Large Language Bayes Is Not Reparameterisation-Invariant
Large Language Bayes (LLB) answers an informal modelling question by sampling candidate probabilistic programs from a language model, running approximate inference on each, and averaging them with weights proportional to an exponentiated evidence bound. We show that this weighting depends on how a model is written. The log marginal likelihood is invariant to reparameterisation; the evidence bound is not. On eight schools the centered and non-centered programs are the same measure to $5.7\times10^{-14}$, yet their weights differ by $6.1\times$; importance weighting reduces this only to $2.2\times$, and reproducing the inference LLB actually runs, a full-covariance Gaussian matched to the p...
| Authors | Jian Xu |
|---|---|
| Primary category | cs.LG |
| Published | 24 September 2026 |
| Last updated at source | 24 September 2026 |
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