Experts Don't Cheat: Learning What You Don't Know By Predicting Pairs (2402.08733v2)

Abstract: Identifying how much a model ${\widehat{p}}{\theta}(Y|X)$ knows about the stochastic real-world process $p(Y|X)$ it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate $p(Y|X)$ and also estimate the remaining gaps between ${\widehat{p}}{\theta}(Y|X)$ and $p(Y|X)$: train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for $p(Y|X)$ and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) LLMing, and partially-observable navigation tasks, outperforming existing techniques.

• The paper introduces a novel paired-response strategy that quantifies epistemic uncertainty through calibrated cheating behavior.
• It extends traditional calibration to a second-order framework, enabling accurate confidence intervals and detection of statistical hallucinations.
• Empirical validations across image classification and reinforcement learning tasks demonstrate the method's superiority over standard uncertainty quantification techniques.

A Principled Approach for Quantifying Model Uncertainty through Paired Predictions and its Applications

Introduction

In the field of generative models, such as LLMs, accurately quantifying what the model does not know is crucial to prevent incorrect outputs or actions, especially in scenarios where model decisions can have significant consequences. Traditional probabilistic predictions struggle to differentiate between variability inherent to the data (aleatoric uncertainty) and the model’s own uncertainty due to lack of knowledge or data (epistemic uncertainty). Existing techniques for quantifying epistemic uncertainty often fall short, particularly when the model underfits the data. This research addresses these challenges by introducing a novel strategy for simultaneously approximating a true stochastic process and estimating the uncertainty in that approximation. The strategy is based on training models to predict paired responses and allowing them to "cheat" under controlled conditions, leading to a method that correlates model "cheating" behavior with its uncertainty about the process being modeled. The approach is shown to accurately estimate model knowledge across various tasks, outperforming existing uncertainty quantification baselines.

Methodology

Key to this paper is the introduction of second-order calibration, a concept that extends traditional (first-order) calibration to require models not only to predict an event's probability accurately but also to estimate the variance around that prediction correctly. The proposed method involves training models to predict independent pairs of responses from the true distribution, allowing the model to observe one response while predicting the other, and then measuring how much observation improves the prediction. The novelty lies in demonstrating that this cheating behavior, when properly calibrated, can serve as a robust indicator of the model's uncertainty.

Theoretical Contributions

The paper provides a rigorous theoretical foundation for the proposed approach. It demonstrates that a model's ability to improve its predictions through cheating is equivalent to being second-order calibrated. Furthermore, the paper proves that, given a second-order calibrated model, it is possible to construct frequentist confidence intervals for the true probabilities of outcomes and effectively detect incorrect model responses (statistical hallucinations) with high probability. This equivalence between paired-response prediction and second-order calibration underpins the development of new tools for uncertainty quantification without making restrictive assumptions about the data distribution.

Empirical Demonstrations

The effectiveness of the proposed method is empirically validated through applications to image classification, synthetic LLMing, and reinforcement learning tasks. These tasks are chosen to represent both discrete and sequential output spaces, as well as partially observable decision-making problems. Across these diverse settings, the method accurately quantifies the model's epistemic uncertainty and demonstrates its practical utility for improving model reliability. Notable is its application to offline reinforcement learning under partial observation, where it successfully avoids unsafe actions by accounting for unobserved confounders in decision-making processes.

Practical Implications and Future Directions

This research provides a significant step forward in understanding and quantifying model uncertainty, with implications for a broad range of AI applications. By improving how models estimate their own knowledge and uncertainty, the approach can contribute to safer AI systems that recognize and communicate their limitations, reducing the risk of unwarranted reliance on their outputs. Looking ahead, extending this approach to more complex and larger-scale models presents an exciting avenue for research. Additionally, exploring ways to operationalize paired predictions in settings where collecting paired responses may be challenging could further broaden the applicability of this strategy.

Concluding Remarks

In conclusion, this paper introduces a robust and theoretically grounded approach to uncertainty quantification for generative models, addressing a critical need in the development of reliable AI systems. Through a combination of theoretical insights and empirical validation, it establishes a framework for more accurately capturing and communicating what models do not know, paving the way for the creation of AI systems that can more safely interact with the real world.