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Tight Low Degree Hardness for Optimizing Pure Spherical Spin Glasses
April 06, 2025 Β· Declared Dead Β· π IEEE Annual Symposium on Foundations of Computer Science
"No code URL or promise found in abstract"
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Authors
Mark Sellke
arXiv ID
2504.04632
Category
math.PR
Cross-listed
cond-mat.dis-nn,
cs.DS,
math-ph
Citations
3
Venue
IEEE Annual Symposium on Foundations of Computer Science
Last Checked
5 months ago
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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