Tight Low Degree Hardness for Optimizing Pure Spherical Spin Glasses

Mark Sellke

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arXiv · 2504.04632

Tight Low Degree Hardness for Optimizing Pure Spherical Spin Glasses

Mark Sellke

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Abstract

We prove constant degree polynomial algorithms cannot optimize pure spherical $p$-spin Hamiltonians beyond the algorithmic threshold $\mathsf{ALG}(p)=2\sqrt{\frac{p-1}{p}}$. 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.

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math.PR cond-mat.dis-nn cs.DS math-ph math.MP

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Mark Sellke. 2025-04-06. Tight Low Degree Hardness for Optimizing Pure Spherical Spin Glasses. https://arxiv.org/abs/2504.04632

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