Bayesian Wind Tunnels for Model Selection
Prior work has shown that transformers can perform exact Bayesian filtering within a fixed hypothesis class. Can they also perform Bayesian model selection -- identifying the correct hypothesis class from data? We introduce model-selection Bayesian wind tunnels: controlled environments where ground-truth posteriors over hypothesis classes are available in closed form. Using fixed-point-free involutions -- whose defining property f(f(x))=x is purely relational -- a 2.8M-parameter transformer achieves 0.01-bit entropy agreement with the Bayesian optimum (3 seeds), with both integer tokens and opaque symbols whose meanings change every episode. This extends to non-nested comparisons: involut...
| Authors | Siddhartha R Dalal, Vishal Misra, Abhay Parekh |
|---|---|
| Primary category | cs.LG |
| Published | 1 July 2026 |
| Last updated at source | 1 July 2026 |
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