An essential element of human mathematical reasoning is our number sense -- an abstract understanding of numbers and their relationships -- which allows us to solve problems involving vast number spaces using limited computational resources. Mathematical reasoning of Large Language Models (LLMs) is often tested on high-level problems (such as Olympiad challenges, geometry, word problems, and puzzles), but their low-level number sense remains less explored. We introduce "Numberland," a 100-problem test to evaluate the numerical reasoning abilities of LLM-based agents. The tasks -- basic operations, advanced calculations (e.g., exponentiation, complex numbers), prime number checks, and the 24 game -- aim to test elementary skills and their integration in solving complex and uncertain problems. We evaluated five LLM-based agents: OpenAI's o1 and o1-mini, Google Gemini, Microsoft Copilot, and Anthropic Claude. They scored 74-95% on the first three tasks that allow deterministic steps to solutions. In the 24 game, which needs trial-and-error search, performance dropped to 10-73%. We tested the top 24 solver (o1 with 73% accuracy) on 25 harder problems, and its score fell to 27%, confirming search as a bottleneck. These results, along with the types of mistakes, suggest a fragile number of LLMs, which is a bit surprising given their prowess in challenging benchmarks. The limits of LLM numerical reasoning highlight the scope of simple, targeted tests to evaluate and explain LLM math skills to ensure safe use.

The Axiom-Based Atlas is a novel framework that structurally represents mathematical theorems as proof vectors over foundational axiom systems. By mapping the logical dependencies of theorems onto vectors indexed by axioms - such as those from Hilbert geometry, Peano arithmetic, or ZFC - we offer a new way to visualize, compare, and analyze mathematical knowledge. This vector-based formalism not only captures the logical foundation of theorems but also enables quantitative similarity metrics - such as cosine distance - between mathematical results, offering a new analytic layer for structural comparison. Using heatmaps, vector clustering, and AI-assisted modeling, this atlas enables the grouping of theorems by logical structure, not just by mathematical domain. We also introduce a prototype assistant (Atlas-GPT) that interprets natural language theorems and suggests likely proof vectors, supporting future applications in automated reasoning, mathematical education, and formal verification. This direction is partially inspired by Terence Tao's recent reflections on the convergence of symbolic and structural mathematics. The Axiom-Based Atlas aims to provide a scalable, interpretable model of mathematical reasoning that is both human-readable and AI-compatible, contributing to the future landscape of formal mathematical systems.

Humans acquire language through implicit learning, absorbing complex patterns without explicit awareness. While LLMs demonstrate impressive linguistic capabilities, it remains unclear whether they exhibit human-like pattern recognition during in-context learning at inferencing level. We adapted three classic artificial language learning experiments spanning morphology, morphosyntax, and syntax to systematically evaluate implicit learning at inferencing level in two state-of-the-art OpenAI models: gpt-4o and o3-mini. Our results reveal linguistic domain-specific alignment between models and human behaviors, o3-mini aligns better in morphology while both models align in syntax.

Issuing timely severe weather warnings helps mitigate potentially disastrous consequences. Recent advancements in Neural Weather Models (NWMs) offer a computationally inexpensive and fast approach for forecasting atmospheric environments on a 0.25{\deg} global grid. For thunderstorms, these environments can be empirically post-processed to predict wind gust distributions at specific locations. With the Pangu-Weather NWM, we apply a hierarchy of statistical and deep learning post-processing methods to forecast hourly wind gusts up to three days ahead. To ensure statistical robustness, we constrain our probabilistic forecasts using generalised extreme-value distributions across five regions in Switzerland. Using a convolutional neural network to post-process the predicted atmospheric environment's spatial patterns yields the best results, outperforming direct forecasting approaches across lead times and wind gust speeds. Our results confirm the added value of NWMs for extreme wind forecasting, especially for designing more responsive early-warning systems.

Large Language Models (LLMs) have made significant strides in problem-solving by incorporating reasoning processes. However, this enhanced reasoning capability results in an increased number of output tokens during inference, leading to higher computational costs. To address this challenge, we propose TwT (Thinking without Tokens), a method that reduces inference-time costs through habitual reasoning distillation with multi-teachers' guidance, while maintaining high performance. Our approach introduces a Habitual Reasoning Distillation method, which internalizes explicit reasoning into the model's habitual behavior through a Teacher-Guided compression strategy inspired by human cognition. Additionally, we propose Dual-Criteria Rejection Sampling (DCRS), a technique that generates a high-quality and diverse distillation dataset using multiple teacher models, making our method suitable for unsupervised scenarios. Experimental results demonstrate that TwT effectively reduces inference costs while preserving superior performance, achieving up to a 13.6% improvement in accuracy with fewer output tokens compared to other distillation methods, offering a highly practical solution for efficient LLM deployment.

Large Language Models (LLMs) offer a promising approach to enhancing Explainable AI (XAI) by transforming complex machine learning outputs into easy-to-understand narratives, making model predictions more accessible to users, and helping bridge the gap between sophisticated model behavior and human interpretability. AI models, such as state-of-the-art neural networks and deep learning models, are often seen as "black boxes" due to a lack of transparency. As users cannot fully understand how the models reach conclusions, users have difficulty trusting decisions from AI models, which leads to less effective decision-making processes, reduced accountabilities, and unclear potential biases. A challenge arises in developing explainable AI (XAI) models to gain users' trust and provide insights into how models generate their outputs. With the development of Large Language Models, we want to explore the possibilities of using human language-based models, LLMs, for model explainabilities. This survey provides a comprehensive overview of existing approaches regarding LLMs for XAI, and evaluation techniques for LLM-generated explanation, discusses the corresponding challenges and limitations, and examines real-world applications. Finally, we discuss future directions by emphasizing the need for more interpretable, automated, user-centric, and multidisciplinary approaches for XAI via LLMs.

Advancements in large language models (LLMs) have enabled the development of intelligent educational tools that support inquiry-based learning across technical domains. In cybersecurity education, where accuracy and safety are paramount, systems must go beyond surface-level relevance to provide information that is both trustworthy and domain-appropriate. To address this challenge, we introduce CyberBOT, a question-answering chatbot that leverages a retrieval-augmented generation (RAG) pipeline to incorporate contextual information from course-specific materials and validate responses using a domain-specific cybersecurity ontology. The ontology serves as a structured reasoning layer that constrains and verifies LLM-generated answers, reducing the risk of misleading or unsafe guidance. CyberBOT has been deployed in a large graduate-level course at Arizona State University (ASU), where more than one hundred students actively engage with the system through a dedicated web-based platform. Computational evaluations in lab environments highlight the potential capacity of CyberBOT, and a forthcoming field study will evaluate its pedagogical impact. By integrating structured domain reasoning with modern generative capabilities, CyberBOT illustrates a promising direction for developing reliable and curriculum-aligned AI applications in specialized educational contexts.

Retrieval Augmented Generation (RAG) frameworks have shown significant promise in leveraging external knowledge to enhance the performance of large language models (LLMs). However, conventional RAG methods often retrieve documents based solely on surface-level relevance, leading to many issues: they may overlook deeply buried information within individual documents, miss relevant insights spanning multiple sources, and are not well-suited for tasks beyond traditional question answering. In this paper, we propose Insight-RAG, a novel framework designed to address these issues. In the initial stage of Insight-RAG, instead of using traditional retrieval methods, we employ an LLM to analyze the input query and task, extracting the underlying informational requirements. In the subsequent stage, a specialized LLM -- trained on the document database -- is queried to mine content that directly addresses these identified insights. Finally, by integrating the original query with the retrieved insights, similar to conventional RAG approaches, we employ a final LLM to generate a contextually enriched and accurate response. Using two scientific paper datasets, we created evaluation benchmarks targeting each of the mentioned issues and assessed Insight-RAG against traditional RAG pipeline. Our results demonstrate that the Insight-RAG pipeline successfully addresses these challenges, outperforming existing methods by a significant margin in most cases. These findings suggest that integrating insight-driven retrieval within the RAG framework not only enhances performance but also broadens the applicability of RAG to tasks beyond conventional question answering.

Physical human-robot interaction (pHRI) remains a key challenge for achieving intuitive and safe interaction with robots. Current advancements often rely on external tactile sensors as interface, which increase the complexity of robotic systems. In this study, we leverage the intrinsic tactile sensing capabilities of collaborative robots to recognize digits drawn by humans on an uninstrumented touchpad mounted to the robot's flange. We propose a dataset of robot joint torque signals along with corresponding end-effector (EEF) forces and moments, captured from the robot's integrated torque sensors in each joint, as users draw handwritten digits (0-9) on the touchpad. The pHRI-DIGI-TACT dataset was collected from different users to capture natural variations in handwriting. To enhance classification robustness, we developed a data augmentation technique to account for reversed and rotated digits inputs. A Bidirectional Long Short-Term Memory (Bi-LSTM) network, leveraging the spatiotemporal nature of the data, performs online digit classification with an overall accuracy of 94\% across various test scenarios, including those involving users who did not participate in training the system. This methodology is implemented on a real robot in a fruit delivery task, demonstrating its potential to assist individuals in everyday life. Dataset and video demonstrations are available at: https://TS-Robotics.github.io/pHRI-DIGI/.

The performance and usability of Large-Language Models (LLMs) are driving their use in explanation generation tasks. However, despite their widespread adoption, LLM explanations have been found to be unreliable, making it difficult for users to distinguish good from bad explanations. To address this issue, we present Rubrik's CUBE, an education-inspired rubric and a dataset of 26k explanations, written and later quality-annotated using the rubric by both humans and six open- and closed-source LLMs. The CUBE dataset focuses on two reasoning and two language tasks, providing the necessary diversity for us to effectively test our proposed rubric. Using Rubrik, we find that explanations are influenced by both task and perceived difficulty. Low quality stems primarily from a lack of conciseness in LLM-generated explanations, rather than cohesion and word choice. The full dataset, rubric, and code will be made available upon acceptance.