Can Generative AI Solve Your In-Context Learning Problem? A Martingale Perspective

This work is about estimating when a conditional generative model (CGM) can solve an in-context learning (ICL) problem. An in-context learning problem comprises a conditional generative model (CGM), a dataset, and a prediction task. The CGM could be a foundation model. The dataset could be a collection of patient histories, test results, and recorded diagnoses. The prediction task could be 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. Bayesian model criticism is a reasonable approach to assess the suitability of a given CGM for an ICL problem from this perspective. However, approaches like posterior predictive checks (PPCs) often assume access to the likelihood and posterior defined by the Bayesian model. To address the unavailability of these distributions in contemporary CGMs, 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. We develop the generative predictive p-value, which enables PPCs and their cousins for contemporary CGMs. The generative predictive p-value is used to determine when the model is appropriate for an ICL problem. Our method only requires generating queries and responses from a CGM and evaluating their log probability. We evaluate our method on synthetic regression and natural language ICL tasks using large language models.