predictive uncertainty

In-context learning (ICL) has emerged as a particularly remarkable characteristic of Large Language Models (LLM): given a pretrained LLM and an observed dataset, LLMs can make predictions for new data points from the same distribution without fine-tuning. Numerous works have postulated ICL as approximately Bayesian inference, rendering this a natural hypothesis. In this work, we analyse this hypothesis from a new angle through the martingale property, a fundamental requirement of a Bayesian learning system for exchangeable data. We show that the martingale property is a necessary condition for unambiguous predictions in such scenarios, and enables a principled, decomposed notion of uncertainty vital in trustworthy, safety-critical systems. We derive actionable checks with corresponding theory and test statistics which must hold if the martingale property is satisfied. We also examine if uncertainty in LLMs decreases as expected in Bayesian learning when more data is observed. In three experiments, we provide evidence for violations of the martingale property, and deviations from a Bayesian scaling behaviour of uncertainty, falsifying the hypothesis that ICL is Bayesian.

Reliable uncertainty estimates are crucial for deploying pretrained models; yet, many strong methods for quantifying uncertainty require retraining, Monte Carlo sampling, or expensive second-order computations and may alter a frozen backbone's predictions. To address this, we introduce Gaussian Process Activations (GAPA), a post-hoc method that shifts Bayesian modeling from weights to activations. GAPA replaces standard nonlinearities with Gaussian-process activations whose posterior mean exactly matches the original activation, preserving the backbone's point predictions by construction while providing closed-form epistemic variances in activation space. To scale to modern architectures, we use a sparse variational inducing-point approximation over cached training activations, combined with local k-nearest-neighbor subset conditioning, enabling deterministic single-pass uncertainty propagation without sampling, backpropagation, or second-order information. Across regression, classification, image segmentation, and language modeling, GAPA matches or outperforms strong post-hoc baselines in calibration and out-of-distribution detection while remaining efficient at test time.

Empowering large language models to accurately express confidence in their answers is essential for trustworthy decision-making. Previous confidence elicitation methods, which primarily rely on white-box access to internal model information or model fine-tuning, have become less suitable for LLMs, especially closed-source commercial APIs. This leads to a growing need to explore the untapped area of black-box approaches for LLM uncertainty estimation. To better break down the problem, we define a systematic framework with three components: prompting strategies for eliciting verbalized confidence, sampling methods for generating multiple responses, and aggregation techniques for computing consistency. We then benchmark these methods on two key tasks-confidence calibration and failure prediction-across five types of datasets (e.g., commonsense and arithmetic reasoning) and five widely-used LLMs including GPT-4 and LLaMA 2 Chat. Our analysis uncovers several key insights: 1) LLMs, when verbalizing their confidence, tend to be overconfident, potentially imitating human patterns of expressing confidence. 2) As model capability scales up, both calibration and failure prediction performance improve. 3) Employing our proposed strategies, such as human-inspired prompts, consistency among multiple responses, and better aggregation strategies can help mitigate this overconfidence from various perspectives. 4) Comparisons with white-box methods indicate that while white-box methods perform better, the gap is narrow, e.g., 0.522 to 0.605 in AUROC. Despite these advancements, none of these techniques consistently outperform others, and all investigated methods struggle in challenging tasks, such as those requiring professional knowledge, indicating significant scope for improvement. We believe this study can serve as a strong baseline and provide insights for eliciting confidence in black-box LLMs.

Complex multi-step reasoning tasks, such as solving mathematical problems, remain challenging for large language models (LLMs). While outcome supervision is commonly used, process supervision via process reward models (PRMs) provides intermediate rewards to verify step-wise correctness in solution traces. However, as proxies for human judgement, PRMs suffer from reliability issues, including susceptibility to reward hacking. In this work, we propose leveraging uncertainty quantification (UQ) to enhance the reliability of step-wise verification with generative reward models for mathematical reasoning tasks. We introduce CoT Entropy, a novel UQ method that outperforms existing approaches in quantifying a PRM's uncertainty in step-wise verification. Our results demonstrate that incorporating uncertainty estimates improves the robustness of judge-LM PRMs, leading to more reliable verification.

Generative Large Language Models (LLMs) are widely utilized for their excellence in various tasks. However, their tendency to produce inaccurate or misleading outputs poses a potential risk, particularly in high-stakes environments. Therefore, estimating the correctness of generative LLM outputs is an important task for enhanced reliability. Uncertainty Estimation (UE) in generative LLMs is an evolving domain, where SOTA probability-based methods commonly employ length-normalized scoring. In this work, we propose Meaning-Aware Response Scoring (MARS) as an alternative to length-normalized scoring for UE methods. MARS is a novel scoring function that considers the semantic contribution of each token in the generated sequence in the context of the question. We demonstrate that integrating MARS into UE methods results in a universal and significant improvement in UE performance. We conduct experiments using three distinct closed-book question-answering datasets across five popular pre-trained LLMs. Lastly, we validate the efficacy of MARS on a Medical QA dataset. Code can be found here.

In-context learning has emerged as a ground-breaking ability of Large Language Models (LLMs) and revolutionized various fields by providing a few task-relevant demonstrations in the prompt. However, trustworthy issues with LLM’s response, such as hallucination, have also been actively discussed. Existing works have been devoted to quantifying the uncertainty in LLM’s response, but they often overlook the complex nature of LLMs and the uniqueness of in-context learning. In this work, we delve into the predictive uncertainty of LLMs associated with in-context learning, highlighting that such uncertainties may stem from both the provided demonstrations (aleatoric uncertainty) and ambiguities tied to the model’s configurations (epistemic uncertainty). We propose a novel formulation and corresponding estimation method to quantify both types of uncertainties. The proposed method offers an unsupervised way to understand the prediction of in-context learning in a plug-and-play fashion. Extensive experiments are conducted to demonstrate the effectiveness of the decomposition. The code and data are available at: https://github.com/lingchen0331/UQ_ICL.

Uncertainty estimation (UE) of model predictions is a crucial step for a variety of tasks such as active learning, misclassification detection, adversarial attack detection, out-of-distribution detection, etc. Most of the works on modeling the uncertainty of deep neural networks evaluate these methods on image classification tasks. Little attention has been paid to UE in natural language processing. To fill this gap, we perform a vast empirical investigation of state-of-the-art UE methods for Transformer models on misclassification detection in named entity recognition and text classification tasks and propose two computationally efficient modifications, one of which approaches or even outperforms computationally intensive methods1.

Uncertainty quantification is a key component of modern machine learning systems. A popular approach for quantifying predictive uncertainty on neural network models is deep ensembles. However, training multiple independently initialized networks leads to prohibitive computational costs at both train time and test time. Alternatively, single-model approaches such as MC-dropout and its variants have been proposed but typically underperform relative to their ensemble-based counterparts. In this work we propose a simple method which brings together distance-awareness and spectral normalization for improving robustness to distributional shift while retaining model calibration. We demonstrate significant gains over baseline methods on benchmark tasks including out-of-distribution detection.

In safety-critical applications, language models should be able to characterize their uncertainty with meaningful probabilities. Many uncertainty quantification approaches require supervised data; however, finding suitable unseen challenging data is increasingly difficult for large language models trained on vast amounts of scraped data. If the model is consistently (and correctly) confident in its predictions, the uncertainty quantification method may consistently overestimate confidence on new and unfamiliar data. Finding data which exhibits enough uncertainty to train supervised uncertainty quantification methods for high-performance models may therefore be challenging, and will increase in difficulty as LLMs saturate datasets. To address this issue, we first introduce the problem of inducing artificial uncertainty in language models, then investigate methods of inducing artificial uncertainty on trivially easy data in the absence of challenging data at training time. We use probes trained to recognize artificial uncertainty on the original model, and find that these probes trained on artificial uncertainty outperform probes trained without artificial uncertainty in recognizing real uncertainty, achieving notably higher calibration on hard data with minimal loss of performance on easy data.

In many machine learning applications, it is important for the model to provide confidence scores that accurately capture its prediction uncertainty. Although modern learning methods have achieved great success in predictive accuracy, generating calibrated confidence scores remains a major challenge. Mixup, a popular yet simple data augmentation technique based on taking convex combinations of pairs of training examples, has been empirically found to significantly improve confidence calibration across diverse applications. However, when and how Mixup helps calibration is still a mystery. In this paper, we theoretically prove that Mixup improves calibration in high-dimensional settings by investigating natural statistical models. Interestingly, the calibration benefit of Mixup increases as the model capacity increases. We support our theories with experiments on common architectures and datasets. In addition, we study how Mixup improves calibration in semi-supervised learning. While incorporating unlabeled data can sometimes make the model less calibrated, adding Mixup training mitigates this issue and provably improves calibration. Our analysis provides new insights and a framework to understand Mixup and calibration.

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often referred to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of attempts so far at handling uncertainty in general and formalizing this distinction in particular.