Modern generative models excel at producing realistic samples--images, text, molecules-- but often lack guarantees about structural properties. A protein generator may produce plausible sequences that violate stability constraints; a network topology generator may create graphs that fail connectivity requirements; a molecule generator may output structures violating chemical valence rules. Standard GAN discriminators provide a global "real vs. fake" signal, but they cannot pinpoint which specific structural constraint failed or guarantee that generated samples satisfy formal specifications. Meanwhile, mathematical logic has developed precise tools for reasoning about structural properties. Ehrenfeucht-Fraïssé (EF) games [1, 2] characterize when two structures are indistinguishable by logical formulas up to a given complexity (quantifier depth k). First-order (FO) and monadic second-order (MSO) logics can express rich structural properties--connectivity, bipartiteness, planarity, acyclicity--that are crucial in applications but invisible to standard discriminators.

Humanitarian organizations face a critical choice: invest in costly commercial APIs or rely on free open-weight models for multilingual human rights monitoring. While commercial systems offer reliability, open-weight alternatives lack empirical validation -- especially for low-resource languages common in conflict zones. This paper presents the first systematic comparison of commercial and open-weight large language models (LLMs) for human-rights-violation detection across seven languages, quantifying the cost-reliability trade-off facing resource-constrained organizations. Across 78,000 multilingual inferences, we evaluate six models -- four instruction-aligned (Claude-Sonnet-4, DeepSeek-V3, Gemini-Flash-2.0, GPT-4.1-mini) and two open-weight (LLaMA-3-8B, Mistral-7B) -- using both standard classification metrics and new measures of cross-lingual reliability: Calibration Deviation (CD), Decision Bias (B), Language Robustness Score (LRS), and Language Stability Score (LSS). Results show that alignment, not scale, determines stability: aligned models maintain near-invariant accuracy and balanced calibration across typologically distant and low-resource languages (e.g., Lingala, Burmese), while open-weight models exhibit significant prompt-language sensitivity and calibration drift. These findings demonstrate that multilingual alignment enables language-agnostic reasoning and provide practical guidance for humanitarian organizations balancing budget constraints with reliability in multilingual deployment.

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 $t^{-1/2}$.

Air pollution remains a critical environmental and public health concern in Indian megacities such as Delhi, Kolkata, and Mumbai, where sudden spikes in pollutant levels challenge timely intervention. Accurate Air Quality Index (AQI) forecasting is difficult due to the coexistence of linear trends, seasonal variations, and volatile nonlinear patterns. This paper proposes a hybrid forecasting framework that integrates LOESS decomposition, ARIMA modeling, and a multi-scale CNN-BiLSTM network with a residual-gated attention mechanism. The LOESS step separates the AQI series into trend, seasonal, and residual components, with ARIMA modeling the smooth components and the proposed deep learning module capturing multi-scale volatility in the residuals. Model hyperparameters are tuned via the Unified Adaptive Multi-Stage Metaheuristic Optimizer (UAMMO), combining multiple optimization strategies for efficient convergence. Experiments on 2021-2023 AQI datasets from the Central Pollution Control Board show that the proposed method consistently outperforms statistical, deep learning, and hybrid baselines across PM2.5, O3, CO, and NOx in three major cities, achieving up to 5-8% lower MSE and higher R^2 scores (>0.94) for all pollutants. These results demonstrate the framework's robustness, sensitivity to sudden pollution events, and applicability to urban air quality management.

Graph-based recommender systems are commonly trained in transductive settings, which limits their applicability to new users, items, or datasets. We propose NBF-Rec, a graph-based recommendation model that supports inductive transfer learning across datasets with disjoint user and item sets. Unlike conventional embedding-based methods that require retraining for each domain, NBF-Rec computes node embeddings dynamically at inference time. We evaluate the method on seven real-world datasets spanning movies, music, e-commerce, and location check-ins. NBF-Rec achieves competitive performance in zero-shot settings, where no target domain data is used for training, and demonstrates further improvements through lightweight fine-tuning. These results show that inductive transfer is feasible in graph-based recommendation and that interaction-level message passing supports generalization across datasets without requiring aligned users or items.

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.

Abstract-- Enabling robot teams to execute natural language commands requires translating high-level instructions into feasible, efficient multi-robot plans. While Large Language Models (LLMs) combined with Planning Domain Description Language (PDDL) offer promise for single-robot scenarios, existing approaches struggle with multi-robot coordination due to brittle task decomposition, poor scalability, and low coordination efficiency. We introduce PIP-LLM, a language-based coordination framework that consists of PDDL-based team-level planning and Integer Programming (IP) based robot-level planning. PIP-LLMs first decomposes the command by translating the command into a team-level PDDL problem and solves it to obtain a team-level plan, abstracting away robot assignment. Each team-level action represents a subtask to be finished by the team. Next, this plan is translated into a dependency graph representing the subtasks' dependency structure. Such a dependency graph is then used to guide the robot-level planning, in which each subtask node will be formulated as an IP-based task allocation problem, explicitly optimizing travel costs and workload while respecting robot capabilities and user-defined constraints. This separation of planning from assignment allows PIP-LLM to avoid the pitfalls of syntax-based decomposition and scale to larger teams. Experiments across diverse tasks show that PIP-LLM improves plan success rate, reduces maximum and average travel costs, and achieves better load balancing compared to state-of-the-art baselines. A long-standing goal in multi-robot research is to create systems that take concise human language commands and automatically generate executable coordination plans for robot teams.

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.

This paper studies Distributionally Robust Optimization (DRO), a fundamental framework for enhancing the robustness and generalization of statistical learning and optimization. An effective ambiguity set for DRO must involve distributions that remain consistent with the nominal distribution while being diverse enough to account for a variety of potential scenarios. Moreover, it should lead to tractable DRO solutions. To this end, we propose a diffusion-based ambiguity set design that captures various adversarial distributions beyond the nominal support space while maintaining consistency with the nominal distribution. Building on this ambiguity modeling, we propose Diffusion-based DRO (D-DRO), a tractable DRO algorithm that solves the inner maximization over the parameterized diffusion model space. We formally establish the stationary convergence performance of D-DRO and empirically demonstrate its superior Out-of-Distribution (OOD) generalization performance in a ML prediction task.