We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have proposed such decompositions, they lack the type of formal guarantees we provide. Our method is based on the new notion of higher-order calibration, which generalizes ordinary calibration to the setting of higher-order predictors that predict _mixtures_ over label distributions at every point. We show how to measure as well as achieve higher-order calibration using access to $k$-snapshots, namely examples where each point has $k$ independent conditional labels. Under higher-order calibration, the estimated aleatoric uncertainty at a point is guaranteed to match the real-world aleatoric uncertainty averaged over all points where the prediction is made. To our knowledge, this is the first formal guarantee of this type that places no assumptions whatsoever on the real-world data distribution. Importantly, higher-order calibration is also applicable to existing higher-order predictors such as Bayesian and ensemble models and provides a natural evaluation metric for such models. We demonstrate through experiments that our method produces meaningful uncertainty decompositions in tasks such as image classification.

We study the feasibility of identifying *epistemic* uncertainty (reflecting a lack of knowledge), as opposed to *aleatoric* uncertainty (reflecting entropy in the underlying distribution), in the outputs of large language models (LLMs) over free-form text. In the absence of ground-truth probabilities, we explore a setting where, in order to (approximately) disentangle a given LLM's uncertainty, a significantly larger model stands in as a proxy for the ground truth. We show that small linear probes trained on the embeddings of frozen, pretrained models accurately predict when larger models will be more confident at the token level and that probes trained on one text domain generalize to others. Going further, we propose a fully unsupervised method that achieves non-trivial accuracy on the same task. Taken together, we interpret these results as evidence that LLMs naturally contain internal representations of different types of uncertainty that could potentially be leveraged to devise more informative indicators of model confidence in diverse practical settings. Code can be found at: https://github.com/KempnerInstitute/llm_uncertainty

Multiple sequence alignments (MSAs) of proteins encode rich biological information and have been workhorses in bioinformatic methods for tasks like protein design and protein structure prediction for decades. Recent breakthroughs like AlphaFold2 that use transformers to attend directly over large quantities of raw MSAs have reaffirmed their importance. Generation of MSAs is highly computationally intensive, however, and no datasets comparable to those used to train AlphaFold2 have been made available to the research community, hindering progress in machine learning for proteins. To remedy this problem, we introduce OpenProteinSet, an open-source corpus of more than 16 million MSAs, associated structural homologs from the Protein Data Bank, and AlphaFold2 protein structure predictions. We have previously demonstrated the utility of OpenProteinSet by successfully retraining AlphaFold2 on it. We expect OpenProteinSet to be broadly useful as training and validation data for 1) diverse tasks focused on protein structure, function, and design and 2) large-scale multimodal machine learning research.