Current mathematical reasoning benchmarks for large language models (LLMs) are approaching saturation, with some achieving > 90% accuracy, and are increasingly compromised by training-set contamination. We introduce Putnam-AXIOM, a benchmark of 522 university-level competition problems drawn from the prestigious William Lowell Putnam Mathematical Competition, and Putnam-AXIOM Variation, an unseen companion set of 100 functional variants generated by programmatically perturbing variables and constants. The variation protocol produces an unlimited stream of equally difficult, unseen instances -- yielding a contamination-resilient test bed. On the Original set, OpenAI's o1-preview -- the strongest evaluated model -- scores 41.9%, but its accuracy drops by 19.6% (46.8% relative decrease) on the paired Variations. The remaining eighteen models show the same downward trend, ten of them with non-overlapping 95% confidence intervals. These gaps suggest memorization and highlight the necessity of dynamic benchmarks. We complement "boxed" accuracy with Teacher-Forced Accuracy (TFA), a lightweight metric that directly scores reasoning traces and automates natural language proof evaluations. Putnam-AXIOM therefore provides a rigorous, contamination-resilient evaluation framework for assessing advanced mathematical reasoning of LLMs. Data and evaluation code are publicly available at https://github.com/brando90/putnam-axiom.

Recent advances in audio-driven talking head generation have achieved impressive results in lip synchronization and emotional expression. However, they largely overlook the crucial task of facial attribute editing. This capability is indispensable for achieving deep personalization and expanding the range of practical applications, including user-tailored digital avatars, engaging online education content, and brand-specific digital customer service. In these key domains, flexible adjustment of visual attributes, such as hairstyle, accessories, and subtle facial features, is essential for aligning with user preferences, reflecting diverse brand identities and adapting to varying contextual demands. In this paper, we present FaceEditTalker, a unified framework that enables controllable facial attribute manipulation while generating high-quality, audio-synchronized talking head videos. Our method consists of two key components: an image feature space editing module, which extracts semantic and detail features and allows flexible control over attributes like expression, hairstyle, and accessories; and an audio-driven video generation module, which fuses these edited features with audio-guided facial landmarks to drive a diffusion-based generator. This design ensures temporal coherence, visual fidelity, and identity preservation across frames. Extensive experiments on public datasets demonstrate that our method achieves comparable or superior performance to representative baseline methods in lip-sync accuracy, video quality, and attribute controllability. Project page: https://peterfanfan.github.io/FaceEditTalker/

Due to the limits of science and its steep learning curve, we must rely on the expertise of others to develop our knowledge and skills.26 Toward this end, social media platforms have revolutionized how netizens--users who are actively engaged in online communities--gain knowledge and skills by facilitating the exchange of costless information with the public (for example, followers or influencers). Businesses around the world also use these platforms along with tools based on generative artificial intelligence (GenAI) to craft synthetic media, hoping to grow revenue by attracting more customers and improving their online experience.28 Generative AI tools can empower cyber threats and have cyberpsychological effects on netizens, allowing malicious actors to craft deepfakes in the form of disinformation, misinformation, and malinformation. Service providers not only must enhance GenAI tools to reduce hallucinations, but they also have a statutory duty to mitigate data-driven biases.

The basic question of delineating those statistical problems that are solvable without making any assumptions on the underlying data distribution has long animated statistics and learning theory. This paper characterizes when a convex M-estimation or stochastic optimization problem is solvable in such an assumption-free setting, providing a precise dividing line between solvable and unsolvable problems. The conditions we identify show, perhaps surprisingly, that Lipschitz continuity of the loss being minimized is not necessary for distribution free minimization, and they are also distinct from classical characterizations of learnability in machine learning.

Weinberger and Saul [2009]), adversarial training of quantum generative models [Dallaire-Demers and Killoran, 2018, Chakrabarti et al., 2019], and facility location optimization [Brimberg, 1995, Xue and Ye, 1997] may seem unrelated at first glance. Yet, all of them can be formulated as two-player zero-sum games where each player optimizes over a structured, convex strategy space. These strategy spaces take a diversity of forms--probability simplices, trace-one positive semidefinite (PSD) matrices, and Euclidean balls--reflecting different algebraic or geometric constraints. While this shared structure suggests the potential for unified solution methods, existing algorithms remain highly fragmented, often tailored to specific geometries in special structured problems. For instance, distance metric learning can be solved using the Frank-Wolfe algorithm [Ying and Li, 2012] or Nesterov's smoothing algorithm [Nesterov, 2007]; quantum zero-sum games can be tackled using the Matrix Multiplicative Weights Update algorithm [Jain and Watrous, 2009, Jain et al., 2022]; the celebrated Fermat-Weber facility location problem can be solved using interior point methods [Xue and Ye, 1997]. This fragmented landscape of algorithms and analyses calls for the design of broadly applicable algorithms for equilibrium learning in structured games.

In safety-critical deep learning applications, robustness measures the ability of neural models that handle imperceptible perturbations in input data, which may lead to potential safety hazards. Existing pre-deployment robustness assessment methods typically suffer from significant trade-offs between computational cost and measurement precision, limiting their practical utility. To address these limitations, this paper conducts a comprehensive comparative analysis of existing robustness definitions and associated assessment methodologies. We propose tower robustness to evaluate robustness, which is a novel, practical metric based on hypothesis testing to quantitatively evaluate probabilistic robustness, enabling more rigorous and efficient pre-deployment assessments. Our extensive comparative evaluation illustrates the advantages and applicability of our proposed approach, thereby advancing the systematic understanding and enhancement of model robustness in safety-critical deep learning applications.

Despite the growing use of large language models (LLMs) in clinical dialogue systems, existing evaluations focus on task completion or fluency, offering little insight into the behavioral and risk management requirements essential for safety-critical systems. This paper presents MATRIX (Multi-Agent simulaTion fRamework for safe Interactions and conteXtual clinical conversational evaluation), a structured, extensible framework for safety-oriented evaluation of clinical dialogue agents. MATRIX integrates three components: (1) a safety-aligned taxonomy of clinical scenarios, expected system behaviors and failure modes derived through structured safety engineering methods; (2) BehvJudge, an LLM-based evaluator for detecting safety-relevant dialogue failures, validated against expert clinician annotations; and (3) PatBot, a simulated patient agent capable of producing diverse, scenario-conditioned responses, evaluated for realism and behavioral fidelity with human factors expertise, and a patient-preference study. Across three experiments, we show that MATRIX enables systematic, scalable safety evaluation. BehvJudge with Gemini 2.5-Pro achieves expert-level hazard detection (F1 0.96, sensitivity 0.999), outperforming clinicians in a blinded assessment of 240 dialogues. We also conducted one of the first realism analyses of LLM-based patient simulation, showing that PatBot reliably simulates realistic patient behavior in quantitative and qualitative evaluations. Using MATRIX, we demonstrate its effectiveness in benchmarking five LLM agents across 2,100 simulated dialogues spanning 14 hazard scenarios and 10 clinical domains. MATRIX is the first framework to unify structured safety engineering with scalable, validated conversational AI evaluation, enabling regulator-aligned safety auditing. We release all evaluation tools, prompts, structured scenarios, and datasets.

Contemporary artificial intelligence (AI) development largely centers on rational decision-making, valued for its measurability and suitability for objective evaluation. Y et in real-world contexts, an intelligent agent's decisions are shaped not only by logic but also by deeper influences such as beliefs, values, and preferences. The diversity of human decision-making styles emerges from these differences, highlighting that "style" is an essential but often overlooked dimension of intelligence. This dissertation introduces playstyle as an alternative lens for observing and analyzing the decision-making behavior of intelligent agents, and examines its foundational meaning and historical context from a philosophical perspective. By analyzing how beliefs and values drive intentions and actions, we construct a two-tier framework for style formation: the external interaction loop with the environment and the internal cognitive loop of deliberation. On this basis, we formalize style-related characteristics and propose measurable indicators such as style capacity, style popularity, and evolutionary dynamics. The study focuses on three core research directions: (1) Defining and measuring playstyle, proposing a general playstyle metric based on discretized state spaces, and extending it to quantify strategic diversity and competitive balance; (2) Expressing and generating playstyle, exploring how reinforcement learning and imitation learning can be used to train agents exhibiting specific stylistic tendencies, and introducing a novel approach for human-like style learning and modeling; and (3) Practical applications, analyzing the potential of these techniques in domains such as game design and interactive entertainment. Finally, the dissertation outlines future extensions, including the role of style as a core element in building artificial general intelligence (AGI). By investigating stylistic variation, we aim to rethink autonomy, value expression, and even offer a tangible perspective on the ultimate i philosophical question: What is the soul?

Extremely low-resource languages, especially those written in rare scripts, as shown in Figure 1, remain largely unsupported by large language models (LLMs). This is due in part to compounding factors such as the lack of training data. This paper delivers the first comprehensive analysis of whether LLMs can acquire such languages purely via in-context learning (ICL), with or without auxiliary alignment signals, and how these methods compare to parameter-efficient fine-tuning (PEFT). We systematically evaluate 20 under-represented languages across three state-of-the-art multilingual LLMs. Our findings highlight the limitation of PEFT when both language and its script are extremely under-represented by the LLM. In contrast, zero-shot ICL with language alignment is impressively effective on extremely low-resource languages, while few-shot ICL or PEFT is more beneficial for languages relatively better represented by LLMs. For LLM practitioners working on extremely low-resource languages, we summarise guidelines grounded by our results on adapting LLMs to low-resource languages, e.g., avoiding fine-tuning a multilingual model on languages of unseen scripts.

The surge in the adoption of Intelligent Tutoring Systems (ITSs) in education, while being integral to curriculum-based learning, can inadvertently exacerbate performance gaps. To address this problem, student profiling becomes crucial for tracking progress, identifying struggling students, and alleviating disparities among students. Such profiling requires measuring student behaviors and performance across different aspects, such as content coverage, learning intensity, and proficiency in different concepts within a learning topic. In this study, we introduce CTGraph, a graph-level representation learning approach to profile learner behaviors and performance in a self-supervised manner. Our experiments demonstrate that CTGraph can provide a holistic view of student learning journeys, accounting for different aspects of student behaviors and performance, as well as variations in their learning paths as aligned to the curriculum structure. We also show that our approach can identify struggling students and provide comparative analysis of diverse groups to pinpoint when and where students are struggling. As such, our approach opens more opportunities to empower educators with rich insights into student learning journeys and paves the way for more targeted interventions.