2025/01/15 by Hongbin Chen, Chen, Hong-Bin, Victor Issa +1 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning and Algorithms #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2501.08786
openalex publication_date 2025/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this short note, we consider models of optimal Bayesian inference of finite-rank tensor products. We add to the model a linear channel parametrized by h. We show that at every interior differentiable point h of the free energy (associated with the model), the overlap concentrates at the gradient of the free energy and the minimum mean-square error converges to a related limit. In other words, the model is replica-symmetric at every differentiable point. At any signal-to-noise ratio, such points h form a full-measure set (hence h=0 belongs to the closure of these points). For a sufficiently low signal-to-noise ratio, we show that every interior point is a differentiable point.