Variational Autoencoders Reveal Hidden Mean-Field Structure in Complex Systems
Researchers established a theoretical framework showing that variational autoencoders (VAEs) can discover and decode latent mean-field structures in many-body systems, with a bound on VAE capacity derived from comparing latent channel rates to bipartite mutual information. The work demonstrates that successful VAE reconstructions provide direct evidence for underlying mean-field theories, with microscopic parameters readable from trained decoders. This bridges machine learning and statistical physics, enabling interpretable generative models for complex systems from neural recordings to physical systems.
The study addresses a key limitation of generative models: while they effectively capture correlations in many-body systems, their learned representations remain difficult to interpret physically. The authors establish an intuitive criterion quantifying VAE capacity to faithfully reconstruct joint probability distributions, deriving a bound by comparing latent channel rates to bipartite mutual information. A central finding is that conditionally independent decoders in successful VAEs are structurally identical to finite-size mean-field factorizations, meaning successful reconstruction directly evidences latent mean-field theory with readable microscopic parameters. Validation on solvable models (Curie-Weiss, Hopfield, Maier-Saupe) successfully recovered order parameters and pattern matrices. Application to salamander retinal recordings showed a two-latent VAE reproduces population statistics with two effective collective variables, recovering stored neural patterns and enabling a generalized Hopfield model matching experimental data.
What's missing
The study does not discuss computational complexity or scalability to larger systems, nor does it address limitations when mean-field assumptions break down in strongly correlated regimes. The generalizability of the approach to non-equilibrium systems or systems with long-range interactions beyond those tested is not explored.
What different sources said
- arXiv cs.LGCenter
Discovering and decoding latent mean-field structure with variational autoencoders
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