Pre-training and in-context learning IS Bayesian inference a la De Finetti

Accurately gauging uncertainty on the underlying environment is a longstanding goal of intelligent systems. We characterize which latent concepts pre-trained sequence models are naturally able to reason with. We go back to De Finetti's predictive view of Bayesian reasoning: instead of modeling latent parameters through priors and likelihoods like topic models do, De Finetti has long advocated for modeling exchangeable (permutation invariant) sequences of observables. According to this view, pre-training autoregressive models formulates informed beliefs based on prior observations ("empirical Bayes"), and forward generation is a simulated instantiation of an environment ("posterior inference"). This connection allows extending in-context learning (ICL) beyond predictive settings, highlighting sequence models' ability to perform explicit statistical inference. In particular, we show the sequence prediction loss over exchangeable documents controls performance on downstream tasks where uncertainty quantification is key. Empirically, we propose and demonstrate several approaches for encoding exchangeability in sequence model architectures: data augmentation, regularization, and causal masking.