The convergence analysis of online learning algorithms is central to machine learning theory, where last-iterate convergence is particularly important, as it captures the learner's actual decisions and describes the evolution of the learning process over time. However, in multi-armed bandits, most existing algorithmic analyses mainly focus on the order of regret, while the last-iterate (simple regret) convergence rate remains less explored -- especially for the widely studied Follow-the-Regularized-Leader (FTRL) algorithms. Recently, a growing line of work has established the Best-of-Both-Worlds (BOBW) property of FTRL algorithms in bandit problems, showing in particular that they achieve logarithmic regret in stochastic bandits. Nevertheless, their last-iterate convergence rate has not yet been studied. Intuitively, logarithmic regret should correspond to a $t^{-1}$ last-iterate convergence rate. This paper partially confirms this intuition through theoretical analysis, showing that the Bregman divergence, defined by the regular function $Ψ(p)=-4\sum_{i=1}^{d}\sqrt{p_i}$ associated with the BOBW FTRL algorithm $1/2$-Tsallis-INF (arXiv:1807.07623), between the point mass on the optimal arm and the probability distribution over the arm set obtained at iteration $t$, decays at a rate of $t^{-1/2}$.

Automatically assessing handwritten mathematical solutions is an important problem in educational technology with practical applications, but it remains a significant challenge due to the diverse formats, unstructured layouts, and symbolic complexity of student work. To address this challenge, we introduce VEHME-a Vision-Language Model for Evaluating Handwritten Mathematics Expressions-designed to assess open-form handwritten math responses with high accuracy and interpretable reasoning traces. VEHME integrates a two-phase training pipeline: (i) supervised fine-tuning using structured reasoning data, and (ii) reinforcement learning that aligns model outputs with multi-dimensional grading objectives, including correctness, reasoning depth, and error localization. To enhance spatial understanding, we propose an Expression-Aware Visual Prompting Module, trained on our synthesized multi-line math expressions dataset to robustly guide attention in visually heterogeneous inputs. Evaluated on AIHub and FERMAT datasets, VEHME achieves state-of-the-art performance among open-source models and approaches the accuracy of proprietary systems, demonstrating its potential as a scalable and accessible tool for automated math assessment. Our training and experiment code is publicly available at our GitHub repository.

As Large Vision-Language Models (LVLMs) are increasingly deployed in domains such as shopping, health, and news, they are exposed to pervasive persuasive content. A critical question is how these models function as persuadees-how and why they can be influenced by persuasive multimodal inputs. Understanding both their susceptibility to persuasion and the effectiveness of different persuasive strategies is crucial, as overly persuadable models may adopt misleading beliefs, override user preferences, or generate unethical or unsafe outputs when exposed to manipulative messages. We introduce MMPersuade, a unified framework for systematically studying multimodal persuasion dynamics in LVLMs. MMPersuade contributes (i) a comprehensive multimodal dataset that pairs images and videos with established persuasion principles across commercial, subjective and behavioral, and adversarial contexts, and (ii) an evaluation framework that quantifies both persuasion effectiveness and model susceptibility via third-party agreement scoring and self-estimated token probabilities on conversation histories. Our study of six leading LVLMs as persuadees yields three key insights: (i) multimodal inputs substantially increase persuasion effectiveness-and model susceptibility-compared to text alone, especially in misinformation scenarios; (ii) stated prior preferences decrease susceptibility, yet multimodal information maintains its persuasive advantage; and (iii) different strategies vary in effectiveness across contexts, with reciprocity being most potent in commercial and subjective contexts, and credibility and logic prevailing in adversarial contexts. By jointly analyzing persuasion effectiveness and susceptibility, MMPersuade provides a principled foundation for developing models that are robust, preference-consistent, and ethically aligned when engaging with persuasive multimodal content.

Speech Language Models (SLMs) have made significant progress in spoken language understanding. Yet it remains unclear whether they can fully perceive non lexical vocal cues alongside spoken words, and respond with empathy that aligns with both emotional and contextual factors. Existing benchmarks typically evaluate linguistic, acoustic, reasoning, or dialogue abilities in isolation, overlooking the integration of these skills that is crucial for human-like, emotionally intelligent conversation. We present EchoMind, the first interrelated, multi-level benchmark that simulates the cognitive process of empathetic dialogue through sequential, context-linked tasks: spoken-content understanding, vocal-cue perception, integrated reasoning, and response generation. All tasks share identical and semantically neutral scripts that are free of explicit emotional or contextual cues, and controlled variations in vocal style are used to test the effect of delivery independent of the transcript. EchoMind is grounded in an empathy-oriented framework spanning 3 coarse and 12 fine-grained dimensions, encompassing 39 vocal attributes, and evaluated using both objective and subjective metrics. Testing 12 advanced SLMs reveals that even state-of-the-art models struggle with high-expressive vocal cues, limiting empathetic response quality. Analyses of prompt strength, speech source, and ideal vocal cue recognition reveal persistent weaknesses in instruction-following, resilience to natural speech variability, and effective use of vocal cues for empathy. These results underscore the need for SLMs that integrate linguistic content with diverse vocal cues to achieve truly empathetic conversational ability.

Big Language Models (LLMs) are changing the way businesses use software, the way people live their lives and the way industries work. Companies like Google, High-Flyer, Anthropic, OpenAI and Meta are making better LLMs. So, it's crucial to look at how each model is different in terms of performance, moral behaviour and usability, as these differences are based on the different ideas that built them. This study compares five top LLMs: Google's Gemini, High-Flyer's DeepSeek, Anthropic's Claude, OpenAI's GPT models and Meta's LLaMA. It performs this by analysing three important factors: Performance and Accuracy, Ethics and Bias Mitigation and Usability and Integration. It was found that Claude has good moral reasoning, Gemini is better at multimodal capabilities and has strong ethical frameworks. DeepSeek is great at reasoning based on facts, LLaMA is good for open applications and ChatGPT delivers balanced performance with a focus on usage. It was concluded that these models are different in terms of how well they work, how easy they are to use and how they treat people ethically, making it a point that each model should be utilised by the user in a way that makes the most of its strengths.

Preserving linguistic diversity is necessary as every language offers a distinct perspective on the world. There have been numerous global initiatives to preserve endangered languages through documentation. This paper is a part of a project which aims to develop a trilingual (Toto-Bangla-English) language learning application to digitally archive and promote the endangered Toto language of West Bengal, India. This application, designed for both native Toto speakers and non-native learners, aims to revitalize the language by ensuring accessibility and usability through Unicode script integration and a structured language corpus. The research includes detailed linguistic documentation collected via fieldwork, followed by the creation of a morpheme-tagged, trilingual corpus used to train a Small Language Model (SLM) and a Transformer-based translation engine. The analysis covers inflectional morphology such as person-number-gender agreement, tense-aspect-mood distinctions, and case marking, alongside derivational strategies that reflect word-class changes. Script standardization and digital literacy tools were also developed to enhance script usage. The study offers a sustainable model for preserving endangered languages by incorporating traditional linguistic methodology with AI. This bridge between linguistic research with technological innovation highlights the value of interdisciplinary collaboration for community-based language revitalization.

Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and interpretable concept that captures intrinsic geometric structure and underpins numerous tasks, from community detection to geometric deep learning. A wide range of discrete curvature models have been proposed for various data representations, including graphs, simplicial complexes, cubical complexes, and point clouds sampled from manifolds. These models not only provide efficient characterizations of data geometry but also constitute essential components in geometric learning frameworks. In this paper, we present the first comprehensive review of existing discrete curvature models, covering their mathematical foundations, computational formulations, and practical applications in data analysis and learning. In particular, we discuss discrete curvature from both Riemannian and metric geometry perspectives and propose a systematic pipeline for curvature-driven data analysis. We further examine the corresponding computational algorithms across different data representations, offering detailed comparisons and insights. Finally, we review state-of-the-art applications of curvature in both supervised and unsupervised learning. This survey provides a conceptual and practical roadmap for researchers to gain a better understanding of discrete curvature as a fundamental tool for geometric understanding and learning.

Prediction-Powered Inference (PPI) is a recently proposed statistical inference technique for parameter estimation that leverages pseudo-labels on both labeled and unlabeled data to construct an unbiased, low-variance estimator. In this work, we extend its core idea to semi-supervised learning (SSL) for model training, introducing a novel unbiased gradient estimator. This extension addresses a key challenge in SSL: while unlabeled data can improve model performance, its benefit heavily depends on the quality of pseudo-labels. Inaccurate pseudo-labels can introduce bias, leading to suboptimal models.To balance the contributions of labeled and pseudo-labeled data, we utilize an interpolation parameter and tune it on the fly, alongside the model parameters, using a one-dimensional online learning algorithm. We verify the practical advantage of our approach through experiments on both synthetic and real datasets, demonstrating improved performance over classic SSL baselines and PPI methods that tune the interpolation parameter offline.

Object state recognition aims to identify the specific condition of objects, such as their positional states (e.g., open or closed) and functional states (e.g., on or off). While recent Vision-Language Models (VLMs) are capable of performing a variety of multimodal tasks, it remains unclear how precisely they can identify object states. To alleviate this issue, we introduce the STAte and Transition UnderStanding Benchmark (STATUS Bench), the first benchmark for rigorously evaluating the ability of VLMs to understand subtle variations in object states in diverse situations. Specifically, STATUS Bench introduces a novel evaluation scheme that requires VLMs to perform three tasks simultaneously: object state identification (OSI), image retrieval (IR), and state change identification (SCI). These tasks are defined over our fully hand-crafted dataset involving image pairs, their corresponding object state descriptions and state change descriptions. Furthermore, we introduce a large-scale training dataset, namely STATUS Train, which consists of 13 million semi-automatically created descriptions. This dataset serves as the largest resource to facilitate further research in this area. In our experiments, we demonstrate that STATUS Bench enables rigorous consistency evaluation and reveal that current state-of-the-art VLMs still significantly struggle to capture subtle object state distinctions. Surprisingly, under the proposed rigorous evaluation scheme, most open-weight VLMs exhibited chance-level zero-shot performance. After fine-tuning on STATUS Train, Qwen2.5-VL achieved performance comparable to Gemini 2.0 Flash. These findings underscore the necessity of STATUS Bench and Train for advancing object state recognition in VLM research.

As information technology advances, education is moving from one-size-fits-all instruction toward personalized learning. However, most methods handle modeling, item selection, and feedback in isolation rather than as a closed loop. This leads to coarse or opaque student models, assumption-bound adaptivity that ignores diagnostic posteriors, and generic, non-actionable feedback. To address these limitations, this paper presents an end-to-end personalized learning agent, EduLoop-Agent, which integrates a Neural Cognitive Diagnosis model (NCD), a Bounded-Ability Estimation Computerized Adaptive Testing strategy (BECAT), and large language models (LLMs). The NCD module provides fine-grained estimates of students' mastery at the knowledge-point level; BECAT dynamically selects subsequent items to maximize relevance and learning efficiency; and LLMs convert diagnostic signals into structured, actionable feedback. Together, these components form a closed-loop framework of ``Diagnosis--Recommendation--Feedback.'' Experiments on the ASSISTments dataset show that the NCD module achieves strong performance on response prediction while yielding interpretable mastery assessments. The adaptive recommendation strategy improves item relevance and personalization, and the LLM-based feedback offers targeted study guidance aligned with identified weaknesses. Overall, the results indicate that the proposed design is effective and practically deployable, providing a feasible pathway to generating individualized learning trajectories in intelligent education.