Hamilton-Jacobi equations for finite-rank matrix inference

2019/04/10 by Jean-Christophe Mourrat, Mourrat, Jean-Christophe · 2 citations
Computer Science · Engineering · #82B44 #82D30 #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Mathematics #FOS: Physical sciences #Matrix Theory and Algorithms #Probability (math.PR) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.1904.05294

openalex publication_date 2019/04/10 · openalex created_date 2019/04/25 · openalex updated_date 2026/07/28

Abstract

We compute the large-scale limit of the free energy associated with the problem of inference of a finite-rank matrix. The method follows the principle put forward in arXiv:1811.01432 which consists in identifying a suitable Hamilton-Jacobi equation satisfied by the limit free energy. We simplify the approach of arXiv:1811.01432 using a notion of weak solution of the Hamilton-Jacobi equation which is more convenient to work with and is applicable whenever the non-linearity in the equation is convex.

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• The Free Energy of an Enriched Continuous Random Energy Model in the Weak Correlation Regime
• Parisi's formula is a Hamilton-Jacobi equation in Wasserstein space

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