@article{Albert_2021_Searching,
 author = {Albert, Samuel and Biroli, Giulio and Ladieu, François and Tourbot, Roland and Urbani, Pierfrancesco},
 title = {Searching for the Gardner Transition in Glassy Glycerol},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2021},
 month = {1},
 number = {2},
 volume = {126},
 pages = {028001},
 url = {https://doi.org/10.1103%2Fphysrevlett.126.028001},
 doi = {10.1103/physrevlett.126.028001}
}

@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{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)},
 year = {2003},
 month = {12},
 number = {6},
 volume = {68},
 pages = {061103},
 url = {https://doi.org/10.1103%2Fphysreve.68.061103},
 doi = {10.1103/physreve.68.061103}
}

@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 = {J Phys A: Math Gen},
 publisher = {IOP Publishing},
 year = {2003},
 month = {10},
 number = {43},
 volume = {36},
 pages = {10937--10953},
 url = {https://doi.org/10.1088%2F0305-4470%2F36%2F43%2F018},
 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 = {J Phys A: Math Gen},
 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{Auffinger_2012_Random,
 author = {Auffinger, Antonio and Ben Arous, Gérard and Černý, Jiří},
 title = {Random Matrices and Complexity of Spin Glasses},
 journal = {Comm. Pure Appl. Math.},
 publisher = {Wiley},
 year = {2012},
 month = {9},
 number = {2},
 volume = {66},
 pages = {165--201},
 url = {https://doi.org/10.1002%2Fcpa.21422},
 doi = {10.1002/cpa.21422}
}

@article{Auffinger_2013_Complexity,
 author = {Auffinger, Antonio and Ben Arous, Gérard},
 title = {Complexity of random smooth functions on the high-dimensional sphere},
 journal = {The Annals of Probability},
 publisher = {Institute of Mathematical Statistics},
 year = {2013},
 month = {11},
 number = {6},
 volume = {41},
 pages = {4214--4247},
 url = {https://doi.org/10.1214%2F13-aop862},
 doi = {10.1214/13-aop862}
}

@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 = {Comm Pure Appl Math},
 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{Berthier_2019_Gardner,
 author = {Berthier, Ludovic and Biroli, Giulio and Charbonneau, Patrick and Corwin, Eric I. and Franz, Silvio and Zamponi, Francesco},
 title = {Gardner physics in amorphous solids and beyond},
 journal = {The Journal of Chemical Physics},
 publisher = {AIP Publishing},
 year = {2019},
 month = {7},
 number = {1},
 volume = {151},
 pages = {010901},
 url = {https://doi.org/10.1063%2F1.5097175},
 doi = {10.1063/1.5097175}
}

@article{Biroli_2016_Breakdown,
 author = {Biroli, Giulio and Urbani, Pierfrancesco},
 title = {Breakdown of elasticity in amorphous solids},
 journal = {Nature Physics},
 publisher = {Springer Science and Business Media LLC},
 year = {2016},
 month = {8},
 number = {12},
 volume = {12},
 pages = {1130--1133},
 url = {https://doi.org/10.1038%2Fnphys3845},
 doi = {10.1038/nphys3845}
}

@article{Biroli_2018_Liu-Nagel,
 author = {Biroli, Giulio and Urbani, Pierfrancesco},
 title = {Liu-Nagel phase diagrams in infinite dimension},
 journal = {SciPost Physics},
 publisher = {Stichting SciPost},
 year = {2018},
 month = {4},
 number = {4},
 volume = {4},
 pages = {020},
 url = {https://doi.org/10.21468%2Fscipostphys.4.4.020},
 doi = {10.21468/scipostphys.4.4.020}
}

@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{Cavagna_1997_An,
 author = {Cavagna, Andrea and Giardina, Irene and Parisi, Giorgio},
 title = {An investigation of the hidden structure of states in a mean-field spin-glass model},
 journal = {Journal of Physics A: Mathematical and General},
 publisher = {IOP Publishing},
 year = {1997},
 month = {10},
 number = {20},
 volume = {30},
 pages = {7021--7038},
 url = {https://doi.org/10.1088%2F0305-4470%2F30%2F20%2F009},
 doi = {10.1088/0305-4470/30/20/009}
}

@article{Cavagna_1997_Structure,
 author = {Cavagna, Andrea and Giardina, Irene and Parisi, Giorgio},
 title = {Structure of metastable states in spin glasses by means of a three replica potential},
 journal = {Journal of Physics A: Mathematical and General},
 publisher = {IOP Publishing},
 year = {1997},
 month = {7},
 number = {13},
 volume = {30},
 pages = {4449--4466},
 url = {https://doi.org/10.1088%2F0305-4470%2F30%2F13%2F004},
 doi = {10.1088/0305-4470/30/13/004}
}

@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_2005_Cavity,
 author = {Cavagna, Andrea and Giardina, Irene and Parisi, Giorgio},
 title = {Cavity method for supersymmetry-breaking spin glasses},
 journal = {Physical Review B},
 publisher = {American Physical Society (APS)},
 year = {2005},
 month = {1},
 number = {2},
 volume = {71},
 pages = {024422},
 url = {https://doi.org/10.1103%2Fphysrevb.71.024422},
 doi = {10.1103/physrevb.71.024422}
}

@article{Charbonneau_2014_Fractal,
 author = {Charbonneau, Patrick and Kurchan, Jorge and Parisi, Giorgio and Urbani, Pierfrancesco and Zamponi, Francesco},
 title = {Fractal free energy landscapes in structural glasses},
 journal = {Nature Communications},
 publisher = {Springer Science and Business Media LLC},
 year = {2014},
 month = {4},
 number = {1},
 volume = {5},
 pages = {3725},
 url = {https://doi.org/10.1038%2Fncomms4725},
 doi = {10.1038/ncomms4725}
}

@article{Charbonneau_2015_Numerical,
 author = {Charbonneau, Patrick and Jin, Yuliang and Parisi, Giorgio and Rainone, Corrado and Seoane, Beatriz and Zamponi, Francesco},
 title = {Numerical detection of the Gardner transition in a mean-field glass former},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2015},
 month = {7},
 number = {1},
 volume = {92},
 pages = {012316},
 url = {https://doi.org/10.1103%2Fphysreve.92.012316},
 doi = {10.1103/physreve.92.012316}
}

@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_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%2Fjp1%3A1995164},
 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}
}

@article{Crisanti_2011_Statistical,
 author = {Crisanti, A. and Leuzzi, L. and Paoluzzi, M.},
 title = {Statistical mechanical approach to secondary processes and structural relaxation in glasses and glass formers},
 journal = {The European Physical Journal E},
 publisher = {Springer Science and Business Media LLC},
 year = {2011},
 month = {9},
 number = {9},
 volume = {34},
 pages = {98},
 url = {https://doi.org/10.1140%2Fepje%2Fi2011-11098-3},
 doi = {10.1140/epje/i2011-11098-3}
}

@article{Cugliandolo_1993_Analytical,
 author = {Cugliandolo, L. F. and Kurchan, J.},
 title = {Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {1993},
 month = {7},
 number = {1},
 volume = {71},
 pages = {173--176},
 url = {https://doi.org/10.1103%2Fphysrevlett.71.173},
 doi = {10.1103/physrevlett.71.173}
}

@article{Dennis_2020_Jamming,
 author = {Dennis, R. C. and Corwin, E. I.},
 title = {Jamming Energy Landscape is Hierarchical and Ultrametric},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2020},
 month = {2},
 number = {7},
 volume = {124},
 pages = {078002},
 url = {https://doi.org/10.1103%2Fphysrevlett.124.078002},
 doi = {10.1103/physrevlett.124.078002}
}

@unpublished{ElAlaoui_2020_Algorithmic,
 author = {El Alaoui, Ahmed and Montanari, Andrea},
 title = {Algorithmic Thresholds in Mean Field Spin Glasses},
 year = {2020},
 url = {http://arxiv.org/abs/2009.11481v1},
 archiveprefix = {arXiv},
 eprint = {2009.11481},
 eprintclass = {cond-mat.stat-mech},
 eprinttype = {arxiv},
 primaryclass = {cond-mat.stat-mech}
}

@article{ElAlaoui_2021_Optimization,
 author = {El Alaoui, Ahmed and Montanari, Andrea and Sellke, Mark},
 title = {Optimization of mean-field spin glasses},
 journal = {The Annals of Probability},
 publisher = {Institute of Mathematical Statistics},
 year = {2021},
 month = {11},
 number = {6},
 volume = {49},
 pages = {2922--2960},
 url = {https://doi.org/10.1214%2F21-aop1519},
 doi = {10.1214/21-aop1519}
}

@unpublished{ElAlaoui_2022_Sampling,
 author = {El Alaoui, Ahmed and Montanari, Andrea and Sellke, Mark},
 title = {Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic
stochastic localization},
 year = {2022},
 month = {3},
 url = {http://arxiv.org/abs/2203.05093v1},
 archiveprefix = {arXiv},
 date = {2022-03-10T00:15:22Z},
 eprint = {2203.05093v1},
 eprintclass = {math.PR},
 eprinttype = {arxiv},
 primaryclass = {cond-mat.stat-mech}
}

@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 = {PRX},
 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}
}

@phdthesis{Folena_2020_The,
 author = {Folena, Giampaolo},
 title = {The mixed $p$-spin model: selecting, following and losing states},
 year = {2020},
 month = {3},
 number = {2020UPASS060},
 url = {https://tel.archives-ouvertes.fr/tel-02883385},
 hal_id = {tel-02883385},
 hal_version = {v1},
 school = {Université Paris-Saclay & Università degli studi La Sapienza (Rome)},
 type = {Theses}
}

@article{Fyodorov_2007_Replica,
 author = {Fyodorov, Yan V. and Williams, Ian},
 title = {Replica Symmetry Breaking Condition Exposed by Random Matrix Calculation of Landscape Complexity},
 journal = {Journal of Statistical Physics},
 publisher = {Springer Science and Business Media LLC},
 year = {2007},
 month = {9},
 number = {5-6},
 volume = {129},
 pages = {1081--1116},
 url = {https://doi.org/10.1007%2Fs10955-007-9386-x},
 doi = {10.1007/s10955-007-9386-x}
}

@article{Gamarnik_2021_The,
 author = {Gamarnik, David and Jagannath, Aukosh},
 title = {The overlap gap property and approximate message passing algorithms for $p$-spin models},
 journal = {The Annals of Probability},
 publisher = {Institute of Mathematical Statistics},
 year = {2021},
 month = {1},
 number = {1},
 volume = {49},
 pages = {180--205},
 url = {https://doi.org/10.1214%2F20-aop1448},
 doi = {10.1214/20-aop1448}
}

@article{Gardner_1985_Spin,
 author = {Gardner, E.},
 title = {Spin glasses with $p$-spin interactions},
 journal = {Nuclear Physics B},
 publisher = {Elsevier BV},
 year = {1985},
 month = {1},
 volume = {257},
 pages = {747--765},
 url = {https://doi.org/10.1016%2F0550-3213%2885%2990374-8},
 doi = {10.1016/0550-3213(85)90374-8}
}

@article{Geirhos_2018_Johari-Goldstein,
 author = {Geirhos, K. and Lunkenheimer, P. and Loidl, A.},
 title = {Johari-Goldstein Relaxation Far Below 
$T_g$: Experimental Evidence for the Gardner Transition in Structural Glasses?},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2018},
 month = {2},
 number = {8},
 volume = {120},
 pages = {085705},
 url = {https://doi.org/10.1103%2Fphysrevlett.120.085705},
 doi = {10.1103/physrevlett.120.085705}
}

@inproceedings{Giardina_2005_Supersymmetry,
 author = {Giardina, Irene and Cavagna, Andrea and Parisi, Giorgio},
 title = {Supersymmetry and metastability in disordered systems},
 publisher = {World Scientific},
 year = {2005},
 month = {9},
 pages = {204--209},
 url = {https://doi.org/10.1142%2F9789812701558_0023},
 doi = {10.1142/9789812701558_0023},
 booksubtitle = {Proceedings of the 31st Workshop of the International School of Solid State Physics, Erice, Sicily, Italy, 20 – 26 July 2004},
 booktitle = {Complexity, Metastability and Nonextensivity},
 editor = {Beck, C and Benedek, G and Rapisarda, A and Tsallis, C}
}

@article{Gross_1985_Mean-field,
 author = {Gross, D. J. and Kanter, I. and Sompolinsky, H.},
 title = {Mean-field theory of the Potts glass},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {1985},
 month = {7},
 number = {3},
 volume = {55},
 pages = {304--307},
 url = {https://doi.org/10.1103%2Fphysrevlett.55.304},
 doi = {10.1103/physrevlett.55.304}
}

@article{Hammond_2020_Experimental,
 author = {Hammond, Andrew P. and Corwin, Eric I.},
 title = {Experimental observation of the marginal glass phase in a colloidal glass},
 journal = {Proceedings of the National Academy of Sciences},
 publisher = {Proceedings of the National Academy of Sciences},
 year = {2020},
 month = {3},
 number = {11},
 volume = {117},
 pages = {5714--5718},
 url = {https://doi.org/10.1073%2Fpnas.1917283117},
 doi = {10.1073/pnas.1917283117}
}

@article{Hicks_2018_Gardner,
 author = {Hicks, C. L. and Wheatley, M. J. and Godfrey, M. J. and Moore, M. A.},
 title = {Gardner Transition in Physical Dimensions},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2018},
 month = {5},
 number = {22},
 volume = {120},
 pages = {225501},
 url = {https://doi.org/10.1103%2Fphysrevlett.120.225501},
 doi = {10.1103/physrevlett.120.225501}
}

@unpublished{Huang_2021_Tight,
 author = {Huang, Brice and Sellke, Mark},
 title = {Tight Lipschitz Hardness for Optimizing Mean Field Spin Glasses},
 year = {2021},
 month = {10},
 url = {http://arxiv.org/abs/2110.07847v1},
 archiveprefix = {arXiv},
 date = {2021-10-15T04:08:35Z},
 eprint = {2110.07847v1},
 eprintclass = {math.PR},
 eprinttype = {arxiv},
 primaryclass = {cond-mat.stat-mech}
}

@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_2022_Analytic,
 author = {JK-D and Kurchan, Jorge},
 title = {Analytic continuation over complex landscapes},
 journal = {Journal of Physics A: Mathematical and Theoretical},
 publisher = {IOP Publishing},
 year = {2022},
 month = {10},
 number = {43},
 volume = {55},
 pages = {434006},
 url = {https://doi.org/10.1088%2F1751-8121%2Fac9cc7},
 doi = {10.1088/1751-8121/ac9cc7},
 collection = {Random Landscapes and Dynamics in Evolution, Ecology and Beyond}
}

@unpublished{Kent-Dobias_2022_How,
 author = {JK-D and Kurchan, Jorge},
 title = {How to count in hierarchical landscapes: a `full' solution to mean-field
complexity},
 year = {2022},
 url = {http://arxiv.org/abs/2207.06161v2},
 archiveprefix = {arXiv},
 eprint = {2207.06161v2},
 eprintclass = {cond-mat.stat-mech},
 eprinttype = {arxiv},
 primaryclass = {cond-mat.stat-mech}
}

@article{Li_2021_Determining,
 author = {Li, Huaping and Jin, Yuliang and Jiang, Ying and Chen, Jeff Z. Y.},
 title = {Determining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning},
 journal = {Proceedings of the National Academy of Sciences},
 publisher = {Proceedings of the National Academy of Sciences},
 year = {2021},
 month = {3},
 number = {11},
 volume = {118},
 pages = {e2017392118},
 url = {https://doi.org/10.1073%2Fpnas.2017392118},
 doi = {10.1073/pnas.2017392118}
}

@article{Liao_2019_Hierarchical,
 author = {Liao, Qinyi and Berthier, Ludovic},
 title = {Hierarchical Landscape of Hard Disk Glasses},
 journal = {Physical Review X},
 publisher = {American Physical Society (APS)},
 year = {2019},
 month = {3},
 number = {1},
 volume = {9},
 pages = {011049},
 url = {https://doi.org/10.1103%2Fphysrevx.9.011049},
 doi = {10.1103/physrevx.9.011049}
}

@inproceedings{Maillard_2020_Landscape,
 author = {Maillard, Antoine and Ben Arous, Gérard and Biroli, Giulio},
 title = {Landscape Complexity for the Empirical Risk of Generalized Linear Models},
 publisher = {PMLR},
 year = {2020},
 month = {7},
 volume = {107},
 pages = {287--327},
 url = {https://proceedings.mlr.press/v107/maillard20a.html},
 booktitle = {Proceedings of The First Mathematical and Scientific Machine Learning Conference},
 editor = {Lu, Jianfeng and Ward, Rachel},
 pdf = {http://proceedings.mlr.press/v107/maillard20a/maillard20a.pdf},
 series = {Proceedings of Machine Learning Research}
}

@article{Maimbourg_2016_Solution,
 author = {Maimbourg, Thibaud and Kurchan, Jorge and Zamponi, Francesco},
 title = {Solution of the Dynamics of Liquids in the Large-Dimensional Limit},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2016},
 month = {1},
 number = {1},
 volume = {116},
 pages = {015902},
 url = {https://doi.org/10.1103%2Fphysrevlett.116.015902},
 doi = {10.1103/physrevlett.116.015902}
}

@article{Mezard_1991_Replica,
 author = {Mézard, Marc and Parisi, Giorgio},
 title = {Replica field theory for random manifolds},
 journal = {Journal de Physique I},
 publisher = {EDP Sciences},
 year = {1991},
 month = {6},
 number = {6},
 volume = {1},
 pages = {809--836},
 url = {https://doi.org/10.1051%2Fjp1%3A1991171},
 doi = {10.1051/jp1:1991171}
}

@article{Mezard_1992_Manifolds,
 author = {Mézard, M. and Parisi, G.},
 title = {Manifolds in random media: two extreme cases},
 journal = {Journal de Physique I},
 publisher = {EDP Sciences},
 year = {1992},
 month = {12},
 number = {12},
 volume = {2},
 pages = {2231--2242},
 url = {https://doi.org/10.1051%2Fjp1%3A1992278},
 doi = {10.1051/jp1:1992278}
}

@article{Parisi_1979_Infinite,
 author = {Parisi, G.},
 title = {Infinite Number of Order Parameters for Spin-Glasses},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {1979},
 month = {12},
 number = {23},
 volume = {43},
 pages = {1754--1756},
 url = {https://doi.org/10.1103%2Fphysrevlett.43.1754},
 doi = {10.1103/physrevlett.43.1754}
}

@article{Parisi_1980_Magnetic,
 author = {Parisi, G},
 title = {Magnetic properties of spin glasses in a new mean field theory},
 journal = {Journal of Physics A: Mathematical and General},
 publisher = {IOP Publishing},
 year = {1980},
 month = {5},
 number = {5},
 volume = {13},
 pages = {1887--1895},
 url = {https://doi.org/10.1088%2F0305-4470%2F13%2F5%2F047},
 doi = {10.1088/0305-4470/13/5/047}
}

@article{Rainone_2015_Following,
 author = {Rainone, Corrado and Urbani, Pierfrancesco and Yoshino, Hajime and Zamponi, Francesco},
 title = {Following the Evolution of Hard Sphere Glasses in Infinite Dimensions under External Perturbations: Compression and Shear Strain},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2015},
 month = {1},
 number = {1},
 volume = {114},
 pages = {015701},
 url = {https://doi.org/10.1103%2Fphysrevlett.114.015701},
 doi = {10.1103/physrevlett.114.015701}
}

@article{Rainone_2016_Following,
 author = {Rainone, Corrado and Urbani, Pierfrancesco},
 title = {Following the evolution of glassy states under external perturbations: the full replica symmetry breaking solution},
 journal = {Journal of Statistical Mechanics: Theory and Experiment},
 publisher = {IOP Publishing},
 year = {2016},
 month = {5},
 number = {5},
 volume = {2016},
 pages = {053302},
 url = {https://doi.org/10.1088%2F1742-5468%2F2016%2F05%2F053302},
 doi = {10.1088/1742-5468/2016/05/053302}
}

@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}
}

@article{Rieger_1992_The,
 author = {Rieger, H.},
 title = {The number of solutions of the Thouless-Anderson-Palmer equations for $p$-spin-interaction spin glasses},
 journal = {Physical Review B},
 publisher = {American Physical Society (APS)},
 year = {1992},
 month = {12},
 number = {22},
 volume = {46},
 pages = {14655--14661},
 url = {https://doi.org/10.1103%2Fphysrevb.46.14655},
 doi = {10.1103/physrevb.46.14655}
}

@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_2021_Dynamical,
 author = {Ros, Valentina and Biroli, Giulio and Cammarota, Chiara},
 title = {Dynamical instantons and activated processes in mean-field glass models},
 journal = {SciPost Physics},
 publisher = {Stichting SciPost},
 year = {2021},
 month = {1},
 number = {1},
 volume = {10},
 pages = {002},
 url = {https://doi.org/10.21468%2Fscipostphys.10.1.002},
 doi = {10.21468/scipostphys.10.1.002}
}

@article{Seguin_2016_Experimental,
 author = {Seguin, A. and Dauchot, O.},
 title = {Experimental Evidence of the Gardner Phase in a Granular Glass},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2016},
 month = {11},
 number = {22},
 volume = {117},
 pages = {228001},
 url = {https://doi.org/10.1103%2Fphysrevlett.117.228001},
 doi = {10.1103/physrevlett.117.228001}
}

@article{Urbani_2017_Shear,
 author = {Urbani, Pierfrancesco and Zamponi, Francesco},
 title = {Shear Yielding and Shear Jamming of Dense Hard Sphere Glasses},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2017},
 month = {1},
 number = {3},
 volume = {118},
 pages = {038001},
 url = {https://doi.org/10.1103%2Fphysrevlett.118.038001},
 doi = {10.1103/physrevlett.118.038001}
}

@article{Xiao_2022_Probing,
 author = {Xiao, Hongyi and Liu, Andrea J. and Durian, Douglas J.},
 title = {Probing Gardner Physics in an Active Quasithermal Pressure-Controlled Granular System of Noncircular Particles},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2022},
 month = {6},
 number = {24},
 volume = {128},
 pages = {248001},
 url = {https://doi.org/10.1103%2Fphysrevlett.128.248001},
 doi = {10.1103/physrevlett.128.248001}
}


@article{Fyodorov_2012_Critical,
 author = {Fyodorov, Yan V. and Nadal, Celine},
 title = {Critical Behavior of the Number of Minima of a Random Landscape at the Glass Transition Point and the {Tracy}-{Widom} Distribution},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2012},
 month = {10},
 number = {16},
 volume = {109},
 pages = {167203},
 url = {https://doi.org/10.1103%2Fphysrevlett.109.167203},
 doi = {10.1103/physrevlett.109.167203}
}

@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{Wainrib_2013_Topological,
 author = {Wainrib, Gilles and Touboul, Jonathan},
 title = {Topological and Dynamical Complexity of Random Neural Networks},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2013},
 month = {3},
 number = {11},
 volume = {110},
 pages = {118101},
 url = {https://doi.org/10.1103%2Fphysrevlett.110.118101},
 doi = {10.1103/physrevlett.110.118101}
}
@article{Stillinger_1984_Packing,
 author = {Stillinger, Frank H. and Weber, Thomas A.},
 title = {Packing Structures and Transitions in Liquids and Solids},
 journal = {Science},
 publisher = {American Association for the Advancement of Science (AAAS)},
 year = {1984},
 month = {9},
 number = {4666},
 volume = {225},
 pages = {983--989},
 url = {https://doi.org/10.1126%2Fscience.225.4666.983},
 doi = {10.1126/science.225.4666.983}
}

@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}
}

@book{Sethna_2006_Statistical,
 author = {Sethna, James P},
 title = {Statistical mechanics},
 publisher = {Oxford University Press},
 year = {2006},
 isbn = {9780198566762},
 subtitle = {Entropy, order parameters, and complexity}
}

@book{Cardy_1996_Scaling,
 author = {Cardy, John},
 title = {Scaling and renormalization in statistical physics},
 publisher = {Cambridge University Press},
 year = {1996},
 isbn = {9780521499590}
}

@article{Raju_2019_Normal,
 author = {Raju, Archishman and Clement, Colin B. and Hayden, Lorien X. and JK-D and Liarte, Danilo B. and Rocklin, D. Zeb and Sethna, James P.},
 title = {Normal Form for Renormalization Groups},
 journal = {Physical Review X},
 publisher = {American Physical Society (APS)},
 year = {2019},
 month = {4},
 number = {2},
 volume = {9},
 pages = {021014},
 url = {https://doi.org/10.1103%2Fphysrevx.9.021014},
 doi = {10.1103/physrevx.9.021014}
}

@article{Kosterlitz_1973_Ordering,
 author = {Kosterlitz, J M and Thouless, D J},
 title = {Ordering, metastability and phase transitions in two-dimensional systems},
 journal = {Journal of Physics C: Solid State Physics},
 publisher = {IOP Publishing},
 year = {1973},
 month = {4},
 number = {7},
 volume = {6},
 pages = {1181--1203},
 url = {https://doi.org/10.1088%2F0022-3719%2F6%2F7%2F010},
 doi = {10.1088/0022-3719/6/7/010}
}

@article{Berezinskii_1971_Destruction,
 author = {Berezinski\u i, V. L.},
 title = {Destruction of Long-range Order in One-dimensional and Two-dimensional Systems having a Continuous Symmetry Group {I}: Classical Systems},
 journal = {Soviet Journal of Experimental and Theoretical Physics},
 year = {1971},
 month = {1},
 volume = {32},
 pages = {493},
 adsurl = {https://ui.adsabs.harvard.edu/abs/1971JETP...32..493B}
}

@article{Kosterlitz_1974_The,
 author = {Kosterlitz, J M},
 title = {The critical properties of the two-dimensional $xy$ model},
 journal = {Journal of Physics C: Solid State Physics},
 publisher = {IOP Publishing},
 year = {1974},
 month = {3},
 number = {6},
 volume = {7},
 pages = {1046--1060},
 url = {https://doi.org/10.1088%2F0022-3719%2F7%2F6%2F005},
 doi = {10.1088/0022-3719/7/6/005}
}

@article{Callaway_2001_Are,
 author = {Callaway, Duncan S. and Hopcroft, John E. and Kleinberg, Jon M. and Newman, M. E. J. and Strogatz, Steven H.},
 title = {Are randomly grown graphs really random?},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2001},
 month = {9},
 number = {4},
 volume = {64},
 pages = {041902},
 url = {https://doi.org/10.1103%2Fphysreve.64.041902},
 doi = {10.1103/physreve.64.041902}
}

@article{Dorogovtsev_2001_Anomalous,
 author = {Dorogovtsev, S. N. and Mendes, J. F. F. and Samukhin, A. N.},
 title = {Anomalous percolation properties of growing networks},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2001},
 month = {11},
 number = {6},
 volume = {64},
 pages = {066110},
 url = {https://doi.org/10.1103%2Fphysreve.64.066110},
 doi = {10.1103/physreve.64.066110}
}

@article{Pelissetto_2013_Renormalization-group,
 author = {Pelissetto, Andrea and Vicari, Ettore},
 title = {Renormalization-group flow and asymptotic behaviors at the {Berezinskii-Kosterlitz-Thouless} transitions},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2013},
 month = {3},
 number = {3},
 volume = {87},
 pages = {032105},
 url = {https://doi.org/10.1103%2Fphysreve.87.032105},
 doi = {10.1103/physreve.87.032105}
}

@article{Thorneywork_2017_Two-dimensional,
 author = {Thorneywork, Alice L. and Abbott, Joshua L. and Aarts, Dirk G.A. L. and Dullens, Roel P. A.},
 title = {Two-Dimensional Melting of Colloidal Hard Spheres},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2017},
 month = {4},
 number = {15},
 volume = {118},
 pages = {158001},
 url = {https://doi.org/10.1103%2Fphysrevlett.118.158001},
 doi = {10.1103/physrevlett.118.158001}
}

@article{Bianconi_2019_Percolation,
 author = {Bianconi, Ginestra and Kryven, Ivan and Ziff, Robert M.},
 title = {Percolation on branching simplicial and cell complexes and its relation to interdependent percolation},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2019},
 month = {12},
 number = {6},
 volume = {100},
 pages = {062311},
 url = {https://doi.org/10.1103%2Fphysreve.100.062311},
 doi = {10.1103/physreve.100.062311}
}

@phdthesis{Kent-Dobias_2020_Novel,
 author = {{\textbf{JK-D}}},
 title = {Novel Critical Phenomena},
 publisher = {ProQuest Dissertations Publishing},
 year = {2020},
 url = {https://search.proquest.com/pqdtglobal/docview/2449126045/abstract/DA3EA013F5F140D1PQ/1},
 isbn = {9798672130477},
 school = {Cornell University}
}

@article{Kent-Dobias_2015_Energy-driven,
 author = {{\textbf{JK-D}} and Bernoff, Andrew J.},
 title = {Energy-driven pattern formation in planar dipole-dipole systems in the presence of weak noise},
 journal = {PRE},
 publisher = {American Physical Society (APS)},
 year = {2015},
 month = {3},
 number = {3},
 volume = {91},
 pages = {032919},
 url = {https://doi.org/10.1103%2Fphysreve.91.032919},
 doi = {10.1103/physreve.91.032919}
}

@article{Kent-Dobias_2017_Essential,
 author = {{\textbf{JK-D}} and Sethna, James P.},
 title = {Essential Singularities in Universal Scaling Functions at the {Ising} Coexistence Line},
 month = {7},
 url = {http://arxiv.org/abs/1707.03791v2},
 eprint = {1707.03791v2},
 eprintclass = {cond-mat.stat-mech},
 eprinttype = {arxiv}
}

@article{Kent-Dobias_2018_Cluster,
 author = {{\textbf{JK-D}} and Sethna, James P.},
 title = {Cluster representations and the {Wolff} algorithm in arbitrary external fields},
 journal = {PRE},
 publisher = {American Physical Society (APS)},
 year = {2018},
 month = {12},
 number = {6},
 volume = {98},
 pages = {063306},
 url = {https://doi.org/10.1103%2Fphysreve.98.063306},
 doi = {10.1103/physreve.98.063306}
}

@article{Kent-Dobias_2020_Elastic,
 author = {{\textbf{JK-D}} and Matty, Michael and Ramshaw, B. J.},
 title = {Elastic properties of hidden order in {URu$_2$Si$_2$} are reproduced by a staggered nematic},
 journal = {PRB},
 publisher = {American Physical Society},
 year = {2020},
 month = {8},
 volume = {102},
 pages = {075129},
 url = {https://link.aps.org/doi/10.1103/PhysRevB.102.075129},
 doi = {10.1103/PhysRevB.102.075129},
 issue = {7},
 numpages = {9}
}

@article{Kent-Dobias_2021_Complex,
 author = {{\textbf{JK-D}} and Kurchan, Jorge},
 title = {Complex complex landscapes},
 journal = {PRR},
 publisher = {American Physical Society (APS)},
 year = {2021},
 month = {4},
 number = {2},
 volume = {3},
 pages = {023064},
 url = {https://doi.org/10.1103%2Fphysrevresearch.3.023064},
 doi = {10.1103/physrevresearch.3.023064}
}

@article{Sethna_2017_Deformation,
 author = {Sethna, James P. and Bierbaum, Matthew K. and Dahmen, Karin A. and Goodrich, Carl P. and Greer, Julia R. and Hayden, Lorien X. and {\textbf{JK-D}} P. and Lee, Edward D. and Liarte, Danilo B. and Ni, Xiaoyue and Quinn, Katherine N. and Raju, Archishman and Rocklin, D. Zeb and Shekhawat, Ashivni and Zapperi, Stefano},
 title = {Deformation of Crystals},
 journal = {Annual Review of Materials Research},
 publisher = {Annual Reviews},
 year = {2017},
 month = {7},
 number = {1},
 volume = {47},
 pages = {217},
 url = {https://doi.org/10.1146%2Fannurev-matsci-070115-032036},
 doi = {10.1146/annurev-matsci-070115-032036},
 subtitle = {Connections with Statistical Physics}
}

@article{Teoh_2020_Visualizing,
 author = {Teoh, Han Kheng and Quinn, Katherine N. and {\textbf{JK-D}} and Clement, Colin B. and Xu, Qingyang and Sethna, James P.},
 title = {Visualizing probabilistic models in Minkowski space with intensive symmetrized Kullback-Leibler embedding},
 journal = {PRR},
 publisher = {American Physical Society},
 year = {2020},
 month = {8},
 volume = {2},
 pages = {033221},
 url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.033221},
 doi = {10.1103/PhysRevResearch.2.033221},
 issue = {3},
 numpages = {16}
}

@article{Kent-Dobias_2021_Glass,
  author = {Dong, Junkai and Elser, Veit and Gyawali, Gaurav and Jee, Kai Yen and {\textbf{JK-D}} and Mandaiya, Avinash and Renz, Megan and Su, Yubo},
  title = {Glass phenomenology in the hard matrix model},
  journal = {Journal of Statistical Mechanics: Theory and Experiment},
  publisher = {IOP Publishing},
  year = {2021},
  month = {10},
  pages = {093302},
  url = {https://doi.org/10.1088/1742-5468/ac1f25},
  volume = {2021}}
}
@article{Martiniani_2023_When,
 author = {Martiniani, Stefano and Casiulis, Mathias},
 title = {When you can't count, sample! Computable entropies beyond equilibrium from basin volumes},
 journal = {Papers in Physics},
 publisher = {Papers in Physics},
 year = {2023},
 month = {2},
 volume = {15},
 pages = {150001},
 url = {https://doi.org/10.4279%2Fpip.150001},
 doi = {10.4279/pip.150001}
}

@article{Kent-Dobias_2024_Arrangement,
 author = {\textbf{JK-D}},
 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_2023_When,
 author = {\textbf{JK-D}},
 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{Kent-Dobias_2023_How,
 author = {\textbf{JK-D} 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{Grigera_2002_Geometric,
 author = {Grigera, Tomás S. and Cavagna, Andrea and Giardina, Irene and Parisi, Giorgio},
 title = {Geometric Approach to the Dynamic Glass Transition},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2002},
 month = {1},
 number = {5},
 volume = {88},
 pages = {055502},
 url = {https://doi.org/10.1103%2Fphysrevlett.88.055502},
 doi = {10.1103/physrevlett.88.055502}
}

@article{Broderix_2000_Energy,
 author = {Broderix, Kurt and Bhattacharya, Kamal K. and Cavagna, Andrea and Zippelius, Annette and Giardina, Irene},
 title = {Energy Landscape of a {Lennard}-{Jones} Liquid: Statistics of Stationary Points},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2000},
 month = {12},
 number = {25},
 volume = {85},
 pages = {5360--5363},
 url = {https://doi.org/10.1103%2Fphysrevlett.85.5360},
 doi = {10.1103/physrevlett.85.5360}
}

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

@article{Gamarnik_2021-10_The,
 author = {Gamarnik, David},
 title = {The overlap gap property: A topological barrier to optimizing over random structures},
 journal = {Proceedings of the National Academy of Sciences},
 publisher = {Proceedings of the National Academy of Sciences},
 year = {2021},
 month = {October},
 number = {41},
 volume = {118},
 pages = {e2108492118},
 url = {http://dx.doi.org/10.1073/pnas.2108492118},
 doi = {10.1073/pnas.2108492118},
 issn = {1091-6490}
}

@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_2024_On,
 author = {JK-D},
 title = {On the topology of solutions to random continuous constraint satisfaction problems},
 year = {2024},
 month = {sep},
 url = {http://arxiv.org/abs/2409.12781v2},
 archiveprefix = {arXiv},
 eprint = {2409.12781v2},
 eprintclass = {cond-mat.dis-nn},
 eprinttype = {arxiv}
}

@inproceedings{Draxler_2018_Essentially,
 author = {Draxler, Felix and Veschgini, Kambis and Salmhofer, Manfred and Hamprecht, Fred},
 title = {Essentially No Barriers in Neural Network Energy Landscape},
 publisher = {PMLR},
 year = {2018},
 month = {10--15 Jul},
 volume = {80},
 pages = {1309--1318},
 url = {https://proceedings.mlr.press/v80/draxler18a.html},
 abstract = {Training neural networks involves finding minima of a high-dimensional non-convex loss function. Relaxing from linear interpolations, we construct continuous paths between minima of recent neural network architectures on CIFAR10 and CIFAR100. Surprisingly, the paths are essentially flat in both the training and test landscapes. This implies that minima are perhaps best seen as points on a single connected manifold of low loss, rather than as the bottoms of distinct valleys.},
 booktitle = {Proceedings of the 35th International Conference on Machine Learning},
 editor = {Dy, Jennifer and Krause, Andreas},
 pdf = {http://proceedings.mlr.press/v80/draxler18a/draxler18a.pdf},
 series = {Proceedings of Machine Learning Research}
}

@article{Frankle_2020_Revisiting,
 author = {Frankle, Jonathan},
 title = {Revisiting ``Qualitatively Characterizing Neural Network Optimization Problems''},
 year = {2020},
 month = {dec},
 url = {http://arxiv.org/abs/2012.06898v1},
 date = {2020-12-12T20:01:33Z},
 eprint = {2012.06898v1},
 eprintclass = {cs.LG},
 eprinttype = {arxiv},
 urldate = {2025-02-13T19:32:17.287212Z}
}

@inproceedings{Garipov_2018_Loss,
 author = {Garipov, Timur and Izmailov, Pavel and Podoprikhin, Dmitrii and Vetrov, Dmitry P and Wilson, Andrew G},
 title = {Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs},
 publisher = {Curran Associates, Inc.},
 year = {2018},
 volume = {31},
 pages = {},
 url = {https://proceedings.neurips.cc/paper_files/paper/2018/file/be3087e74e9100d4bc4c6268cdbe8456-Paper.pdf},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {Bengio, S. and Wallach, H. and Larochelle, H. and Grauman, K. and Cesa-Bianchi, N. and Garnett, R.}
}

@article{Goodfellow_2014_Qualitatively,
 author = {Goodfellow, Ian J. and Vinyals, Oriol and Saxe, Andrew M.},
 title = {Qualitatively characterizing neural network optimization problems},
 year = {2014},
 month = {dec},
 url = {http://arxiv.org/abs/1412.6544v6},
 date = {2014-12-19T21:55:01Z},
 eprint = {1412.6544v6},
 eprintclass = {cs.NE},
 eprinttype = {arxiv},
 urldate = {2025-02-13T19:29:53.705054Z}
}

@inproceedings{Vlaar_2022_What,
 author = {Vlaar, Tiffany J and Frankle, Jonathan},
 title = {What Can Linear Interpolation of Neural Network Loss Landscapes Tell Us?},
 publisher = {PMLR},
 year = {2022},
 month = {17--23 Jul},
 volume = {162},
 pages = {22325--22341},
 url = {https://proceedings.mlr.press/v162/vlaar22a.html},
 abstract = {Studying neural network loss landscapes provides insights into the nature of the underlying optimization problems. Unfortunately, loss landscapes are notoriously difficult to visualize in a human-comprehensible fashion. One common way to address this problem is to plot linear slices of the landscape, for example from the initial state of the network to the final state after optimization. On the basis of this analysis, prior work has drawn broader conclusions about the difficulty of the optimization problem. In this paper, we put inferences of this kind to the test, systematically evaluating how linear interpolation and final performance vary when altering the data, choice of initialization, and other optimizer and architecture design choices. Further, we use linear interpolation to study the role played by individual layers and substructures of the network. We find that certain layers are more sensitive to the choice of initialization, but that the shape of the linear path is not indicative of the changes in test accuracy of the model. Our results cast doubt on the broader intuition that the presence or absence of barriers when interpolating necessarily relates to the success of optimization.},
 booktitle = {Proceedings of the 39th International Conference on Machine Learning},
 editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
 pdf = {https://proceedings.mlr.press/v162/vlaar22a/vlaar22a.pdf},
 series = {Proceedings of Machine Learning Research}
}

@inproceedings{Wang_2023_Plateau,
 author = {Wang, Xiang and Wang, Annie N. and Zhou, Mo and Ge, Rong},
 title = {Plateau in Monotonic Linear Interpolation --- A ``Biased'' View of Loss Landscape for Deep Networks},
 year = {2023},
 url = {https://openreview.net/forum?id=z289SIQOQna},
 booktitle = {The Eleventh International Conference on Learning Representations }
}

@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},
 archiveprefix = {arXiv},
 eprint = {2312.16143},
 eprintclass = {cs.LG},
 eprinttype = {arxiv}
}

@article{Neyshabur_2017_Implicit,
 author = {Neyshabur, Behnam},
 title = {Implicit Regularization in Deep Learning},
 year = {2017},
 month = {sep},
 url = {http://arxiv.org/abs/1709.01953v2},
 date = {2017-09-06T18:12:04Z},
 eprint = {1709.01953v2},
 eprintclass = {cs.LG},
 eprinttype = {arxiv},
 urldate = {2025-02-13T20:12:50.483287Z}
}

@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},
 number = {24},
 volume = {55},
 pages = {244008},
 url = {http://dx.doi.org/10.1088/1751-8121/ac6d8e},
 doi = {10.1088/1751-8121/ac6d8e},
 issn = {1751-8121}
}

@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{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},
 archiveprefix = {arXiv},
 eprint = {2309.04788},
 eprintclass = {cs.LG},
 eprinttype = {arxiv}
}

@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}
}

@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}
}