Optimization Algorithms for Multi-species Spherical Spin Glasses
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10955_2024_Article_3242.pdf
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Author(s)
Huang, Brice
Sellke, Mark
Date Issued
February 24, 2024
Journal
Journal of Statistical Physics
Publisher
Springer Science and Business Media LLC
Citation
Huang, B., Sellke, M. Optimization Algorithms for Multi-species Spherical Spin Glasses. J Stat Phys 191, 29 (2024).
Version
Final published version
Abstract
This paper develops approximate message passing algorithms to optimize multi-species spherical spin glasses. We first show how to efficiently achieve the algorithmic threshold energy identified in our companion work (Huang and Sellke in arXiv preprint, 2023. arXiv:2303.12172), thus confirming that the Lipschitz hardness result proved therein is tight. Next we give two generalized algorithms which produce multiple outputs and show all of them are approximate critical points. Namely, in an r-species model we construct $$2^r$$
2 r approximate critical points when the external field is stronger than a “topological trivialization" phase boundary, and exponentially many such points in the complementary regime. We also compute the local behavior of the Hamiltonian around each. These extensions are relevant for another companion work (Huang and Sellke in arXiv preprint, 2023. arXiv:2308.09677) on topological trivialization of the landscape.
2 r approximate critical points when the external field is stronger than a “topological trivialization" phase boundary, and exponentially many such points in the complementary regime. We also compute the local behavior of the Hamiltonian around each. These extensions are relevant for another companion work (Huang and Sellke in arXiv preprint, 2023. arXiv:2308.09677) on topological trivialization of the landscape.
Subjects
Mathematical Physics
Statistical and Nonlinear Physics
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10955-024-03242-7
