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|
@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},
pages = {11311--11320},
url = {https://doi.org/10.1088%2F0305-4470%2F37%2F47%2F001},
doi = {10.1088/0305-4470/37/47/001}
}
@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}
}
@article{Biroli_1999_Dynamical,
author = {Biroli, Giulio},
title = {Dynamical {TAP} approach to mean field glassy systems},
journal = {Journal of Physics A: Mathematical and General},
publisher = {IOP Publishing},
year = {1999},
month = {11},
number = {48},
volume = {32},
pages = {8365--8388},
url = {https://doi.org/10.1088%2F0305-4470%2F32%2F48%2F301},
doi = {10.1088/0305-4470/32/48/301}
}
@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{Bray_2007_Statistics,
author = {Bray, Alan J. and Dean, David S.},
title = {Statistics of Critical Points of {Gaussian} Fields on Large-Dimensional Spaces},
journal = {Physical Review Letters},
publisher = {American Physical Society (APS)},
year = {2007},
month = {4},
number = {15},
volume = {98},
pages = {150201},
url = {https://doi.org/10.1103%2Fphysrevlett.98.150201},
doi = {10.1103/physrevlett.98.150201}
}
@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{Cavagna_1998_Stationary,
author = {Cavagna, Andrea and Giardina, Irene and Parisi, Giorgio},
title = {Stationary points of the {Thouless}-{Anderson}-{Palmer} free energy},
journal = {Physical Review B},
publisher = {American Physical Society (APS)},
year = {1998},
month = {5},
number = {18},
volume = {57},
pages = {11251--11257},
url = {https://doi.org/10.1103%2Fphysrevb.57.11251},
doi = {10.1103/physrevb.57.11251}
}
@article{Cavagna_2001_Fragile,
author = {Cavagna, A},
title = {Fragile vs.\ strong liquids: A saddles-ruled scenario},
journal = {Europhysics Letters (EPL)},
publisher = {IOP Publishing},
year = {2001},
month = {2},
number = {4},
volume = {53},
pages = {490--496},
url = {https://doi.org/10.1209%2Fepl%2Fi2001-00179-4},
doi = {10.1209/epl/i2001-00179-4}
}
@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_1993_The,
author = {Crisanti, A. and Horner, H. and Sommers, H.-J.},
title = {The spherical $p$-spin interaction spin-glass model},
journal = {Zeitschrift für Physik B Condensed Matter},
publisher = {Springer Science and Business Media LLC},
year = {1993},
month = {6},
number = {2},
volume = {92},
pages = {257--271},
url = {https://doi.org/10.1007%2Fbf01312184},
doi = {10.1007/bf01312184}
}
@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{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{Franz_1995_Recipes,
author = {Franz, Silvio and Parisi, Giorgio},
title = {Recipes for Metastable States in Spin Glasses},
journal = {Journal de Physique I},
publisher = {EDP Sciences},
year = {1995},
month = {11},
number = {11},
volume = {5},
pages = {1401--1415},
url = {https://doi.org/10.1051%2Fjp1%3A1995201},
doi = {10.1051/jp1:1995201}
}
@article{Franz_1998_EffectivePotential,
author = {Franz, Silvio and Parisi, Giorgio},
title = {Effective potential in glassy systems: theory and simulations},
journal = {Physica A: Statistical Mechanics and its Applications},
publisher = {Elsevier BV},
year = {1998},
month = {12},
number = {3-4},
volume = {261},
pages = {317--339},
url = {https://doi.org/10.1016%2Fs0378-4371%2898%2900315-x},
doi = {10.1016/s0378-4371(98)00315-x}
}
@article{Fyodorov_2007_Density,
author = {Fyodorov, Y. V. and Sommers, H.-J. and Williams, I.},
title = {Density of stationary points in a high dimensional random energy landscape and the onset of glassy behavior},
journal = {JETP Letters},
publisher = {Pleiades Publishing Ltd},
year = {2007},
month = {5},
number = {5},
volume = {85},
pages = {261--266},
url = {https://doi.org/10.1134%2Fs0021364007050098},
doi = {10.1134/s0021364007050098}
}
@article{Ikeda_2023_Bose-Einstein-like,
author = {Ikeda, Harukuni},
title = {Bose--Einstein-like condensation of deformed random matrix: a replica approach},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
publisher = {IOP Publishing},
year = {2023},
month = {2},
number = {2},
volume = {2023},
pages = {023302},
url = {https://doi.org/10.1088%2F1742-5468%2Facb7d6},
doi = {10.1088/1742-5468/acb7d6}
}
@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},
volume = {49},
pages = {314--320},
url = {https://projecteuclid.org:443/euclid.bams/1183505112}
}
@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{Kirkpatrick_1987_p-spin-interaction,
author = {Kirkpatrick, T. R. and Thirumalai, D.},
title = {$p$-spin-interaction spin-glass models: Connections with the structural glass problem},
journal = {Physical Review B},
publisher = {American Physical Society (APS)},
year = {1987},
month = {10},
number = {10},
volume = {36},
pages = {5388--5397},
url = {https://doi.org/10.1103%2Fphysrevb.36.5388},
doi = {10.1103/physrevb.36.5388}
}
@article{Kirkpatrick_2015_Colloquium,
author = {Kirkpatrick, T. R. and Thirumalai, D.},
title = {\textit{Colloquium}: Random first order transition theory concepts in biology and physics},
journal = {Reviews of Modern Physics},
publisher = {American Physical Society (APS)},
year = {2015},
month = {3},
number = {1},
volume = {87},
pages = {183--209},
url = {https://doi.org/10.1103%2Frevmodphys.87.183},
doi = {10.1103/revmodphys.87.183}
}
@article{Kurchan_1996_Phase,
author = {Kurchan, Jorge and Laloux, Laurent},
title = {Phase space geometry and slow dynamics},
journal = {Journal of Physics A: Mathematical and General},
publisher = {IOP Publishing},
year = {1996},
month = {5},
number = {9},
volume = {29},
pages = {1929--1948},
url = {https://doi.org/10.1088%2F0305-4470%2F29%2F9%2F009},
doi = {10.1088/0305-4470/29/9/009}
}
@article{Rice_1944_Mathematical,
author = {Rice, S. O.},
title = {Mathematical Analysis of Random Noise},
journal = {Bell System Technical Journal},
publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
year = {1944},
month = {7},
number = {3},
volume = {23},
pages = {282--332},
url = {https://doi.org/10.1002%2Fj.1538-7305.1944.tb00874.x},
doi = {10.1002/j.1538-7305.1944.tb00874.x}
}
@article{Ros_2019_Complex,
author = {Ros, Valentina and Ben Arous, Gérard and Biroli, Giulio and Cammarota, Chiara},
title = {Complex Energy Landscapes in Spiked-Tensor and Simple Glassy Models: Ruggedness, Arrangements of Local Minima, and Phase Transitions},
journal = {Physical Review X},
publisher = {American Physical Society (APS)},
year = {2019},
month = {1},
number = {1},
volume = {9},
pages = {011003},
url = {https://doi.org/10.1103%2Fphysrevx.9.011003},
doi = {10.1103/physrevx.9.011003}
}
@article{Ros_2019_Complexity,
author = {Ros, V. and Biroli, G. and Cammarota, C.},
title = {Complexity of energy barriers in mean-field glassy systems},
journal = {EPL (Europhysics Letters)},
publisher = {IOP Publishing},
year = {2019},
month = {5},
number = {2},
volume = {126},
pages = {20003},
url = {https://doi.org/10.1209%2F0295-5075%2F126%2F20003},
doi = {10.1209/0295-5075/126/20003}
}
@article{Ros_2020_Distribution,
author = {Ros, Valentina},
title = {Distribution of rare saddles in the $p$-spin energy landscape},
journal = {Journal of Physics A: Mathematical and Theoretical},
publisher = {IOP Publishing},
year = {2020},
month = {3},
number = {12},
volume = {53},
pages = {125002},
url = {https://doi.org/10.1088%2F1751-8121%2Fab73ac},
doi = {10.1088/1751-8121/ab73ac}
}
@article{Stillinger_2013_Glass,
author = {Stillinger, Frank H. and Debenedetti, Pablo G.},
title = {Glass Transition Thermodynamics and Kinetics},
journal = {Annual Review of Condensed Matter Physics},
publisher = {Annual Reviews},
year = {2013},
month = {4},
number = {1},
volume = {4},
pages = {263--285},
url = {https://doi.org/10.1146%2Fannurev-conmatphys-030212-184329},
doi = {10.1146/annurev-conmatphys-030212-184329}
}
@article{Sellke_2023_The,
author = {Sellke, Mark},
title = {The Threshold Energy of Low Temperature {Langevin} Dynamics for Pure
Spherical Spin Glasses},
year = {2023},
month = {5},
url = {http://arxiv.org/abs/2305.07956v1},
date = {2023-05-13T16:05:12Z},
eprint = {2305.07956v1},
eprintclass = {cond-mat.dis-nn},
eprinttype = {arxiv}
}
@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{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}
}
@article{Annesi_2023_Star-shaped,
author = {Annesi, Brandon Livio and Lauditi, Clarissa and Lucibello, Carlo and Malatesta, Enrico M. and Perugini, Gabriele and Pittorino, Fabrizio and Saglietti, Luca},
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},
pages = {227301},
url = {http://dx.doi.org/10.1103/PhysRevLett.131.227301},
doi = {10.1103/physrevlett.131.227301},
issn = {1079-7114}
}
@article{Pacco_2023_Curvature-driven,
author = {Pacco, Alessandro and Biroli, Giulio and Ros, Valentina},
title = {Curvature-driven pathways interpolating between stationary points: the case of the pure spherical 3-spin model},
year = {2023},
month = {11},
url = {http://arxiv.org/abs/2311.18411v1},
date = {2023-11-30T10:00:26Z},
eprint = {2311.18411v1},
eprintclass = {cond-mat.dis-nn},
eprinttype = {arxiv},
urldate = {2023-12-02T20:20:20.011554Z}
}
@article{Stein_1995_Broken,
author = {Stein, D. L. and Newman, C. M.},
title = {Broken ergodicity and the geometry of rugged landscapes},
journal = {Physical Review E},
publisher = {American Physical Society (APS)},
year = {1995},
month = {6},
number = {6},
volume = {51},
pages = {5228--5238},
url = {https://doi.org/10.1103%2Fphysreve.51.5228},
doi = {10.1103/physreve.51.5228}
}
@article{Krzakala_2007_Landscape,
author = {Krzakala, Florent and Kurchan, Jorge},
title = {Landscape analysis of constraint satisfaction problems},
journal = {Physical Review E},
publisher = {American Physical Society (APS)},
year = {2007},
month = {8},
number = {2},
volume = {76},
pages = {021122},
url = {https://doi.org/10.1103%2Fphysreve.76.021122},
doi = {10.1103/physreve.76.021122}
}
@article{Altieri_2021_Properties,
author = {Altieri, Ada and Roy, Felix and Cammarota, Chiara and Biroli, Giulio},
title = {Properties of Equilibria and Glassy Phases of the Random Lotka-Volterra Model with Demographic Noise},
journal = {Physical Review Letters},
publisher = {American Physical Society (APS)},
year = {2021},
month = {6},
number = {25},
volume = {126},
pages = {258301},
url = {https://doi.org/10.1103%2Fphysrevlett.126.258301},
doi = {10.1103/physrevlett.126.258301}
}
@article{Yang_2023_Stochastic,
author = {Yang, Ning and Tang, Chao and Tu, Yuhai},
title = {Stochastic Gradient Descent Introduces an Effective Landscape-Dependent Regularization Favoring Flat Solutions},
journal = {Physical Review Letters},
publisher = {American Physical Society (APS)},
year = {2023},
month = {6},
number = {23},
volume = {130},
pages = {237101},
url = {https://doi.org/10.1103%2Fphysrevlett.130.237101},
doi = {10.1103/physrevlett.130.237101}
}
@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}
}
@article{Baldassi_2021_Unveiling,
author = {Baldassi, Carlo and Lauditi, Clarissa and Malatesta, Enrico M. and Perugini, Gabriele and Zecchina, Riccardo},
title = {Unveiling the Structure of Wide Flat Minima in Neural Networks},
journal = {Physical Review Letters},
publisher = {American Physical Society (APS)},
year = {2021},
month = {12},
number = {27},
volume = {127},
pages = {278301},
url = {http://dx.doi.org/10.1103/PhysRevLett.127.278301},
doi = {10.1103/physrevlett.127.278301},
issn = {1079-7114}
}
@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}
}
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