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.

Variational Pseudo Marginal Methods for Jet Reconstruction in Particle Physics

Reconstructing jets, which provide vital insights into the properties and histories of subatomic particles produced in high-energy collisions, is a main problem in data analyses in collider physics. This intricate task deals with estimating the latent structure of a jet (binary tree) and involves parameters such as particle energy, momentum, and types. While Bayesian methods offer a natural approach for handling uncertainty and leveraging prior knowledge, they face significant challenges due to the super-exponential growth of potential jet topologies as the number of observed particles increases. To address this, we introduce a Combinatorial Sequential Monte Carlo approach for inferring jet latent structures. As a second contribution, we leverage the resulting estimator to develop a variational inference algorithm for parameter learning. Building on this, we introduce a variational family using a pseudo-marginal framework for a fully Bayesian treatment of all variables, unifying the generative model with the inference process. We illustrate our method's effectiveness through experiments using data generated with a collider physics generative model, highlighting superior speed and accuracy across a range of tasks.