Transformers Can Learn Posterior Predictive Distributions In-Context
Prior-data fitted networks (PFNs) have recently emerged as a powerful approach for Bayesian prediction tasks, approximating the posterior predictive distribution (PPD) through in-context learning. Despite their strong empirical performance and ability to go beyond point predictions, theoretical understandings of the algorithmic capability of transformers to learn distributions in context are still lacking. Focusing on Gaussian process regression problems, we show by construction that transformers can implement a gradient descent algorithm targeting the posterior predictive mean and variance, followed by nonlinear mappings that yield binned probabilities of PPD. We study the error bounds o...
| Authors | Gyeonghun Kang, Changwoo J. Lee, Xiang Cheng |
|---|---|
| Primary category | stat.ML |
| Published | 26 May 2026 |
| Last updated at source | 26 May 2026 |
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