# Optimization Algorithms for Multi-Species Spherical Spin Glasses

arXiv: https://arxiv.org/abs/2308.09672 · HTML: https://mlsanity.com/paper/2308.09672/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2023.

## 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)

This paper develops approximate message passing algorithms to optimize multi-species spherical spin glasses. We first show how to efficiently achieve the algorithmic threshold energy identified in our companion work, thus confirming that the Lipschitz hardness result proved therein is tight. Next we give two generalized algorithms which produce multiple outputs and show all of them are approximate critical points. Namely, in an r-species model we construct 2r approximate critical points when the external field is stronger than a "topological trivialization" phase boundary, and exponentially many such points in the complementary regime. We also compute the local behavior of the Hamiltonian around each. These extensions are relevant for another companion work on topological trivialization of the landscape.