arXiv subjects

Eyke Hüllermeier

Publications and source records attributed to Eyke Hüllermeier.

At least 19 recordsLinked to original sources

arXiv2026

Linear-LLM-SCM: Benchmarking LLMs for Coefficient Elicitation in Linear-Gaussian Causal Models

Large language models (LLMs) have shown potential in identifying qualitative causal relations, but their ability to perform quantitative causal reasoning---estimating effect sizes that parametrize functional relationships---remains underexplored in continuous domains. We introduce Linear-LLM-SCM, a plug-and-play framework for evaluating LLMs on Linear Gaussian structural causal model parametrization when a directed acyclic graph (DAG) is given. The framework decomposes a DAG into local parent-child sets and prompts an LLM to produce a regression-style structural equation per node, which is aggregated and compared against available ground-truth parameters. Our experiments with seven real-world DAGs effect ground truth illustrate limitations of LLMs as quantitative causal parameterizers. Across most models, we observe variability in coefficient estimates and sensitivity to structural perturbations. We open-sourced the framework to further encourage the community to work on studies toward the use of LLM for causal effect elicitation in safety-critical domain, e.g., healthcare.

cs.LG↗

arXiv2026

The Boundaries of Automation: A Theory of Persistent Human Participation

The rapid progress of AI has intensified the long-standing pursuit of automation: replacing human participation with algorithms wherever possible. Implicit in this pursuit is the assumption that humans remain in the loop only because current AI systems are not yet sufficiently capable. This paper challenges that assumption. Rather than asking how far automation can extend, we ask where its conceptual limits lie and argue that human participation may persist even with highly capable AI systems for three distinct reasons. Technical or complementarity grounds arise when humans contribute capabilities or perspectives unavailable to AI. Normative or developmental grounds arise when participation itself is valuable for human agency or learning. Most importantly, emergence grounds arise from target emergence: in some activities, the target is not fully specified in advance but instead emerges through the interaction itself. In these cases, human participation is not merely a means of improving execution but is constitutive of the target being produced. Human--AI co-construction, understood as the joint production of outcomes by humans and AI systems, is therefore not simply a temporary response to imperfect AI, but a persistent feature of activities whose objectives emerge through participation. This perspective has important implications for the limits of automation and for the design, evaluation, and ethics of future AI systems.

cs.AI↗

arXiv2026

Evaluating Epistemic Uncertainty: Beyond OOD Detection and Active Learning

Current evaluation of epistemic uncertainty relies on tasks such as out-ofdistribution detection and active learning. However, the Bayes-optimal decision strategies for these tasks do not coincide with the scores commonly used to quantify epistemic uncertainty. Building on the epistemic reject-option framework, we evaluate epistemic uncertainty using its ability to identify regret, the reducible error. Formulating selective prediction as a constrained optimization over coverage, expected risk, and regret, we prove the optimal selector is a thresholded convex combination of the ground-truth aleatoric and epistemic uncertainties. This theoretical unification exposes a weakness in recent uncertainty disentanglement literature: we demonstrate that standard correlation metrics between learned components do not necessarily predict their actual operational utility. We instead propose to evaluate the achievable risk, regret, coverage surface of the decomposition as a diagnostic for joint disentanglement and utility. Benchmarking standard methods on datasets with dense human annotations reveals that decision-theoretic rankings can disagree substantially with proxy-task rankings, including pairwise rank inversions between methods that are top-ranked on one criterion and bottom-ranked on other.

cs.LG↗

arXiv2026

Quantification of Credal Uncertainty: A Distance-Based Approach

Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set, particularly in multiclass classification, remains underexplored. In this paper, we propose a distance-based approach to quantify total, aleatoric, and epistemic uncertainty for credal sets. Concretely, we introduce a family of such measures within the framework of Integral Probability Metrics (IPMs). The resulting quantities admit clear semantic interpretations, satisfy natural theoretical desiderata, and remain computationally tractable for common choices of IPMs. We instantiate the framework with the total variation distance and obtain simple, efficient uncertainty measures for multiclass classification. In the binary case, this choice recovers established uncertainty measures, for which a principled multiclass generalization has so far been missing. Empirical results confirm practical usefulness, with favorable performance at low computational cost.

cs.AI↗

arXiv2026

Optimal Conformal Prediction under Epistemic Uncertainty

Conformal prediction (CP) is a widely used frequentist framework to quantify uncertainty by constructing prediction sets with user-specified marginal coverage guarantees. In practice, CP is typically applied on top of probabilistic classifiers, which are able to express aleatoric but not epistemic uncertainty. In this paper, we consider the question of how to optimally employ CP on top of a more expressive formalism, namely credal sets, which can express both aleatoric and epistemic uncertainty. More specifically, we propose probabilistic Bernoulli prediction sets (BPS) and derive a variant that achieves conditional coverage for valid credal sets while remaining minimal in expected size. We then address the more realistic scenario in which the validity of the credal sets is not guaranteed. Assuming access to calibration data with ground-truth distributions over labels, we apply conformal risk control to BPS and derive a PAC-style guarantee: with high probability over the data, the achieved conditional coverage is at least the desired level. We validate our theoretical findings empirically over various datasets.

stat.ML↗

arXiv2026

An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression

Uncertainty quantification is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this work, we provide a formal way of representing uncertainty in continuous space, using a general parametric formulation, allowing for tractable analysis and evaluation of uncertainty measures. Within this framework, we propose a set of axioms that enable rigorous assessment of total, aleatoric, and epistemic uncertainty measures. Together, this allows for a theoretical examination of uncertainty measures and their corresponding properties. As a specific example, we compare the widely used entropy- and variance-based measures with respect to established predictive models and analyze their limitations and challenges in uncertainty quantification. Our work provides a principled way to understand and develop uncertainty measures in supervised regression, offering theoretical insights and practical guidelines for reliable uncertainty assessment.

cs.LG↗

arXiv2026

Uncertainty Quantification for Regression: A Unified Framework based on kernel scores

Regression tasks, notably in safety-critical domains, require reliable uncertainty quantification, yet the literature remains largely classification-focused. To address this, we introduce a family of measures for total, aleatoric, and epistemic uncertainty in multivariate regression based on strictly proper kernel scores. The framework provides a principled recipe for designing new uncertainty measures whose behavior, such as tail sensitivity or out-of-distribution responsiveness, is governed by the choice of the underlying kernel, while also encompassing existing measures under a joint analysis. We prove explicit correspondences between properties of the kernel and behavior of resulting uncertainty measures, yielding concrete design guidelines for practitioners. Extensive experiments across structured regression tasks, including spatial and functional domains, demonstrate effectiveness on downstream tasks such as out-of-distribution detection and active learning, and reveal that different kernel choices lead to distinct trade-offs, offering practitioners guidance for task-specific selection.

cs.LG↗

arXiv2026

OperatorSHAP: Fast and Accurate Shapley Value Estimation for Neural Operators

Understanding model predictions is essential for physical applications, where outputs often inform safety-critical decisions, such as structural load assessment, weather warnings, and clinical diagnosis. Shapley values satisfy many desirable properties as an attribution method, but their computational cost during inference hinders their practical use. Current amortized explainers, such as FastSHAP, are limited to homogeneous inputs, which is problematic for physical applications where data often comes from irregular grids and geometries. We introduce OperatorSHAP, a grid-agnostic attribution method and training procedure that allows us to train FastSHAP-like explainers for neural operators. We establish a theoretical framework for attributions in function space, connecting to Aumann-Shapley values. We further show that OperatorSHAP's explanations are consistent with state-of-the-art discrete Shapley values across resolutions and transfer across grid sizes without retraining.

cs.LG↗

arXiv2026

Uncertainty quantification via conformal prediction in data assimilation

Quantifying the evolution of uncertainty is critical to both probabilistic forecasting and data assimilation in numerical weather prediction. In this study, we investigate the applicability of conformal prediction (CP), a recent machine learning (ML) method, to quantify uncertainty in a controlled, idealized setting. We use the one dimensional modified shallow water model, designed to mimic the convective process. CP provides a set of possible outcomes with a chosen confidence level. Here, we compare and evaluate the average empirical coverage, the average interval length, miss low, miss high and average interval score loss (AISL) for three variants of CP, namely a) Standard CP, b) Normalized CP and c) Conformalized Quantile Regression. We further compare these CP-based uncertainty estimates with traditional ensemble-based measures such as standard deviation intervals and ensemble spread. In addition, we investigate the integration of CP-derived uncertainty within the data assimilation cycle through CP perturbations. Our results highlight the strengths and limitations of each approach, providing insight into the effectiveness of CP to complement common ensemble-based uncertainty quantification in simplified atmospheric models.

cs.LG↗

arXiv2026

Reliable Conformal Prediction for Ordinal Classification Using the Ranked Probability Score

Ordinal classification (OC) arises in high-stakes domains such as medicine and finance, where uncertainty quantification must account for the severity of ordinal errors. Conformal prediction (CP) provides distribution-free prediction sets with marginal coverage guarantees; however, its practical effectiveness depends critically on the choice of nonconformity function. We introduce a CP method for ordinal classification based on the ranked probability score (RPS), a proper scoring rule defined over cumulative predictive distributions. Although it reflects ordinal risk quite naturally, it has largely been neglected in conformal ordinal prediction (COP). When used as a measure of nonconformity, RPS yields median-centered contiguous prediction sets by construction. The method is model-agnostic, supports both assessed and grouped ordered categorical outcomes, and permits efficient implementation compared to greedy interval selection procedures. Across multiple ordinal image and tabular datasets, RPS-based CP produces contiguous prediction sets and strikes a favorable balance between prediction set width and the magnitude of ordinal miscoverage relative to existing CP methods.

cs.LG↗

arXiv2026

Information Leakage Detection through Approximate Bayes-optimal Prediction

In today's data-driven world, the proliferation of publicly available information raises security concerns due to the information leakage (IL) problem. IL involves unintentionally exposing sensitive information to unauthorized parties via observable system information. Conventional statistical approaches rely on estimating mutual information (MI) between observable and secret information for detecting ILs, face challenges of the curse of dimensionality, convergence, computational complexity, and MI misestimation. Though effective, emerging supervised machine learning based approaches to detect ILs are limited to binary system sensitive information and lack a comprehensive framework. To address these limitations, we establish a theoretical framework using statistical learning theory and information theory to quantify and detect IL accurately. Using automated machine learning, we demonstrate that MI can be accurately estimated by approximating the typically unknown Bayes predictor's log-loss and accuracy. Based on this, we show how MI can effectively be estimated to detect ILs. Our method performs superior to state-of-the-art baselines in an empirical study considering synthetic and real-world OpenSSL TLS server datasets.

stat.ML↗

arXiv2026

From ASR to ASP: Evaluating Prompt Attack Vulnerabilities Against Open-Source LLMs

Recent studies demonstrate that Large Language Models (LLMs) are vulnerable to attacks that generate harmful or sensitive outputs. As open-source LLMs are increasingly adopted in high-impact applications such as finance, law, and healthcare, systematically investigating their security risks is becoming increasingly important towards trustworthy LLM era. This paper comprehensively studies effective prompt injection attacks against 14 widely used open-source and three closed-source LLMs on five attack benchmarks. Moreover, existing evaluation metrics mostly only consider the attack success rate, overlooking uncertainty in model responses. Our proposed Attack Success Probability (ASP) additionally captures uncertain behaviors for evaluation, where the model may initially refuse a harmful request but subsequently provide harmful guidance or vice versa, reflecting inconsistency and ambiguity in attack feasibility. By systematically analyzing the effectiveness of prompt injection attacks, we propose a straightforward and effective hypnotism attack; results show that this attack causes aligned language models, including Stablelm2, Mistral, Openchat, and Vicuna, to generate objectionable behaviors, achieving around 90% ASP. They also indicate that ignore prefix attacks can break all 14 open-source LLMs, achieving over 60% ASP on a multi-categorical dataset. We find that moderately well-known LLMs exhibit higher vulnerability to prompt injection attacks, highlighting the need to raise public awareness and prioritize efficient mitigation strategies.

cs.CR↗

arXiv2026

What Uncertainties Do We Need for Dynamical Systems?

The distinction between aleatoric and epistemic uncertainty has received considerable attention in machine learning research, mainly in the context of supervised learning but also in other settings such as generative modeling. In this paper, we offer a machine learning perspective on uncertainty modeling for dynamical systems, which has been studied much less so far. In particular, we ask: what uncertainties do we need for dynamical systems? We discuss sources of uncertainty, clarify their nature (aleatoric or epistemic), and consider how the objectives of representing and quantifying uncertainty vary across different tasks.

cs.LG↗

arXiv2026

Calibrated Preference Learning: The Case of Label Ranking

Calibration, the alignment of predicted probabilities with true outcome frequencies, is essential for reliable decision-making. While extensively studied for classification and regression, calibration has not been formally addressed for probabilistic label ranking, where the goal is to predict a distribution over orderings of a label set. Naively treating rankings as classes ignores their structure and fails to capture important modalities such as pairwise and top-k predictions. We formalize calibration for label ranking and develop a hierarchy of notions covering full rankings, sub-rankings, and top-k rankings. We prove that full-rank calibration implies the others but not conversely, and sub-ranking and top-k calibration are incomparable. Empirically, we find popular label ranking models are often poorly calibrated, with substantial differences between sub-ranking and top-k metrics. Applying our framework to RLHF reward models, we find that calibration correlates strongly but not perfectly with benchmark accuracy, suggesting it captures a meaningful quality dimension beyond top-1 accuracy. These findings motivate future work on understanding the downstream effects of miscalibration and developing methods to correct it.

cs.LG↗

arXiv2026

Unification and Optimization of Robust Supervised Learning

The literature has proposed various robust alternatives to empirical risk minimisation to address failure modes such as distribution shift, label noise and finite-sample degeneracies. Examples include distributionally robust optimization, label smoothing, vicinal risk minimization, and Mixup. However, such approaches are typically developed in isolation, forcing practitioners to commit a priori to a single failure mode even when the dominant mode for the task is unclear. To address this, we organize a broad class of existing methods along three common design axes and derive a tractable training procedure that decomposes robust learning into sequential stages (reference distribution enrichment, input-space perturbation, label-space perturbation, and sample-level aggregation), each with a choice of stance (pessimistic, neutral, or optimistic). This results in a unified design space in which joint hyperparameter optimization can compose and configure robustness strategies suited to the task at hand. Across tabular, image, and reward modeling benchmarks, joint hyperparameter optimization is competitive with the best single-method baseline in each setting, offering a reliable default for practitioners who do not know a priori which failure mode dominates their task.

cs.LG↗

arXiv2026

CLANE: Continual Learning of Actions on Neuromorphic Hardware from Event Cameras

Recognizing and continuously learning novel human actions without forgetting prior classes is a requirement for emerging AR/VR and robotics applications. For these applications, both on-device processing and learning are essential for privacy and low-latency adaptation. Event cameras address the efficiency of visual sensing with sparse, asynchronous output that is naturally compatible with neuromorphic processing. Yet no prior system has deployed a continual on-device learning pipeline for event-based action recognition using neuromorphic hardware. We present CLANE, Continual Learning of Actions on Neuromorphic Hardware from Event Cameras, deployed end-to-end on Intel Loihi 2. CLANE combines a spiking 2D CNN for spatiotemporal feature extraction with CLP-SNN as its on-chip learning head, extended to action clips via a Temporal Aggregation Layer and a fixed-point Normalization Layer, both novel Loihi 2 modules. On THU E-ACT-50, a 50-class dataset captured under real-world conditions, CLANE achieves 70.4% accuracy in a continual learning task while delivering more than 100x energy reduction and 16x lower latency over a sequential CNN+GRU+CLP edge GPU baseline, validated through iso-algorithm cross-platform benchmarking across three evaluation levels.

cs.LG↗

arXiv2026

Proxy-Based Approximation of Shapley and Banzhaf Interactions

Shapley and Banzhaf interactions capture the complex dynamics inherent in modern machine learning applications. However, current estimators for these higher-order interactions trade off between speed and accuracy. To overcome this limitation, we introduce ProxySHAP. ProxySHAP reconciles the high sample efficiency of tree-based proxy models with a principled path to consistency via residual correction. On a theoretical level, we derive a polynomial-time generalization of interventional TreeSHAP to compute exact interaction indices for tree ensembles, successfully bypassing exponential tree-depth dependencies in prior methods. Furthermore, we formally analyze the residual adjustment strategy, characterizing the specific conditions under which Maximum Sample Reuse (MSR) corrects proxy bias without its variance scaling exponentially with interaction size. Extensive benchmarking demonstrates that ProxySHAP sets a new state-of-the-art standard for approximation quality, including in large-scale applications with thousands of features. By achieving the lowest error in both small- and large-budget regimes, ProxySHAP significantly outperforms the prior best estimators ProxySPEX and KernelSHAP-IQ, while also delivering superior performance on downstream explainability tasks.

cs.LG↗

arXiv2026

Uncertainty Quantification as a Principled Foundation for Explainable Artificial Intelligence: A Case Study of Counterfactual Explanations

In this paper we argue that, to its detriment, transparency research overlooks many foundational concepts of artificial intelligence. As an illustrating example we focus on uncertainty quantification in the context of counterfactual explainability, demonstrating that its broader adoption could address key challenges in the field. To this end, we show how uncertainty can provide a principled unifying framework for counterfactual explainability by expressing the core counterfactual properties in terms of uncertainty, allowing us to build two variants of an explainer upon them -- one based solely on uncertainty estimates and another pairing them with distance measured in the feature space. Our comprehensive experiments illustrate highly competitive performance of our framework when compared to many state-of-the-art methods despite its radically simple design. More broadly, the paper demonstrates that integrating artificial intelligence fundamentals into transparency research promises to yield more reliable, robust and understandable predictive models. We posit that making artificial intelligence explainability truly uncertainty-aware is the first step towards this goal.

cs.LG↗