The Replica-Symmetric Free Energy for Ising Spin Glasses with Orthogonally Invariant Couplings

Cited 9|Views14

Abstract

We study a variant of the Sherrington-Kirkpatrick (S-K) spin glass model withexternal field, where the random symmetric couplings matrix does not consist ofi.i.d. entries but is instead orthogonally invariant in law. For sufficientlyhigh temperature, we prove a replica-symmetric formula for the first-orderlimit of the model free energy. Our analysis is an adaptation of a conditionalsecond-moment-method argument previously introduced by Bolthausen for studyingthe high-temperature regime of the S-K model, where one conditions on theiterates of an Approximate Message Passing (AMP) algorithm for solving the TAPequations for the model magnetization. We apply this method using a memory-freeversion of AMP that is tailored to the orthogonally invariant structure of themodel couplings.

Translated text

Key words

Mean-field spin glasses,Free probability,AMP algorithms,60F10,60K35

Bibtex

AI Read Science

AI Summary

AI Summary is the key point extracted automatically understanding the full text of the paper, including the background, methods, results, conclusions, icons and other key content, so that you can get the outline of the paper at a glance.

Example

Background

Key content

Introduction

Methods

Results

Related work

Fund

Key content

Pretraining has recently greatly promoted the development of natural language processing (NLP)
We show that M6 outperforms the baselines in multimodal downstream tasks, and the large M6 with 10 parameters can reach a better performance
We propose a method called M6 that is able to process information of multiple modalities and perform both single-modal and cross-modal understanding and generation
The model is scaled to large model with 10 billion parameters with sophisticated deployment, and the 10 -parameter M6-large is the largest pretrained model in Chinese
Experimental results show that our proposed M6 outperforms the baseline in a number of downstream tasks concerning both single modality and multiple modalities We will continue the pretraining of extremely large models by increasing data to explore the limit of its performance

Try using models to generate summary,it takes about 60s

Must-Reading Tree

Example

Generate MRT to find the research sequence of this paper