This work is about estimating when a conditional generative model (CGM) can solve an in-context learning (ICL) problem. An in-context learning (ICL) problem comprises a CGM, a dataset, and a prediction task. The CGM could be a multi-modal foundation model; the dataset, a collection of patient histories, test results, and recorded diagnoses; and the prediction task to communicate a diagnosis to a new patient. A Bayesian interpretation of ICL assumes that the CGM computes a posterior predictive distribution over an unknown Bayesian model defining a joint distribution over latent explanations and observable data. From this perspective, Bayesian model criticism is a reasonable approach to assess the suitability of a given CGM for an ICL problem. However, such approaches---like posterior predictive checks (PPCs)---often assume that we can sample from the likelihood and posterior defined by the Bayesian model, which are not explicitly given for contemporary CGMs. To address this, we show when ancestral sampling from the predictive distribution of a CGM is equivalent to sampling datasets from the posterior predictive of the assumed Bayesian model. Then we develop the generative predictive $p$-value, which enables PPCs and their cousins for contemporary CGMs. The generative predictive $p$-value can be used in a statistical decision procedure to determine when the model is appropriate for an ICL problem. Our method only requires generating queries and responses from a CGM and evaluating its response log probability. Using large language models, we empirically evaluate our method on tasks involving tabular data, imaging data, and natural language data.

This paper proposes a step toward approximate Bayesian inference in on-policy actor-critic deep reinforcement learning. It is implemented through three changes to the Asynchronous Advantage Actor-Critic (A3C) algorithm: (1) applying a ReLU function to advantage estimates, (2) spectral normalization of actor-critic weights, and (3) incorporating *dropout as a Bayesian approximation*. We prove under standard assumptions that restricting policy updates to positive advantages optimizes for value by maximizing a lower bound on the value function plus an additive term. We show that the additive term is bounded proportional to the Lipschitz constant of the value function, which offers theoretical grounding for spectral normalization of critic weights. Finally, our application of dropout corresponds to approximate Bayesian inference over both the actor and critic parameters, which enables *adaptive state-aware* exploration around the modes of the actor via Thompson sampling. We demonstrate significant improvements for median and interquartile mean metrics over A3C, PPO, SAC, and TD3 on the MuJoCo continuous control benchmark and improvement over PPO in the challenging ProcGen generalization benchmark.

Probabilistic prediction aims to compute predictive distributions rather than single point predictions. These distributions enable practitioners to quantify uncertainty, compute risk, and detect outliers. However, most probabilistic methods assume parametric responses, such as Gaussian or Poisson distributions. When these assumptions fail, such models lead to bad predictions and poorly calibrated uncertainty. In this paper, we propose Treeffuser, an easy-to-use method for probabilistic prediction on tabular data. The idea is to learn a conditional diffusion model where the score function is estimated using gradient-boosted trees. The conditional diffusion model makes Treeffuser flexible and non-parametric, while the gradient-boosted trees make it robust and easy to train on CPUs. Treeffuser learns well-calibrated predictive distributions and can handle a wide range of regression tasks---including those with multivariate, multimodal, and skewed responses. We study Treeffuser on synthetic and real data and show that it outperforms existing methods, providing better calibrated probabilistic predictions. We further demonstrate its versatility with an application to inventory allocation under uncertainty using sales data from Walmart. We implement Treeffuser in https://github.com/blei-lab/treeffuser.

This paper presents a method for estimating the hallucination rate for in-context learning (ICL) with generative AI. In ICL, a conditional generative model (CGM) is prompted with a dataset and a prediction question and asked to generate a response. One interpretation of ICL assumes that the CGM computes the posterior predictive of an unknown Bayesian model, which implicitly defines a joint distribution over observable datasets and latent mechanisms. This joint distribution factorizes into two components: the model prior over mechanisms and the model likelihood of datasets given a mechanism. With this perspective, we define a \textit{hallucination} as a generated response to the prediction question with low model likelihood given the mechanism. We develop a new method that takes an ICL problem and estimates the probability that a CGM will generate a hallucination. Our method only requires generating prediction questions and responses from the CGM and evaluating its response log probability. We empirically evaluate our method using large language models for synthetic regression and natural language ICL tasks.

Large language models (LLMs) demonstrate surprising capabilities, but we do not understand how they are implemented. One hypothesis suggests that these capabilities are primarily executed by small subnetworks within the LLM, known as circuits. But how can we evaluate this hypothesis? In this paper, we formalize a set of criteria that a circuit is hypothesized to meet and develop a suite of hypothesis tests to evaluate how well circuits satisfy them. The criteria focus on the extent to which the LLM's behavior is preserved, the degree of localization of this behavior, and whether the circuit is minimal. We apply these tests to six circuits described in the research literature. We find that synthetic circuits -- circuits that are hard-coded in the model -- align with the idealized properties. Circuits discovered in Transformer models satisfy the criteria to varying degrees. To facilitate future empirical studies of circuits, we created the \textit{circuitry} package, a wrapper around the \textit{TransformerLens} library, which abstracts away lower-level manipulations of hooks and activations. The software is available at \url{https://github.com/blei-lab/circuitry}.