Bayesian manifolds in large pretrained transformers

Determine whether large pretrained transformer language models trained on natural text exhibit geometric Bayesian manifolds comparable to those observed in small transformers trained in Bayesian wind tunnels, specifically including orthogonal key bases, progressive query–key alignment, score–gradient structures, and low-dimensional value manifolds parameterized by posterior entropy.

Background

The paper introduces Bayesian wind tunnels—controlled tasks with analytic posteriors—showing that small transformers realize Bayesian inference through identifiable geometric structures: orthogonal key bases, progressive query–key alignment, and a low-dimensional value manifold parameterized by posterior entropy. These diagnostics provide a mechanistic bridge between behavior and internal computation.

Because natural-language tasks lack closed-form posteriors, directly verifying Bayesian computation in LLMs requires alternative evidence. The authors propose using the same geometric diagnostics to probe frontier LLMs, but explicitly note that whether similar manifolds appear in large models trained on natural text remains unresolved.