Large language models (LLMs) such as ChatGPT o1, ChatGPT o3, and DeepSeek R1 have shown great potential in solving difficult problems. However, current LLM evaluation benchmarks are limited to one-step interactions. Some of the existing sequence decision-making environments, such as TextStarCraftII and LLM-PySC2, are too complicated and require hours of interaction to complete a game. In this paper, we introduce LLM-Cave, a benchmark and light environment for LLM reasoning and decision-making systems. This environment is a classic instance in the era of Symbolism. Artificial intelligence enables the agent to explore the environment and avoid potential losses by reasoning about nearby dangers using partial observable state information. In the experiment, we evaluated the sequential reasoning ability, decision-making performance and computational efficiency of mainstream large language models (LLMs) such as GPT-4o-mini, o1-mini, and DeepSeek-R1. Experiments show that while Deepseek-R1 achieved the highest success rate on complex reasoning tasks, smaller models like 4o-mini significantly narrowed the performance gap on challenges by employing Chain of Speculation and Planner-Critic strategies, at the expense of reduced computational efficiency. This indicates that structured, multi-step reasoning combined with an LLM-based feedback mechanism can substantially enhance an LLM's decision-making capabilities, providing a promising direction for improving reasoning in weaker models and suggesting a new reasoning-centered benchmark for LLM assessment. Our code is open-sourced in https://github.com/puleya1277/CaveEnv.

In the supervised binary classification setting, score-oriented losses have been introduced with the aim of optimizing a chosen performance metric directly during the training phase, thus avoiding \textit{a posteriori} threshold tuning. To do this, in their construction, the decision threshold is treated as a random variable provided with a certain \textit{a priori} distribution. In this paper, we use a recently introduced multidimensional threshold-based classification framework to extend such score-oriented losses to multiclass classification, defining the Multiclass Score-Oriented Loss (MultiSOL) functions. As also demonstrated by several classification experiments, this proposed family of losses is designed to preserve the main advantages observed in the binary setting, such as the direct optimization of the target metric and the robustness to class imbalance, achieving performance comparable to other state-of-the-art loss functions and providing new insights into the interaction between simplex geometry and score-oriented learning.

Hardware-in-the-Loop (HIL) testing is essential for automotive validation but suffers from fragmented and underutilized test artifacts. This paper presents HIL-GPT, a retrieval-augmented generation (RAG) system integrating domain-adapted large language models (LLMs) with semantic retrieval. HIL-GPT leverages embedding fine-tuning using a domain-specific dataset constructed via heuristic mining and LLM-assisted synthesis, combined with vector indexing for scalable, traceable test case and requirement retrieval. Experiments show that fine-tuned compact models, such as \texttt{bge-base-en-v1.5}, achieve a superior trade-off between accuracy, latency, and cost compared to larger models, challenging the notion that bigger is always better. An A/B user study further confirms that RAG-enhanced assistants improve perceived helpfulness, truthfulness, and satisfaction over general-purpose LLMs. These findings provide insights for deploying efficient, domain-aligned LLM-based assistants in industrial HIL environments.

This technical report presents a comprehensive formal verification approach for probabilistic agent systems modeling ballistic rocket flight trajectories using Probabilistic Alternating-Time Temporal Logic (PATL). We describe an innovative verification framework specifically designed for analyzing critical safety properties of ballistic rockets engineered to achieve microgravity conditions for scientific experimentation. Our model integrates authentic flight telemetry data encompassing velocity vectors, pitch angles, attitude parameters, and GPS coordinates to construct probabilistic state transition systems that rigorously account for environmental stochasticity, particularly meteorological variability. We formalize mission-critical safety properties through PATL specifications to systematically identify trajectory deviation states where the rocket risks landing in prohibited or hazardous zones. The verification framework facilitates real-time safety monitoring and enables automated intervention mechanisms, including emergency engine disengagement protocols, when predefined safety thresholds are exceeded. Experimental validation demonstrates the practical effectiveness and reliability of our approach in ensuring mission safety while maintaining scientific mission objectives.

Large language models have made significant progress in mathematical reasoning, which serves as an important testbed for AI and could impact scientific research if further advanced. By scaling reasoning with reinforcement learning that rewards correct final answers, LLMs have improved from poor performance to saturating quantitative reasoning competitions like AIME and HMMT in one year. However, this approach faces fundamental limitations. Pursuing higher final answer accuracy doesn't address a key issue: correct answers don't guarantee correct reasoning. Moreover, many mathematical tasks like theorem proving require rigorous step-by-step derivation rather than numerical answers, making final answer rewards inapplicable. To push the limits of deep reasoning, we believe it is necessary to verify the comprehensiveness and rigor of mathematical reasoning. Self-verification is particularly important for scaling test-time compute, especially for open problems without known solutions. Towards self-verifiable mathematical reasoning, we investigate how to train an accurate and faithful LLM-based verifier for theorem proving. We then train a proof generator using the verifier as the reward model, and incentivize the generator to identify and resolve as many issues as possible in their own proofs before finalizing them. To maintain the generation-verification gap as the generator becomes stronger, we propose to scale verification compute to automatically label new hard-to-verify proofs, creating training data to further improve the verifier. Our resulting model, DeepSeekMath-V2, demonstrates strong theorem-proving capabilities, achieving gold-level scores on IMO 2025 and CMO 2024 and a near-perfect 118/120 on Putnam 2024 with scaled test-time compute.

Abstract--This paper describes the design and the realization of a prototype of the novel guide robot BUDD-e for visually impaired users. The robot has been tested in a real scenario with the help of visually disabled volunteers at ASST Grande Ospedale Metropolitano Niguarda, in Milan. The results of the experimental campaign are throughly described in the paper, displaying its remarkable performance and user-acceptance. Index T erms--Assistive technologies, autonomous navigation, autonomous robotics, autonomous guide for visually impaired users. According to [1], in 2020 the number of totally blind people was estimated to about 49.1 million (about 0.6 % of the world population), while people with severe and moderate vision problems were estimated to 33.6 million (about 0.4 % of the world population) and 221.4 million (about 2.8 % of the world population), respectively. Furthermore, due to an aging population, it is estimated that the rate of people affected by vision problems will continue to increase in the coming decades [2]. People with visual impairments currently face a number of issues when it comes to visiting public spaces and using services. It is very difficult for blind and partially sighted persons to access shared places (areas where cars, buses, pedestrians, and cyclists share the same space) alone since important inclusive environmental aids are frequently removed in communal areas. As discussed in [3], navigating inside a shopping mall for a blind or low-vision person can be tiring and stressful. Shopping in groceries is practically impossible and shopping centers often don't have enough staff on duty to offer help. Emanuele Lettieri is with the Department of Management, Economics and Industrial Engineering, Politecnico di Milano, Via Lambruschini 4, Milan, Italy (e-mail: emanuele.lettieri@polimi.it).

Originating in psychology, $\textit{Theory of Mind}$ (ToM) has attracted significant attention across multiple research communities, especially logic, economics, and robotics. Most psychological work does not aim at formalizing those central concepts, namely $\textit{goals}$, $\textit{intentions}$, and $\textit{beliefs}$, to automate a ToM-based computational process, which, by contrast, has been extensively studied by logicians. In this paper, we offer a different perspective by proposing a computational framework viewed through the lens of game theory. On the one hand, the framework prescribes how to make boudedly rational decisions while maintaining a theory of mind about others (and recursively, each of the others holding a theory of mind about the rest); on the other hand, it employs statistical techniques and approximate solutions to retain computability of the inherent computational problem.

Vision-Language-Action (VLA) models have recently attracted growing attention in end-to-end autonomous driving for their strong reasoning capabilities and rich world knowledge. However, existing VLAs often suffer from limited numerical reasoning ability and overly simplified input-output mappings, which hinder their performance in complex driving scenarios requiring step-by-step causal reasoning. To address these challenges, we propose CoT4AD, a novel VLA framework that introduces Chain-of-Thought (CoT) reasoning for autonomous driving to enhance both numerical and causal reasoning in Vision-Language Models (VLMs). CoT4AD integrates visual observations and language instructions to perform semantic reasoning, scene understanding, and trajectory planning. During training, it explicitly models a perception-question-prediction-action CoT to align the reasoning space with the action space across multiple driving tasks. During inference, it performs implicit CoT reasoning to enable consistent numerical reasoning and robust decision-making in dynamic environments. Extensive experiments on both real-world and simulated benchmarks, including nuScenes and Bench2Drive, demonstrate that CoT4AD achieves state-of-the-art performance in both open-loop and closed-loop evaluations. Code will be released upon paper acceptance.

Document visual question answering (DocVQA) requires models to jointly reason over textual content and spatial layout, yet current systems exhibit a sharp accuracy--efficiency trade-off: large teacher models achieve strong grounding but are too expensive for deployment, while compact students suffer substantial drops in localization performance. We propose DocVAL, a validated chain-of-thought distillation framework that transfers the spatial reasoning ability of a large teacher into a deployable student VLM through three key components: (1) teacher supervision with validation-time text detection to filter and denoise training signals, (2) a multi-module validator (VAL) that enforces answer correctness and geometric consistency while producing fine-grained, pixel-level error feedback, and (3) a two-stage student training scheme that first learns from validated CoT traces and then undergoes iterative refinement driven by VAL feedback. Our student (Gemma-3 12B) achieves 91.4\% ANLS and 82.4\% mAP on DocVQA as a pure VLM requiring no text detection or OCR at inference. Extensive ablations demonstrate that validated feedback contributes 6.3 mAP gain and iterative refinement accounts for 9.7 mAP improvement. We release 95k high-quality, validator-verified CoT traces to advance spatial reasoning research in document understanding.

Explainability of decision-making AI systems (XAI), and specifically neural networks (NNs), is a key requirement for deploying AI in sensitive areas [18]. A recent trend in explaining NNs is based on formal methods and logic, providing explanations for the decisions of machine learning systems [24, 31, 32, 41, 42, 44] accompanied by provable guarantees regarding their correctness. Yet, rigorous exploration of the continuous feature space requires to estimate decision boundaries with complex shapes. This, however, remains a challenge because existing explanations [24, 31, 32, 41, 42, 44] constrain only individual features and hence fail capturing relationships among the features that are essential to understand the reasons behind the multi-parametrized classification process. We address the need to provide interpretations of NN systems that are as meaningful as possible using a novel concept of Space Explanations, delivered by a flexible symbolic reasoning framework where Craig interpolation [12] is at the heart of the machinery.