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 -spin Hamiltonians beyond the algorithmic threshold . 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