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We study efficient optimization of the Hamiltonians of multi-species spherical spin glasses.
A recurring theorem on determinants
Olga Taussky · 1949
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Real and Complex Analysis P. 2
Walter Rudin · 1970
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Phase diagrams of liquid helium mixtures and metamagnets: experiment and mean field theory
John M Kincaid and Ezechiel Godert David Cohen · 1975
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Solvable model of a spin-glass
David Sherrington and Scott Kirkpatrick · 1975
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Factoring absolutely convergent series
Robert E Jamison and William H Ruckle · 1976
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Infinite number of order parameters for spin-glasses
Giorgio Parisi · 1979
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Dynamic theory of the spin-glass phase
Haim Sompolinsky and Annette Zippelius · 1981
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I Ya Korenblit and EF Shender · 1985
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Marc Mézard and Miguel Angel Virasoro · 1985
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AC Zaanen · 1986
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Some rigorous results on the Sherrington-Kirkpatrick spin glass model
Michael Aizenman, Joel L Lebowitz, and David Ruelle · 1987
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Antiferromagnetic ising spin glass
Ya V Fyodorov, I Ya Korenblit, and EF Shender · 1987
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Phase transitions in frustrated metamagnets
Ya V Fyodorov, I Ya Korenblit, and EF Shender · 1987
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A mathematical reformulation of Derrida’s REM and GREM
David Ruelle · 1987
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Harry Joe · 1992
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Leticia F. Cugliandolo and Jorge Kurchan · 1994
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G Ben Arous and Alice Guionnet · 1995
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The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: the high temperature case
Francis Comets and Jacques Neveu · 1995
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Jean-Dominique Deuschel and Ofer Zeitouni · 1995
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G Ben Arous and Alice Guionnet · 1997
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Aging of spherical spin glasses
G Ben Arous, Amir Dembo, and Alice Guionnet · 2001
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The thermodynamic limit in mean field spin glass models
Francesco Guerra and Fabio Lucio Toninelli · 2002
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Extended variational principle for the Sherrington-Kirkpatrick spin-glass model
Michael Aizenman, Robert Sims, and Shannon L Starr · 2003
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The complexity of the spherical
Andrea Crisanti, Luca Leuzzi, and Tommaso Rizzo · 2003
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Complexity in mean-field spin-glass models: Ising p-spin
Andrea Crisanti, Luca Leuzzi, and Tommaso Rizzo · 2005
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Gérard Ben Arous, Amir Dembo, and Alice Guionnet · 2006
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Giorgio Parisi · 2006
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Free energy of the spherical mean field model
Michel Talagrand · 2006
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The Parisi formula
Michel Talagrand · 2006
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Gibbs states and the set of solutions of random constraint satisfaction problems
Florent Krzakala, Andrea Montanari, Federico Ricci-Tersenghi, Guilhem Semerjian, and Lenka Zdeborová · 2007
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Phase transitions in the coloring of random graphs
Lenka Zdeborová and Florent Krzakala · 2007
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Algorithmic barriers from phase transitions
Dimitris Achlioptas and Amin Coja-Oghlan · 2008
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KKM-type theorems for products of simplicegues and cutting sets and measures by straight lines
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Combinatorial approach to the interpolation method and scaling limits in sparse random graphs
Mohsen Bayati, David Gamarnik, and Prasad Tetali · 2010
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Mean Field Models for Spin Glasses: Volume I
Michel Talagrand · 2010
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Optimization—theory and applications: problems with ordinary differential equations
Lamberto Cesari · 2012
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Weakly differentiable functions: Sobolev spaces and functions of bounded variation
William P Ziemer · 2012
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Complexity of random smooth functions on the high-dimensional sphere
Optimization of Mean-Field Spin Glasses
Ahmed El Alaoui, Andrea Montanari, and Mark Sellke · 2021
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Matrix concentration inequalities and free probability
Afonso S Bandeira, March T Boedihardjo, and Ramon van Handel · 2021
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Triviality of the geometry of mixed
David Belius, Jiří Černý, Shuta Nakajima, and Marius Schmidt · 2021
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The high-dimensional asymptotics of first order methods with random data
Michael Celentano, Chen Cheng, and Andrea Montanari · 2021
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Average Gromov hyperbolicity and the Parisi ansatz
Sourav Chatterjee and Leila Sloman · 2021
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Antonio Auffinger and Gérard Ben Arous · 2013
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Random matrices and complexity of spin glasses
Antonio Auffinger, Gérard Ben Arous, and Jiří Černý · 2013
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High-dimensional random fields and random matrix theory
Yan V. Fyodorov · 2013
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The Parisi ultrametricity conjecture
Dmitry Panchenko · 2013
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Tomáš Roubíček · 2013
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Multi-species mean field spin glasses. rigorous results
Adriano Barra, Pierluigi Contucci, Emanuele Mingione, and Daniele Tantari · 2015
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Dmitry Panchenko · 2015
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Diffusions interacting through a random matrix: universality via stochastic Taylor expansion
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Universality for langevin-like spin glass dynamics
Amir Dembo, Eyal Lubetzky, and Ofer Zeitouni · 2021
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The overlap gap property and approximate message passing algorithms for
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Algorithmic obstructions in the random number partitioning problem
David Gamarnik and Eren C. Kızıldağ · 2021
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Tight Lipschitz Hardness for Optimizing Mean Field Spin Glasses
Brice Huang and Mark Sellke · 2021
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The ground state energy and concentration of complexity in spherical bipartite models
Pax Kivimae · 2021
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Complexity of bipartite spherical spin glasses
Benjamin McKenna · 2021
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Optimization of the Sherrington–Kirkpatrick Hamiltonian
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Following the Ground States of Full-RSB Spherical Spin Glasses
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TAP Approach for Multi-Species Spherical Spin Glasses II: the Free Energy of the Pure Models
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Concentration of the complexity of spherical pure
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Spectral Gap Estimates for Mixed
Arka Adhikari, Christian Brennecke, Changji Xu, and Horng-Tzer Yau · 2022
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Entropic independence: optimal mixing of down-up random walks
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Algorithmic Pure States for the Negative Spherical Perceptron
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Free energy in multi-species mixed p-spin spherical models
Erik Bates and Youngtak Sohn · 2022
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Algorithms and barriers in the symmetric binary perceptron model
David Gamarnik, Eren C Kızıldağ, Will Perkins, and Changji Xu · 2022
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Optimal low-degree hardness of maximum independent set
Alexander S Wein · 2022
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Local algorithms for Maximum Cut and Minimum Bisection on locally treelike regular graphs of large degree
Ahmed El Alaoui, Andrea Montanari, and Mark Sellke · 2023
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Optimization algorithms for multi-species spherical spin glasses
Brice Huang and Mark Sellke · 2023
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Strong topological trivialization of multi-species spherical spin glasses
Brice Huang and Mark Sellke · 2023
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Random Max-CSPs Inherit Algorithmic Hardness from Spin Glasses
Chris Jones, Kunal Marwaha, Juspreet Singh Sandhu, and Jonathan Shi · 2023
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The Threshold Energy of Low Temperature Langevin Dynamics for Pure Spherical Spin Glasses
Mark Sellke · 2023
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