Rajeev Verma

Rajeev Verma, Daniel Barrejón, Eric Nalisnick

We study the statistical properties of learning to defer (L2D) to multiple experts. In particular, we address the open problems of deriving a consistent surrogate loss, confidence calibration, and principled ensembling of experts. Firstly, we derive two consistent surrogates -- one based on a softmax parameterization, the other on a one-vs-all (OvA) parameterization -- that are analogous to the single expert losses proposed by Mozannar and Sontag (2020) and Verma and Nalisnick (2022), respectively. We then study the frameworks' ability to estimate P( m_j = y | x ), the probability that the jth expert will correctly predict the label for x. Theory shows the softmax-based loss causes mis-calibration to propagate between the estimates while the OvA-based loss does not (though in practice, we find there are trade offs). Lastly, we propose a conformal inference technique that chooses a subset of experts to query when the system defers. We perform empirical validation on tasks for galaxy, skin lesion, and hate speech classification.

Alejandro Monroy Muñoz, Rajeev Verma, Alexander Timans

Real-time online object tracking in videos constitutes a core task in computer vision, with wide-ranging applications including video surveillance, motion capture, and robotics. Deployed tracking systems usually lack formal safety assurances to convey when tracking is reliable and when it may fail, at best relying on heuristic measures of model confidence to raise alerts. To obtain such assurances we propose interpreting object tracking as a sequential hypothesis test, wherein evidence for or against tracking failures is gradually accumulated over time. Leveraging recent advancements in the field, our sequential test (formalized as an e-process) quickly identifies when tracking failures set in whilst provably containing false alerts at a desired rate, and thus limiting potentially costly re-calibration or intervention steps. The approach is computationally light-weight, requires no extra training or fine-tuning, and is in principle model-agnostic. We propose both supervised and unsupervised variants by leveraging either ground-truth or solely internal tracking information, and demonstrate its effectiveness for two established tracking models across four video benchmarks. As such, sequential testing can offer a statistically grounded and efficient mechanism to incorporate safety assurances into real-time tracking systems.

Tim Tomov, Dominik Fuchsgruber, Rajeev Verma et al.

LLM decoding often relies on the model's predictive distribution to generate an output. Consequently, misalignment with respect to the true generating distribution leads to suboptimal decisions in practice. While a natural solution is to calibrate the model's output distribution, for LLMs, this is ill-posed at the combinatorially vast level of free-form language. We address this by building on the insight that in many tasks, these free-form outputs can be interpreted in a semantically meaningful latent structure, for example, discrete class labels, integers, or sets. We introduce task calibration as a paradigm to calibrate the model's predictive distribution in the task-induced latent space. We apply a decision-theoretic result to show that Minimum Bayes Risk (MBR) decoding on the task-calibrated latent distribution is the optimal decoding strategy on latent model beliefs. Empirically, it consistently improves generation quality across different tasks and baselines. We also introduce Task Calibration Error (TCE), an application-aware calibration metric that quantifies the excess loss due to miscalibration. Our work demonstrates that task calibration enables more reliable model decisions across various tasks and applications.

Dharmesh Tailor, Aditya Patra, Rajeev Verma et al.

The learning to defer (L2D) framework allows autonomous systems to be safe and robust by allocating difficult decisions to a human expert. All existing work on L2D assumes that each expert is well-identified, and if any expert were to change, the system should be re-trained. In this work, we alleviate this constraint, formulating an L2D system that can cope with never-before-seen experts at test-time. We accomplish this by using meta-learning, considering both optimization- and model-based variants. Given a small context set to characterize the currently available expert, our framework can quickly adapt its deferral policy. For the model-based approach, we employ an attention mechanism that is able to look for points in the context set that are similar to a given test point, leading to an even more precise assessment of the expert's abilities. In the experiments, we validate our methods on image recognition, traffic sign detection, and skin lesion diagnosis benchmarks.

Alexander Timans, Rajeev Verma, Eric Nalisnick et al.

Machine learning systems deployed in the real world must operate under dynamic and often unpredictable distribution shifts. This challenges the validity of statistical safety assurances on the system's risk established beforehand. Common risk control frameworks rely on fixed assumptions and lack mechanisms to continuously monitor deployment reliability. In this work, we propose a general framework for the real-time monitoring of risk violations in evolving data streams. Leveraging the 'testing by betting' paradigm, we propose a sequential hypothesis testing procedure to detect violations of bounded risks associated with the model's decision-making mechanism, while ensuring control on the false alarm rate. Our method operates under minimal assumptions on the nature of encountered shifts, rendering it broadly applicable. We illustrate the effectiveness of our approach by monitoring risks in outlier detection and set prediction under a variety of shifts.

Jakub Podolak, Rajeev Verma

We study the source of uncertainty in DeepSeek R1-32B by analyzing its self-reported verbal confidence on question answering (QA) tasks. In the default answer-then-confidence setting, the model is regularly over-confident, whereas semantic entropy - obtained by sampling many responses - remains reliable. We hypothesize that this is because of semantic entropy's larger test-time compute, which lets us explore the model's predictive distribution. We show that granting DeepSeek the budget to explore its distribution by forcing a long chain-of-thought before the final answer greatly improves its verbal score effectiveness, even on simple fact-retrieval questions that normally require no reasoning. Furthermore, a separate reader model that sees only the chain can reconstruct very similar confidences, indicating the verbal score might be merely a statistic of the alternatives surfaced during reasoning. Our analysis concludes that reliable uncertainty estimation requires explicit exploration of the generative space, and self-reported confidence is trustworthy only after such exploration.

Rajeev Verma, Volker Fischer, Eric Nalisnick

Modern challenges of robustness, fairness, and decision-making in machine learning have led to the formulation of multi-distribution learning (MDL) frameworks in which a predictor is optimized across multiple distributions. We study the calibration properties of MDL to better understand how the predictor performs uniformly across the multiple distributions. Through classical results on decomposing proper scoring losses, we first derive the Bayes optimal rule for MDL, demonstrating that it maximizes the generalized entropy of the associated loss function. Our analysis reveals that while this approach ensures minimal worst-case loss, it can lead to non-uniform calibration errors across the multiple distributions and there is an inherent calibration-refinement trade-off, even at Bayes optimality. Our results highlight a critical limitation: despite the promise of MDL, one must use caution when designing predictors tailored to multiple distributions so as to minimize disparity.

Anurag Singh, Julian Rodemann, Rajeev Verma et al.

While high-stakes ML applications demand strict regulations, strategic ML providers often evade them to lower development costs. To address this challenge, we cast AI regulation as a mechanism design problem under uncertainty and introduce regulation mechanisms: a framework that maps empirical evidence from models to a license for some market share. The providers can select from a set of licenses, effectively forcing them to bet on their model's ability to fulfil regulation. We aim at regulation mechanisms that achieve perfect market outcome, i.e. (a) drive non-compliant providers to self-exclude, and (b) ensure participation from compliant providers. We prove that a mechanism has perfect market outcome if and only if the set of non-compliant distributions forms a credal set, i.e., a closed, convex set of probability measures. This result connects mechanism design and imprecise probability by establishing a duality between regulation mechanisms and the set of non-compliant distributions. We also demonstrate these mechanisms in practice via experiments on regulating use of spurious features for prediction and fairness. Our framework provides new insights at the intersection of mechanism design and imprecise probability, offering a foundation for development of enforceable AI regulations.

Rajeev Verma, Eric Nalisnick

The learning to defer (L2D) framework has the potential to make AI systems safer. For a given input, the system can defer the decision to a human if the human is more likely than the model to take the correct action. We study the calibration of L2D systems, investigating if the probabilities they output are sound. We find that Mozannar & Sontag's (2020) multiclass framework is not calibrated with respect to expert correctness. Moreover, it is not even guaranteed to produce valid probabilities due to its parameterization being degenerate for this purpose. We propose an L2D system based on one-vs-all classifiers that is able to produce calibrated probabilities of expert correctness. Furthermore, our loss function is also a consistent surrogate for multiclass L2D, like Mozannar & Sontag's (2020). Our experiments verify that not only is our system calibrated, but this benefit comes at no cost to accuracy. Our model's accuracy is always comparable (and often superior) to Mozannar & Sontag's (2020) model's in tasks ranging from hate speech detection to galaxy classification to diagnosis of skin lesions.

Richard McKinley, Lorenz Grunder, Rik Wepfer et al.

The detection of new or enlarged white-matter lesions in multiple sclerosis is a vital task in the monitoring of patients undergoing disease-modifying treatment for multiple sclerosis. However, the definition of 'new or enlarged' is not fixed, and it is known that lesion-counting is highly subjective, with high degree of inter- and intra-rater variability. Automated methods for lesion quantification hold the potential to make the detection of new and enlarged lesions consistent and repeatable. However, the majority of lesion segmentation algorithms are not evaluated for their ability to separate progressive from stable patients, despite this being a pressing clinical use-case. In this paper we show that change in volumetric measurements of lesion load alone is not a good method for performing this separation, even for highly performing segmentation methods. Instead, we propose a method for identifying lesion changes of high certainty, and establish on a dataset of longitudinal multiple sclerosis cases that this method is able to separate progressive from stable timepoints with a very high level of discrimination (AUC = 0.99), while changes in lesion volume are much less able to perform this separation (AUC = 0.71). Validation of the method on a second external dataset confirms that the method is able to generalize beyond the setting in which it was trained, achieving an accuracy of 83% in separating stable and progressive timepoints. Both lesion volume and count have previously been shown to be strong predictors of disease course across a population. However, we demonstrate that for individual patients, changes in these measures are not an adequate means of establishing no evidence of disease activity. Meanwhile, directly detecting tissue which changes, with high confidence, from non-lesion to lesion is a feasible methodology for identifying radiologically active patients.

Richard McKinley, Rik Wepfer, Fabian Aschwanden et al.

Segmentation of white matter lesions and deep grey matter structures is an important task in the quantification of magnetic resonance imaging in multiple sclerosis. In this paper we explore segmentation solutions based on convolutional neural networks (CNNs) for providing fast, reliable segmentations of lesions and grey-matter structures in multi-modal MR imaging, and the performance of these methods when applied to out-of-centre data. We trained two state-of-the-art fully convolutional CNN architectures on the 2016 MSSEG training dataset, which was annotated by seven independent human raters: a reference implementation of a 3D Unet, and a more recently proposed 3D-to-2D architecture (DeepSCAN). We then retrained those methods on a larger dataset from a single centre, with and without labels for other brain structures. We quantified changes in performance owing to dataset shift, and changes in performance by adding the additional brain-structure labels. We also compared performance with freely available reference methods. Both fully-convolutional CNN methods substantially outperform other approaches in the literature when trained and evaluated in cross-validation on the MSSEG dataset, showing agreement with human raters in the range of human inter-rater variability. Both architectures showed drops in performance when trained on single-centre data and tested on the MSSEG dataset. When trained with the addition of weak anatomical labels derived from Freesurfer, the performance of the 3D Unet degraded, while the performance of the DeepSCAN net improved. Overall, the DeepSCAN network predicting both lesion and anatomical labels was the best-performing network examined.