# Tight Low Degree Hardness for Optimizing Pure Spherical Spin Glasses

arXiv: https://arxiv.org/abs/2504.04632 · HTML: https://mlsanity.com/paper/2504.04632/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2025.

## Built on by (most cited first, 1 of 1)

- [Ultrametric OGP - parametric RDT symmetric binary perceptron connection](https://mlsanity.com/paper/2604.19712/) (2026)

## Abstract (arXiv)

We prove constant degree polynomial algorithms cannot optimize pure spherical p-spin Hamiltonians beyond the algorithmic threshold mathsfALG(p)=2√fracp-1p. 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.