How Well Do Prior-Data Fitted Networks Amortize Bayesian Inference?
Prior-data fitted networks (PFNs) are trained to approximate the Bayesian posterior predictive distribution (PPD) of a synthetic prior, yet results about the approximation quality are surprisingly thin. Taking an empirical risk minimization perspective, we decompose the deployment error of PFNs into prior, context, and amortization error, and measure the latter against a reference PPD under a realistic prior. Results show that PFNs generally recover the targeted PPD very well. Nevertheless, we find that parts of the residual amortization error persist, especially in \textit{rare} settings under the prior pretraining distribution, even when scaling the model size, which manifests in disagr...
| Authors | Manuel Hülskamp, Julius Kobialka, Emanuel Sommer et al. |
|---|---|
| Primary category | stat.ML |
| Published | 9 October 2026 |
| Last updated at source | 9 October 2026 |
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