fcpa.21875},
 doi = {10.1002/cpa.21875}
}

@unpublished{Beneventano_2023_On,
 author = {Beneventano, Pierfrancesco},
 title = {On the Trajectories of {SGD} Without Replacement},
 year = {2023},
 month = {dec},
 url = {http://arxiv.org/abs/2312.16143},
 note = {arXiv preprint},
 archiveprefix = {arXiv},
 eprint = {2312.16143},
 eprintclass = {cs.LG},
 eprinttype = {arxiv}
}

@article{Bray_1980_Metastable,
 author = {Bray, A J and Moore, M A},
 title = {Metastable states in spin glasses},
 journal = {Journal of Physics C: Solid State Physics},
 publisher = {IOP Publishing},
 year = {1980},
 month = {7},
 number = {19},
 volume = {13},
 pages = {L469--L476},
 url = {https://doi.org/10.1088%2F0022-3719%2F13%2F19%2F002},
 doi = {10.1088/0022-3719/13/19/002}
}

@article{Castellani_2005_Spin-glass,
 author = {Castellani, Tommaso and Cavagna, Andrea},
 title = {Spin-glass theory for pedestrians},
 journal = {Journal of Statistical Mechanics: Theory and Experiment},
 publisher = {IOP Publishing},
 year = {2005},
 month = {5},
 number = {05},
 volume = {2005},
 pages = {P05012},
 url = {https://doi.org/10.1088%2F1742-5468%2F2005%2F05%2Fp05012},
 doi = {10.1088/1742-5468/2005/05/p05012}
}

@article{Crisanti_1992_The,
 author = {Crisanti, A. and Sommers, H.-J.},
 title = {The spherical $p$-spin interaction spin glass model: the statics},
 journal = {Zeitschrift für Physik B Condensed Matter},
 publisher = {Springer Science and Business Media LLC},
 year = {1992},
 month = {10},
 number = {3},
 volume = {87},
 pages = {341--354},
 url = {https://doi.org/10.1007%2Fbf01309287},
 doi = {10.1007/bf01309287}
}

@article{Crisanti_1995_Thouless-Anderson-Palmer,
 author = {Crisanti, A. and Sommers, H.-J.},
 title = {{Thouless-Anderson-Palmer} Approach to the Spherical $p$-Spin Spin Glass Model},
 journal = {Journal de Physique I},
 publisher = {EDP Sciences},
 year = {1995},
 month = {7},
 number = {7},
 volume = {5},
 pages = {805--813},
 url = {https://doi.org/10.1051/jp1:1995164},
 doi = {10.1051/jp1:1995164}
}

@article{Crisanti_2004_Spherical,
 author = {Crisanti, A. and Leuzzi, L.},
 title = {Spherical $2+p$ Spin-Glass Model: An Exactly Solvable Model for Glass to Spin-Glass Transition},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2004},
 month = {11},
 number = {21},
 volume = {93},
 pages = {217203},
 url = {https://doi.org/10.1103%2Fphysrevlett.93.217203},
 doi = {10.1103/physrevlett.93.217203}
}

@article{Crisanti_2006_Spherical,
 author = {Crisanti, A. and Leuzzi, L.},
 title = {Spherical $2+p$ spin-glass model: An analytically solvable model with a glass-to-glass transition},
 journal = {Physical Review B},
 publisher = {American Physical Society (APS)},
 year = {2006},
 month = {1},
 number = {1},
 volume = {73},
 pages = {014412},
 url = {https://doi.org/10.1103%2Fphysrevb.73.014412},
 doi = {10.1103/physrevb.73.014412}
}

@book{DeWitt_1992_Supermanifolds,
 author = {DeWitt, Bryce S.},
 title = {Supermanifolds},
 publisher = {Cambridge University Press},
 year = {1992},
 address = {Cambridge ; New York},
 edition = {2nd ed},
 isbn = {9780521413206 9780521423779},
 keyword = {Supermanifolds (Mathematics), Mathematical physics},
 series = {Cambridge monographs on mathematical physics}
}

@article{Erba_2024_Quenches,
 author = {Erba, Vittorio and Behrens, Freya and Krzakala, Florent and Zdeborová, Lenka},
 title = {Quenches in the {Sherrington–Kirkpatrick} model},
 journal = {Journal of Statistical Mechanics: Theory and Experiment},
 publisher = {IOP Publishing},
 year = {2024},
 month = {August},
 number = {8},
 volume = {2024},
 pages = {083302},
 url = {http://dx.doi.org/10.1088/1742-5468/ad685a},
 doi = {10.1088/1742-5468/ad685a},
 issn = {1742-5468}
}

@article{Folena_2020_Rethinking,
 author = {Folena, Giampaolo and Franz, Silvio and Ricci-Tersenghi, Federico},
 title = {Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed $p$-Spin Model},
 journal = {Physical Review X},
 publisher = {American Physical Society},
 year = {2020},
 month = {8},
 volume = {10},
 pages = {031045},
 url = {https://link.aps.org/doi/10.1103/PhysRevX.10.031045},
 doi = {10.1103/PhysRevX.10.031045},
 issue = {3},
 numpages = {26}
}

@article{Folena_2021_Gradient,
 author = {Folena, Giampaolo and Franz, Silvio and Ricci-Tersenghi, Federico},
 title = {Gradient descent dynamics in the mixed $p$-spin spherical model: finite-size simulations and comparison with mean-field integration},
 journal = {Journal of Statistical Mechanics: Theory and Experiment},
 publisher = {IOP Publishing},
 year = {2021},
 month = {3},
 number = {3},
 volume = {2021},
 pages = {033302},
 url = {https://doi.org/10.1088%2F1742-5468%2Fabe29f},
 doi = {10.1088/1742-5468/abe29f}
}

@article{Folena_2023_On,
 author = {Folena, Giampaolo and Zamponi, Francesco},
 title = {On weak ergodicity breaking in mean-field spin glasses},
 journal = {SciPost Physics},
 publisher = {Stichting SciPost},
 year = {2023},
 month = {9},
 number = {3},
 volume = {15},
 pages = {109},
 url = {https://doi.org/10.21468%2Fscipostphys.15.3.109},
 doi = {10.21468/scipostphys.15.3.109}
}

@article{Franz_2016_The,
 author = {Franz, Silvio and Parisi, Giorgio},
 title = {The simplest model of jamming},
 journal = {Journal of Physics A: Mathematical and Theoretical},
 publisher = {IOP Publishing},
 year = {2016},
 month = {February},
 number = {14},
 volume = {49},
 pages = {145001},
 url = {http://dx.doi.org/10.1088/1751-8113/49/14/145001},
 doi = {10.1088/1751-8113/49/14/145001},
 issn = {1751-8121}
}

@article{Franz_2017_Universality,
 author = {Franz, Silvio and Parisi, Giorgio and Sevelev, Maxime and Urbani, Pierfrancesco and Zamponi, Francesco},
 title = {Universality of the {SAT-UNSAT} (jamming) threshold in non-convex continuous constraint satisfaction problems},
 journal = {SciPost Physics},
 publisher = {Stichting SciPost},
 year = {2017},
 month = {June},
 number = {3},
 volume = {2},
 pages = {019},
 url = {http://dx.doi.org/10.21468/SciPostPhys.2.3.019},
 doi = {10.21468/scipostphys.2.3.019},
 issn = {2542-4653}
}

@article{Franz_2019_Critical,
 author = {Franz, Silvio and Sclocchi, Antonio and Urbani, Pierfrancesco},
 title = {Critical Jammed Phase of the Linear Perceptron},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2019},
 month = {September},
 number = {11},
 volume = {123},
 pages = {115702},
 url = {http://dx.doi.org/10.1103/PhysRevLett.123.115702},
 doi = {10.1103/physrevlett.123.115702},
 issn = {1079-7114}
}

@article{Fyodorov_2004_Complexity,
 author = {Fyodorov, Yan V.},
 title = {Complexity of Random Energy Landscapes, Glass Transition, and Absolute Value of the Spectral Determinant of Random Matrices},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2004},
 month = {6},
 number = {24},
 volume = {92},
 pages = {240601},
 url = {https://doi.org/10.1103%2Fphysrevlett.92.240601},
 doi = {10.1103/physrevlett.92.240601}
}

@article{Fyodorov_2019_A,
 author = {Fyodorov, Yan V.},
 title = {A Spin Glass Model for Reconstructing Nonlinearly Encrypted Signals Corrupted by Noise},
 journal = {Journal of Statistical Physics},
 publisher = {Springer Science and Business Media LLC},
 year = {2019},
 month = {1},
 number = {5},
 volume = {175},
 pages = {789--818},
 url = {https://doi.org/10.1007%2Fs10955-018-02217-9},
 doi = {10.1007/s10955-018-02217-9}
}

@article{Fyodorov_2020_Counting,
 author = {Fyodorov, Y. V. and Tublin, R.},
 title = {Counting Stationary Points of the Loss Function in the Simplest Constrained Least-square Optimization},
 journal = {Acta Physica Polonica B},
 publisher = {Jagiellonian University},
 year = {2020},
 number = {7},
 volume = {51},
 pages = {1663},
 url = {http://dx.doi.org/10.5506/APhysPolB.51.1663},
 doi = {10.5506/aphyspolb.51.1663},
 issn = {1509-5770}
}

@article{Fyodorov_2022_Optimization,
 author = {Fyodorov, Yan V and Tublin, Rashel},
 title = {Optimization landscape in the simplest constrained random least-square problem},
 journal = {Journal of Physics A: Mathematical and Theoretical},
 publisher = {IOP Publishing},
 year = {2022},
 month = {May},
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 volume = {55},
 pages = {244008},
 url = {http://dx.doi.org/10.1088/1751-8121/ac6d8e},
 doi = {10.1088/1751-8121/ac6d8e},
 issn = {1751-8121}
}

@book{Hatcher_2002_Algebraic,
 author = {Hatcher, Allen},
 title = {Algebraic topology},
 publisher = {Cambridge University Press},
 year = {2002},
 address = {Cambridge},
 isbn = {9780521791601},
 keyword = {Algebraic topology}
}

@article{Kac_1943_On,
 author = {Kac, M.},
 title = {On the average number of real roots of a random algebraic equation},
 journal = {Bulletin of the American Mathematical Society},
 publisher = {American Mathematical Society},
 year = {1943},
 month = {4},
 number = {4},
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 pages = {314--320},
 url = {https://projecteuclid.org:443/euclid.bams/1183505112}
}

@article{Kamali_2023_Dynamical,
 author = {Kamali, Persia Jana and Urbani, Pierfrancesco},
 title = {Dynamical mean field theory for models of confluent tissues and beyond},
 journal = {SciPost Physics},
 publisher = {Stichting SciPost},
 year = {2023},
 month = {November},
 number = {5},
 volume = {15},
 pages = {219},
 url = {http://dx.doi.org/10.21468/SciPostPhys.15.5.219},
 doi = {10.21468/scipostphys.15.5.219},
 issn = {2542-4653}
}

@unpublished{Kamali_2023_Stochastic,
 author = {Kamali, Persia Jana and Urbani, Pierfrancesco},
 title = {Stochastic Gradient Descent outperforms Gradient Descent in recovering a high-dimensional signal in a glassy energy landscape},
 year = {2023},
 month = {sep},
 url = {http://arxiv.org/abs/2309.04788},
 note = {arXiv preprint},
 archiveprefix = {arXiv},
 eprint = {2309.04788},
 eprintclass = {cs.LG},
 eprinttype = {arxiv}
}

@article{Kent-Dobias_2023_How,
 author = {Kent-Dobias, Jaron and Kurchan, Jorge},
 title = {How to count in hierarchical landscapes: a full solution to mean-field complexity},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2023},
 month = {6},
 number = {6},
 volume = {107},
 pages = {064111},
 url = {https://doi.org/10.1103/PhysRevE.107.064111},
 doi = {10.1103/PhysRevE.107.064111}
}

@article{Kent-Dobias_2023_When,
 author = {Kent-Dobias, Jaron},
 title = {When is the average number of saddle points typical?},
 journal = {Europhysics Letters},
 publisher = {IOP Publishing},
 year = {2023},
 month = {8},
 number = {6},
 volume = {143},
 pages = {61003},
 url = {https://doi.org/10.1209%2F0295-5075%2Facf521},
 doi = {10.1209/0295-5075/acf521}
}

@unpublished{Kent-Dobias_2024_Algorithm-independent,
 author = {Kent-Dobias, Jaron},
 title = {Algorithm-independent bounds on complex optimization through the statistics of marginal optima},
 year = {2024},
 url = {https://arxiv.org/abs/2407.02092},
 note = {arXiv preprint},
 archiveprefix = {arXiv},
 eprint = {2407.02092},
 primaryclass = {cond-mat.dis-nn}
}

@article{Kent-Dobias_2024_Arrangement,
 author = {Kent-Dobias, Jaron},
 title = {Arrangement of nearby minima and saddles in the mixed spherical energy landscapes},
 journal = {SciPost Physics},
 publisher = {Stichting SciPost},
 year = {2024},
 month = {1},
 number = {1},
 volume = {16},
 pages = {001},
 url = {http://dx.doi.org/10.21468/SciPostPhys.16.1.001},
 doi = {10.21468/scipostphys.16.1.001},
 issn = {2542-4653}
}

@article{Kent-Dobias_2024_Conditioning,
 author = {Kent-Dobias, Jaron},
 title = {Conditioning the complexity of random landscapes on marginal optima},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2024},
 month = {December},
 number = {6},
 volume = {110},
 pages = {064148},
 url = {http://dx.doi.org/10.1103/PhysRevE.110.064148},
 doi = {10.1103/physreve.110.064148},
 issn = {2470-0053}
}

@article{Mezard_2009_Constraint,
 author = {Mézard, Marc and Mora, Thierry},
 title = {Constraint satisfaction problems and neural networks: A statistical physics perspective},
 journal = {Journal of Physiology-Paris},
 publisher = {Elsevier BV},
 year = {2009},
 month = {January},
 number = {1–2},
 volume = {103},
 pages = {107--113},
 url = {http://dx.doi.org/10.1016/j.jphysparis.2009.05.013},
 doi = {10.1016/j.jphysparis.2009.05.013},
 issn = {0928-4257}
}

@unpublished{Montanari_2023_Solving,
 author = {Montanari, Andrea and Subag, Eliran},
 title = {Solving overparametrized systems of random equations: I. Model and algorithms for approximate solutions},
 year = {2023},
 month = {jun},
 url = {http://arxiv.org/abs/2306.13326},
 note = {arXiv preprint},
 archiveprefix = {arXiv},
 eprint = {2306.13326},
 eprintclass = {math.PR},
 eprinttype = {arxiv}
}

@unpublished{Montanari_2024_On,
 author = {Montanari, Andrea and Subag, Eliran},
 title = {On {Smale}'s 17th problem over the reals},
 year = {2024},
 month = {may},
 url = {http://arxiv.org/abs/2405.01735},
 note = {arXiv preprint},
 archiveprefix = {arXiv},
 eprint = {2405.01735},
 eprintclass = {cs.DS},
 eprinttype = {arxiv}
}

@article{Muller_2006_Marginal,
 author = {Müller, Markus and Leuzzi, Luca and Crisanti, Andrea},
 title = {Marginal states in mean-field glasses},
 journal = {Physical Review B},
 publisher = {American Physical Society (APS)},
 year = {2006},
 month = {10},
 number = {13},
 volume = {74},
 pages = {134431},
 url = {https://doi.org/10.1103%2Fphysrevb.74.134431},
 doi = {10.1103/physrevb.74.134431}
}

@article{Rice_1939_The,
 author = {Rice, S. O.},
 title = {The Distribution of the Maxima of a Random Curve},
 journal = {American Journal of Mathematics},
 publisher = {JSTOR},
 year = {1939},
 month = {4},
 number = {2},
 volume = {61},
 pages = {409},
 url = {https://doi.org/10.2307%2F2371510},
 doi = {10.2307/2371510}
}

@phdthesis{Tublin_2022_A,
 author = {Tublin, Rashel},
 title = {A Few Results in Random Matrix Theory and Random Optimization},
 year = {2022},
 month = {September},
 url = {https://kclpure.kcl.ac.uk/portal/en/studentTheses/a-few-results-in-random-matrix-theory-and-random-optimization},
 school = {King's College London}
}

@article{Urbani_2023_A,
 author = {Urbani, Pierfrancesco},
 title = {A continuous constraint satisfaction problem for the rigidity transition in confluent tissues},
 journal = {Journal of Physics A: Mathematical and Theoretical},
 publisher = {IOP Publishing},
 year = {2023},
 month = {February},
 number = {11},
 volume = {56},
 pages = {115003},
 url = {http://dx.doi.org/10.1088/1751-8121/acb742},
 doi = {10.1088/1751-8121/acb742},
 issn = {1751-8121}
}

@article{Urbani_2024_Quantum,
 author = {Urbani, Pierfrancesco},
 title = {Quantum exploration of high-dimensional canyon landscapes},
 journal = {Journal of Statistical Mechanics: Theory and Experiment},
 publisher = {IOP Publishing},
 year = {2024},
 month = {August},
 number = {8},
 volume = {2024},
 pages = {083301},
 url = {http://dx.doi.org/10.1088/1742-5468/ad0635},
 doi = {10.1088/1742-5468/ad0635},
 issn = {1742-5468}
}

@unpublished{Urbani_2024_Statistical,
 author = {Urbani, Pierfrancesco},
 title = {Statistical physics of complex systems: glasses, spin glasses, continuous constraint satisfaction problems, high-dimensional inference and neural networks},
 year = {2024},
 month = {may},
 url = {http://arxiv.org/abs/2405.06384},
 note = {arXiv preprint},
 archiveprefix = {arXiv},
 eprint = {2405.06384},
 eprintclass = {cond-mat.dis-nn},
 eprinttype = {arxiv}
}

@unpublished{Vivo_2024_Random,
 author = {Vivo, Pierpaolo},
 title = {Random Linear Systems with Quadratic Constraints: from Random Matrix Theory to replicas and back},
 year = {2024},
 month = {jan},
 url = {http://arxiv.org/abs/2401.03209},
 note = {arXiv preprint},
 archiveprefix = {arXiv},
 eprint = {2401.03209},
 eprintclass = {cond-mat.stat-mech},
 eprinttype = {arxiv}
}

@inproceedings{SaraoMannelli_2019_Who,
 author = {Sarao Mannelli, Stefano and Biroli, Giulio and Cammarota, Chiara and Krzakala, Florent and Zdeborová, Lenka},
 title = {Who is Afraid of Big Bad Minima? {A}nalysis of gradient-flow in spiked matrix-tensor models},
 publisher = {Curran Associates, Inc.},
 year = {2019},
 volume = {32},
 pages = {},
 url = {https://proceedings.neurips.cc/paper_files/paper/2019/file/fbad540b2f3b5638a9be9aa6a4d8e450-Paper.pdf},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {Wallach, H. and Larochelle, H. and Beygelzimer, A. and d'Alché-Buc, F. and Fox, E. and Garnett, R.}
}

@inproceedings{SaraoMannelli_2019_Passed,
 author = {Sarao Mannelli, Stefano and Krzakala, Florent and Urbani, Pierfrancesco and Zdeborová, Lenka},
 title = {Passed \& Spurious: Descent Algorithms and Local Minima in Spiked Matrix-Tensor Models},
 publisher = {PMLR},
 year = {2019},
 month = {09--15 Jun},
 volume = {97},
 pages = {4333--4342},
 url = {https://proceedings.mlr.press/v97/mannelli19a.html},
 abstract = {In this work we analyse quantitatively the interplay between the loss landscape and performance of descent algorithms in a prototypical inference problem, the spiked matrix-tensor model. We study a loss function that is the negative log-likelihood of the model. We analyse the number of local minima at a fixed distance from the signal/spike with the Kac-Rice formula, and locate trivialization of the landscape at large signal-to-noise ratios. We evaluate analytically the performance of a gradient flow algorithm using integro-differential PDEs as developed in physics of disordered systems for the Langevin dynamics. We analyze the performance of an approximate message passing algorithm estimating the maximum likelihood configuration via its state evolution. We conclude by comparing the above results: while we observe a drastic slow down of the gradient flow dynamics even in the region where the landscape is trivial, both the analyzed algorithms are shown to perform well even in the part of the region of parameters where spurious local minima are present.},
 booktitle = {Proceedings of the 36th International Conference on Machine Learning},
 editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
 pdf = {http://proceedings.mlr.press/v97/mannelli19a/mannelli19a.pdf},
 series = {Proceedings of Machine Learning Research}
}