Mathematical modeling is a cornerstone of scientific discovery and engineering practice, enabling the translation of real-world problems into formal systems across domains such as physics, biology, and economics. Unlike mathematical reasoning, which assumes a predefined formulation, modeling requires open-ended problem analysis, abstraction, and principled formalization. While Large Language Models (LLMs) have shown strong reasoning capabilities, they fall short in rigorous model construction, limiting their utility in real-world problem-solving. To this end, we formalize the task of LLM-powered real-world mathematical modeling, where agents must analyze problems, construct domain-appropriate formulations, and generate complete end-to-end solutions. We introduce MM-Bench, a curated benchmark of 111 problems from the Mathematical Contest in Modeling (MCM/ICM) 1, spanning the years 2000 to 2025 and across ten diverse domains such as physics, biology, and economics. To tackle this task, we propose MM-Agent, an expertinspired framework that decomposes mathematical modeling into four stages: openended problem analysis, structured model formulation, computational problem solving, and report generation. Experiments on MM-Bench show that MM-Agent significantly outperforms baseline agents, achieving an 11.88% improvement over human expert solutions while requiring only 15 minutes and $0.88 per task using GPT-4o. Furthermore, under official MCM/ICM protocols, MM-Agent assisted two undergraduate teams in winning the Finalist Award (top 2.0% among 27,456 teams) in MCM/ICM 2025, demonstrating its practical effectiveness as a modeling copilot.

The multi-armed bandit (MAB) is a fundamental online decision-making framework that has been extensively studied over the past two decades. To mitigate the high cost and slow convergence of purely online learning, modern MAB approaches have explored hybrid paradigms that leverage offline data to warm-start online learning. However, existing approaches face a significant limitation by assuming that the offline and online data are homogeneous--they share the same feedback structure and are drawn from the same underlying distribution. This assumption is often violated in practice, where offline data often originate from diverse sources and evolving environments, resulting in feedback heterogeneity and distributional shifts. In this work, we tackle the challenge of learning across this offline-online gap by developing a general hybrid bandit framework that incorporates heterogeneous offline data to improve online performance. We study two hybrid settings: (1) using reward-based offline data to accelerate online learning in preference-based bandits (i.e., dueling bandits), and (2) using preference-based offline data to improve online standard MAB algorithms. For both settings, we design novel algorithms and derive tight regret bounds that match or improve upon existing benchmarks despite heterogeneity. Empirical evaluations on both synthetic and real-world datasets further show the superior performance of our proposed methods over baseline algorithms.

Large-scale machine learning models deliver strong performance across a wide range of tasks but come with significant computational and resource constraints. To mitigate these challenges, local smaller models are often deployed alongside larger models, relying on routing and deferral mechanisms to offload complex tasks.

Artificial intelligence (AI) now permeates critical infrastructures and decisionmaking systems where failures produce social, economic, and democratic harm. This position paper challenges the entrenched belief that regulation and innovation are opposites. As evidenced by analogies from aviation, pharmaceuticals, and welfare systems and recent cases of synthetic misinformation, bias and unaccountable decision-making, the absence of well-designed regulation has already created immeasurable damage. Regulation, when thoughtful and adaptive, is not a brake on innovation--it is its foundation. The present position paper examines the EU AIAct as a model of risk-based, responsibility-driven regulation that addresses the Collingridge Dilemma: acting early enough to prevent harm, yet flexibly enough to sustain innovation. Its adaptive mechanisms--regulatory sandboxes, small and medium enterprises (SMEs) support, real-world testing, fundamental rights impact assessment (FRIA)--demonstrate how regulation can accelerate responsibly, rather than delay, technological progress. The position paper summarises how governance tools transform perceived burdens into tangible advantages: legal certainty, consumer trust, and ethical competitiveness.

While RLHF has demonstrated promising results, many algorithms are highly sensitive to misspecifications in the underlying preference model (e.g., the Bradley-Terry model), the reference policy, or the reward function, resulting in undesirable fine-tuning. To address model misspecification, we propose a doubly robust preference optimization algorithm that remains consistent when either the preference model or the reference policy is correctly specified (without requiring both). Our proposal demonstrates superior and more robust performance than state-of-the-art algorithms, both in theory and in practice.

Perturbation-based explanations are widely utilized to enhance the transparency of machine-learning models in practice. However, their reliability is often compromised by the unknown model behavior under the specific perturbations used. This paper investigates the relationship between uncertainty calibration - the alignment of model confidence with actual accuracy - and perturbation-based explanations. We show that models systematically produce unreliable probability estimates when subjected to explainability-specific perturbations and theoretically prove that this directly undermines global and local explanation quality. To address this, we introduce ReCalX, a novel approach to recalibrate models for improved explanations while preserving their original predictions. Empirical evaluations across diverse models and datasets demonstrate that ReCalX consistently reduces perturbationspecific miscalibration most effectively while enhancing explanation robustness and the identification of globally important input features.

The prediction of learning curves for Natural Language Processing (NLP) models enables informed decision-making to meet specific performance objectives, while reducing computational overhead and lowering the costs associated with dataset acquisition and curation. In this work, we formulate the prediction task as a multitask learning problem, where each task's data is modelled as being organized within a two-layer hierarchy. To model the shared information and dependencies across tasks and hierarchical levels, we employ latent variable multi-output Gaussian Processes, enabling to account for task correlations and supporting zero-shot prediction of learning curves (LCs). We demonstrate that this approach facilitates the development of probabilistic scaling laws at lower costs. Applying an active learning strategy, LCs can be queried to reduce predictive uncertainty and provide predictions close to ground truth scaling laws.

Language is the dress of thought.

Hallucinations in large language models (LLMs) pose significant safety concerns that impede their broader deployment. Recent research in hallucination detection has demonstrated that LLMs' internal representations contain truthfulness hints, which can be harnessed for detector training. However, the performance of these detectors is heavily dependent on the internal representations of predetermined tokens, fluctuating considerably when working on free-form generations with varying lengths and sparse distributions of hallucinated entities. To address this, we propose HaMI, a novel approach that enables robust detection of hallucinations through adaptive selection and learning of critical tokens that are most indicative of hallucinations. We achieve this robustness by an innovative formulation of the Hallucination detection task as Multiple Instance (HaMI) learning over token-level representations within a sequence, thereby facilitating a joint optimisation of token selection and hallucination detection on generation sequences of diverse forms. Comprehensive experimental results on four hallucination benchmarks show that HaMI significantly outperforms existing state-of-the-art approaches.

Time series analysis is a fundamental component of machine learning, especially in astrophysics and cosmology where temporal data abound. This chapter provides a pedagogical review of time series analysis techniques from a machine learning perspective. We cover the basic concepts of time series (stationarity, autocorrelation, seasonality), classical statistical models (autoregressive, moving average, ARIMA, exponential smoothing, state-space models), and modern machine learning approaches. In particular, we discuss how traditional statistical methods lay the groundwork, and then explore machine learning methods for time series, including feature-based regression, tree-based ensemble methods, hidden Markov models, Gaussian processes, and deep learning models (recurrent neural networks, convolutional networks, transformers). Throughout, we illustrate with examples drawn from multiple domains (e.g. astronomy, weather forecasting, finance) to emphasize common principles. The goal is to equip readers with both the theoretical understanding and practical context to apply machine learning techniques for time series analysis in their research.