Thermodynamic Response Functions in Singular Bayesian Models
Singular statistical models-including mixtures, matrix factorization, and neural networks-violate regular asymptotics due to parameter non-identifiability and degenerate Fisher geometry. Although singular learning theory characterizes marginal likelihood behavior through invariants such as the real log canonical threshold and singular fluctuation, these quantities remain difficult to interpret operationally. At the same time, widely used criteria such as WAIC and WBIC appear disconnected from underlying singular geometry. We show that posterior tempering induces a one-parameter deformation of the posterior distribution whose associated observables generate a hierarchy of thermodynamic res...
| Authors | Sean Plummer |
|---|---|
| Primary category | stat.ML |
| Published | 5 March 2026 |
| Last updated at source | 5 March 2026 |
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