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Tight Low Degree Hardness for Optimizing Pure Spherical Spin Glasses

Probability 2025-04-08 v1 Disordered Systems and Neural Networks Data Structures and Algorithms Mathematical Physics math.MP

Abstract

We prove constant degree polynomial algorithms cannot optimize pure spherical pp-spin Hamiltonians beyond the algorithmic threshold ALG(p)=2p1p\mathsf{ALG}(p)=2\sqrt{\frac{p-1}{p}}. The proof goes by transforming any hypothetical such algorithm into a Lipschitz one, for which hardness was shown previously by the author and B. Huang.

Keywords

Cite

@article{arxiv.2504.04632,
  title  = {Tight Low Degree Hardness for Optimizing Pure Spherical Spin Glasses},
  author = {Mark Sellke},
  journal= {arXiv preprint arXiv:2504.04632},
  year   = {2025}
}

Comments

18 pages

R2 v1 2026-06-28T22:48:47.117Z