Algorithmic Pure States for the Negative Spherical Perceptron

Alaoui, A. El; Sellke, Mark

doi:10.1007/s10955-022-02976-6

Cited by 9 publications

(2 citation statements)

References 41 publications

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“…We prove Theorem 1 with an explicit algorithm based on AMP, following a recent line of work [ 4 , 5 , 21 , 24 , 26 ]. Such algorithms are shown to be Lipschitz (up to modification on a set with probability) in [ 15 , Sect.…”

Section: Introductionmentioning

confidence: 99%

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Optimization Algorithms for Multi-species Spherical Spin Glasses

Huang,

Sellke

2024

J Stat Phys

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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.

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Section: Introductionmentioning

confidence: 99%

“…Similarly to [ 5 , 24 ], our algorithm has two phases, a “root-finding" phase and a “tree-descending" phase. Roughly speaking, the set of points reachable by our algorithm has the geometry of a densely branching ultrametric tree, which is rooted at the origin when and more generally at a random point correlated with .…”

Section: Introductionmentioning

confidence: 99%