Subtle Risks, Critical Failures: A Framework for Diagnosing Physical Safety of LLMs for Embodied Decision Making

Large Language Models (LLMs) are increasingly used for decision making in embodied agents, yet existing safety evaluations often rely on coarse success rates and domain-specific setups, making it difficult to diagnose why and where these models fail. This obscures our understanding of embodied safety and limits the selective deployment of LLMs in high-risk physical environments. We introduce SAFEL, the framework for systematically evaluating the physical safety of LLMs in embodied decision making. SAFEL assesses two key competencies: (1) rejecting unsafe commands via the Command Refusal Test, and (2) generating safe and executable plans via the Plan Safety Test. Critically, the latter is decomposed into functional modules, goal interpretation, transition modeling, action sequencing, enabling fine-grained diagnosis of safety failures. To support this framework, we introduce EMBODYGUARD, a PDDL-grounded benchmark containing 942 LLM-generated scenarios covering both overtly malicious and contextually hazardous instructions. Evaluation across 13 state-of-the-art LLMs reveals that while models often reject clearly unsafe commands, they struggle to anticipate and mitigate subtle, situational risks. Our results highlight critical limitations in current LLMs and provide a foundation for more targeted, modular improvements in safe embodied reasoning.

Explain with Visual Keypoints Like a Real Mentor! A Benchmark for Multimodal Solution Explanation

With the rapid advancement of mathematical reasoning capabilities in Large Language Models (LLMs), AI systems are increasingly being adopted in educational settings to support students' comprehension of problem-solving processes. However, a critical component remains underexplored in current LLM-generated explanations: visual explanation. In real-world instructional contexts, human tutors routinely employ visual aids - such as diagrams, markings, and highlights - to enhance conceptual clarity. To bridge this gap, we introduce a novel task of visual solution explanation, which requires generating explanations that incorporate newly introduced visual elements essential for understanding (e.g., auxiliary lines, annotations, or geometric constructions). To evaluate model performance on this task, we propose MathExplain, a multimodal benchmark consisting of 997 math problems annotated with visual keypoints and corresponding explanatory text that references those elements. Our empirical results show that while some closed-source models demonstrate promising capabilities on visual solution-explaining, current open-source general-purpose models perform inconsistently, particularly in identifying relevant visual components and producing coherent keypoint-based explanations. We expect that visual solution-explaining and the MathExplain dataset will catalyze further research on multimodal LLMs in education and advance their deployment as effective, explanation-oriented AI tutors. Code and data will be released publicly.