Discovering and decoding latent mean-field structure with variational autoencoders

2026-06-07 · Source: Machine Learning · Field: Science & Research — Physical Sciences & Chemistry, Artificial Intelligence & Machine Learning, Life Sciences & Biology · Depth: Expert, quick

Summary

Generative models are increasingly used to capture correlations in many-body systems, yet their learned representations often lack physical interpretability. This research establishes an intuitive criterion quantifying a variational autoencoder's (VAE) capacity to faithfully reconstruct a many-body system's joint probability distribution. A bound on VAE capacity is derived by comparing the latent channel rate to the data's bipartite mutual information. The study demonstrates that any successful VAE's conditionally independent decoder is structurally identical to a finite-size mean-field factorization. This implies that successful reconstruction directly evidences a latent mean-field theory, with its microscopic parameters readable from the trained decoder. The findings are validated on solvable models like Curie-Weiss, Hopfield, and Maier-Saupe, recovering the full Hopfield pattern matrix. Applied to Salamander retinal recordings, a two-latent VAE reproduced population statistics with two collective variables, recovering "stored patterns" and enabling a generalized Hopfield model for experimental data.

Key takeaway

For research scientists modeling complex many-body systems, this work offers a novel way to interpret VAEs. You can now use a VAE's successful reconstruction as direct evidence for an underlying latent mean-field theory. This allows you to extract the microscopic parameters of that theory directly from the trained decoder, providing physical interpretability to otherwise opaque generative models and guiding further theoretical development.

Key insights

A VAE's successful reconstruction of many-body systems reveals a latent mean-field theory, decodable from its structure.

Principles

• VAE capacity relates to data's bipartite mutual information.
• Successful VAE decoders mimic mean-field factorization.
• Decoder parameters reveal microscopic theory.

Method

A bound on VAE capacity is obtained by comparing the rate of the latent channel to the bipartite mutual information of the data. This bound quantifies reconstruction fidelity.

In practice

• Recover Hopfield pattern matrices from equilibrium samples.
• Identify collective variables in neural population data.
• Formulate generalized Hopfield models from VAE outputs.

Topics

• Variational Autoencoders
• Many-Body Systems
• Mean-Field Theory
• Latent Variable Models
• Statistical Mechanics
• Neural Population Dynamics

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.