This thesis investigates how foundation models can be systematically leveraged to enhance robotic capabilities, enabling more effective localization, interaction, and manipulation in unstructured environments. The work is structured around four core lines of inquiry, each addressing a fundamental challenge in robotics while collectively contributing to a cohesive framework for semantics-aware robotic intelligence.

Interpretable-by-design models are crucial for fostering trust, accountability, and safe adoption of automated decision-making models in real-world applications. In this paper we formalize the ground for the MIMOSA (Mining Interpretable Models explOiting Sophisticated Algorithms) framework, a comprehensive methodology for generating predictive models that balance interpretability with performance while embedding key ethical properties. We formally define here the supervised learning setting across diverse decision-making tasks and data types, including tabular data, time series, images, text, transactions, and trajectories. We characterize three major families of interpretable models: feature importance, rule, and instance based models. For each family, we analyze their interpretability dimensions, reasoning mechanisms, and complexity. Beyond interpretability, we formalize three critical ethical properties, namely causality, fairness, and privacy, providing formal definitions, evaluation metrics, and verification procedures for each. We then examine the inherent trade-offs between these properties and discuss how privacy requirements, fairness constraints, and causal reasoning can be embedded within interpretable pipelines. By evaluating ethical measures during model generation, this framework establishes the theoretical foundations for developing AI systems that are not only accurate and interpretable but also fair, privacy-preserving, and causally aware, i.e., trustworthy.

Reinforcement learning with verifiable rewards (RLVR) has recently enhanced the reasoning capabilities of large language models (LLMs), particularly for mathematical problem solving. However, a fundamental limitation remains: as the sampling budget increases, the advantage of RLVR-trained models over their pretrained bases often diminishes or even vanishes, revealing a strong dependence on the base model's restricted search space. We attribute this phenomenon to the widespread use of the reverse Kullback-Leibler (KL) divergence regularizer, whose mode-seeking behavior keeps the policy trapped inside the base model's support region and hampers wider exploration. To address this issue, we propose RAPO (Rewards-Aware Policy Optimization), an algorithm to promote broader yet focused exploration. Our method (i) utilizes the forward KL penalty to replace the reverse KL penalty for out-of-distribution exploration, and (ii) reweights the reference policy to facilitate adaptive in-distribution exploration. We train Qwen2.5-3B and 7B models with RAPO on the 8K SimpleRL-Zero dataset, without supervised fine-tuning, and evaluate them on AIME2024 and AIME2025. Results show that RAPO consistently improves problem-solving performance. Notably, RAPO enables models to surpass the base model's performance ceiling and solves previously intractable problems, advancing the frontier of RLVR for challenging reasoning tasks.

Benchmarks for competition-style reasoning have advanced evaluation in mathematics and programming, yet physics remains comparatively explored. Most existing physics benchmarks evaluate only final answers, which fail to capture reasoning processes, while recent stepwise methods rely on heuristic LLM-as-judge scoring or restrictive linear assumptions, limiting reliability and diagnostic validity. We introduce PRISM-Physics, a process-level evaluation framework and benchmark for complex physics reasoning problems. Solutions are represented as directed acyclic graphs (DAGs) of formulas, explicitly encoding causal dependencies among intermediate steps to enable fine-grained, interpretable, and theoretically grounded scoring. We prove the optimality of the DAG representation and the corresponding scoring policy. Combining with a fully rule-based method for symbolic formula equivalence matching that we developed, we ensure consistent validation across diverse formulations without heuristic judgments. Results show that our evaluation framework is more aligned with human experts' scoring. Experiments on state-of-the-art LLMs reveal persistent reasoning failures in physics, while step-level scoring offers both diagnostic insight and rich signals for later training. By combining structural rigor, theoretical guarantees, and symbolic validation, PRISM-Physics provides a principled foundation for advancing process-level evaluation and guiding the development of models with deeper scientific reasoning capabilities.

Human cognition is theorized to operate in two modes: fast, intuitive System 1 thinking and slow, deliberate System 2 thinking. While current Large Reasoning Models (LRMs) excel at System 2 thinking, their inability to perform fast thinking leads to high computational overhead and latency. In this work, we enable LRMs to approximate human intelligence through dynamic thinking speed adjustment, optimizing accuracy-efficiency trade-offs. Our approach addresses two key questions: (1) how to control thinking speed in LRMs, and (2) when to adjust it for optimal performance. For the first question, we identify the steering vector that governs slow-fast thinking transitions in LRMs' representation space. Using this vector, we achieve the first representation editing-based test-time scaling effect, outperforming existing prompt-based scaling methods. For the second question, we apply real-time difficulty estimation to signal reasoning segments of varying complexity. Combining these techniques, we propose the first reasoning strategy that enables fast processing of easy steps and deeper analysis for complex reasoning. Without any training or additional cost, our plug-in module delivers an average +1.3% accuracy with -8.6% token usage across leading LRMs and advanced reasoning benchmarks. All of our algorithms are implemented based on vLLM and are expected to support broader applications and inspire future research.

AI search depends on linking large language models (LLMs) with vast external knowledge sources. Yet web pages, PDF files, and other raw documents are not inherently LLM-ready: they are long, noisy, and unstructured. Conventional retrieval methods treat these documents as verbatim text and return raw passages, leaving the burden of fragment assembly and contextual reasoning to the LLM. This gap underscores the need for a new retrieval paradigm that redefines how models interact with documents. We introduce the Model-Document Protocol (MDP), a general framework that formalizes how raw text is bridged to LLMs through consumable knowledge representations. Rather than treating retrieval as passage fetching, MDP defines multiple pathways that transform unstructured documents into task-specific, LLM-ready inputs. These include agentic reasoning, which curates raw evidence into coherent context; memory grounding, which accumulates reusable notes to enrich reasoning; and structured leveraging, which encodes documents into formal representations such as graphs or key-value caches. All three pathways share the same goal: ensuring that what reaches the LLM is not raw fragments but compact, structured knowledge directly consumable for reasoning. As an instantiation, we present MDP-Agent, which realizes the protocol through an agentic process: constructing document-level gist memories for global coverage, performing diffusion-based exploration with vertical exploitation to uncover layered dependencies, and applying map-reduce style synthesis to integrate large-scale evidence into compact yet sufficient context. Experiments on information-seeking benchmarks demonstrate that MDP-Agent outperforms baselines, validating both the soundness of the MDP framework and the effectiveness of its agentic instantiation.

This paper presents a comprehensive cross-platform evaluation of reasoning capabilities in contemporary foundation models, establishing an infrastructure-agnostic benchmark across three computational paradigms: HPC supercomputing (MareNostrum 5), cloud platforms (Nebius AI Studio), and university clusters (a node with eight H200 GPUs). We evaluate 15 foundation models across 79 problems spanning eight academic domains (Physics, Mathematics, Chemistry, Economics, Biology, Statistics, Calculus, and Optimization) through three experimental phases: (1) Baseline establishment: Six models (Mixtral-8x7B, Phi-3, LLaMA 3.1-8B, Gemma-2-9b, Mistral-7B, OLMo-7B) evaluated on 19 problems using MareNostrum 5, establishing methodology and reference performance; (2) Infrastructure validation: The 19-problem benchmark repeated on university cluster (seven models including Falcon-Mamba state-space architecture) and Nebius AI Studio (nine state-of-the-art models: Hermes-4 70B/405B, LLaMA 3.1-405B/3.3-70B, Qwen3 30B/235B, DeepSeek-R1, GPT-OSS 20B/120B) to confirm infrastructure-agnostic reproducibility; (3) Extended evaluation: Full 79-problem assessment on both university cluster and Nebius platforms, probing generalization at scale across architectural diversity. The findings challenge conventional scaling assumptions, establish training data quality as more critical than model size, and provide actionable guidelines for model selection across educational, production, and research contexts. The tri-infrastructure methodology and 79-problem benchmark enable longitudinal tracking of reasoning capabilities as foundation models evolve.

Karl Marx once wrote that ``the human essence is the ensemble of social relations'', suggesting that individuals are not isolated entities but are fundamentally shaped by their interactions with other entities, within which contexts play a constitutive and essential role. With the advent of computers and artificial intelligence, these contexts are no longer limited to purely human--human interactions: human--machine interactions are included as well. Then a central question emerges: How can machines better understand our situations and purposes? To address this challenge, researchers have recently introduced the concept of context engineering. Although it is often regarded as a recent innovation of the agent era, we argue that related practices can be traced back more than twenty years. Since the early 1990s, the field has evolved through distinct historical phases, each shaped by the intelligence level of machines: from early human--computer interaction frameworks built around primitive computers, to today's human--agent interaction paradigms driven by intelligent agents, and potentially to human--level or superhuman intelligence in the future. In this paper, we situate context engineering, provide a systematic definition, outline its historical and conceptual landscape, and examine key design considerations for practice. By addressing these questions, we aim to offer a conceptual foundation for context engineering and sketch its promising future. This paper is a stepping stone for a broader community effort toward systematic context engineering in AI systems.

Self-improvement has emerged as a mainstream paradigm for advancing the reasoning capabilities of large vision-language models (LVLMs), where models explore and learn from successful trajectories iteratively. However, we identify a critical issue during this process: the model excels at generating high-quality trajectories for simple queries (i.e., head data) but struggles with more complex ones (i.e., tail data). This leads to an imbalanced optimization that drives the model to prioritize simple reasoning skills, while hindering its ability to tackle more complex reasoning tasks. Over iterations, this imbalance becomes increasingly pronounced--a dynamic we term the "Matthew effect"--which ultimately hinders further model improvement and leads to performance bottlenecks. To counteract this challenge, we introduce four efficient strategies from two perspectives: distribution-reshaping and trajectory-resampling, to achieve head-tail re-balancing during the exploration-and-learning self-improvement process. Extensive experiments on Qwen2-VL-7B-Instruct and InternVL2.5-4B models across visual reasoning tasks demonstrate that our methods consistently improve visual reasoning capabilities, outperforming vanilla self-improvement by 3.86 points on average.

Humans can naturally identify, reason about, and explain anomalies in their environment. In computer vision, this long-standing challenge remains limited to industrial defects or unrealistic, synthetically generated anomalies, failing to capture the richness and unpredictability of real-world anomalies. In this work, we introduce CAVE, the first benchmark of real-world visual anomalies. CAVE supports three open-ended tasks: anomaly description, explanation, and justification; with fine-grained annotations for visual grounding and categorizing anomalies based on their visual manifestations, their complexity, severity, and commonness. These annotations draw inspiration from cognitive science research on how humans identify and resolve anomalies, providing a comprehensive framework for evaluating Vision-Language Models (VLMs) in detecting and understanding anomalies. We show that state-of-the-art VLMs struggle with visual anomaly perception and commonsense reasoning, even with advanced prompting strategies. By offering a realistic and cognitively grounded benchmark, CAVE serves as a valuable resource for advancing research in anomaly detection and commonsense reasoning in VLMs.