We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the math reasoning capabilities of large language models (LLMs). Applying RLVR to the base model Qwen2.5-Math-1.5B, we identify a single example that elevates model performance on MATH500 from 36.0% to 73.6% (8.6% improvement beyond format correction), and improves the average performance across six common mathematical reasoning benchmarks from 17.6% to 35.7% (7.0% non-format gain). This result matches the performance obtained using the 1.2k DeepScaleR subset (MATH500: 73.6%, average: 35.9%), which contains the aforementioned example. Furthermore, RLVR with only two examples even slightly exceeds these results (MATH500: 74.8%, average: 36.6%). Similar substantial improvements are observed across various models (Qwen2.5-Math-7B, Llama3.2-3B-Instruct, DeepSeek-R1-Distill-Qwen-1.5B), RL algorithms (GRPO and PPO), and different math examples. In addition, we identify some interesting phenomena during 1-shot RLVR, including cross-category generalization, increased frequency of self-reflection, and sustained test performance improvement even after the training accuracy has saturated, a phenomenon we term post-saturation generalization. Moreover, we verify that the effectiveness of 1-shot RLVR primarily arises from the policy gradient loss, distinguishing it from the "grokking" phenomenon. We also show the critical role of promoting exploration (e.g., by incorporating entropy loss with an appropriate coefficient) in 1-shot RLVR training. We also further discuss related observations about format correction, label robustness and prompt modification. These findings can inspire future work on RLVR efficiency and encourage a re-examination of recent progress and the underlying mechanisms in RLVR. All resources are open source at https://github.com/ypwang61/One-Shot-RLVR.

A generalizable reward model is crucial in Reinforcement Learning from Human Feedback (RLHF) as it enables correctly evaluating unseen prompt-response pairs. However, existing reward models lack this ability, as they are typically trained by increasing the reward gap between chosen and rejected responses, while overlooking the prompts that the responses are conditioned on. Consequently, when the trained reward model is evaluated on prompt-response pairs that lie outside the data distribution, neglecting the effect of prompts may result in poor generalization of the reward model. To address this issue, we decompose the reward value into two independent components: prompt-free reward and prompt-related reward. Prompt-free reward represents the evaluation that is determined only by responses, while the prompt-related reward reflects the reward that derives from both the prompt and the response. We extract these two components from an information-theoretic perspective, which requires no extra models. Subsequently, we propose a new reward learning algorithm by prioritizing data samples based on their prompt-free reward values. Through toy examples, we demonstrate that the extracted prompt-free and prompt-related rewards effectively characterize two parts of the reward model. Further, standard evaluations show that our method improves both the alignment performance and the generalization capability of the reward model.

Reward shaping in multi-agent reinforcement learning (MARL) for complex tasks remains a significant challenge. Existing approaches often fail to find optimal solutions or cannot efficiently handle such tasks. We propose HYPRL, a specification-guided reinforcement learning framework that learns control policies w.r.t. hyperproperties expressed in HyperLTL. Hyperproperties constitute a powerful formalism for specifying objectives and constraints over sets of execution traces across agents. To learn policies that maximize the satisfaction of a HyperLTL formula $ϕ$, we apply Skolemization to manage quantifier alternations and define quantitative robustness functions to shape rewards over execution traces of a Markov decision process with unknown transitions. A suitable RL algorithm is then used to learn policies that collectively maximize the expected reward and, consequently, increase the probability of satisfying $ϕ$. We evaluate HYPRL on a diverse set of benchmarks, including safety-aware planning, Deep Sea Treasure, and the Post Correspondence Problem. We also compare with specification-driven baselines to demonstrate the effectiveness and efficiency of HYPRL.

In recent years, large language models (LLMs) have shown remarkable capabilities in various artificial intelligence problems. However, they fail to plan reliably, even when prompted with a detailed definition of the planning task. Attempts to improve their planning capabilities, such as chain-of-thought prompting, fine-tuning, and explicit "reasoning" still yield incorrect plans and usually fail to generalize to larger tasks. In this paper, we show how to use LLMs to generate correct plans, even for out-of-distribution tasks of increasing size. For a given planning domain, we ask an LLM to generate several domain-dependent heuristic functions in the form of Python code, evaluate them on a set of training tasks within a greedy best-first search, and choose the strongest one. The resulting LLM-generated heuristics solve many more unseen test tasks than state-of-the-art domain-independent heuristics for classical planning. They are even competitive with the strongest learning algorithm for domain-dependent planning. These findings are especially remarkable given that our proof-of-concept implementation is based on an unoptimized Python planner and the baselines all build upon highly optimized C++ code. In some domains, the LLM-generated heuristics expand fewer states than the baselines, revealing that they are not only efficiently computable, but sometimes even more informative than the state-of-the-art heuristics. Overall, our results show that sampling a set of planning heuristic function programs can significantly improve the planning capabilities of LLMs.

In this paper we show that visual diffusion models can serve as effective geometric solvers: they can directly reason about geometric problems by working in pixel space. We first demonstrate this on the Inscribed Square Problem, a long-standing problem in geometry that asks whether every Jordan curve contains four points forming a square. We then extend the approach to two other well-known hard geometric problems: the Steiner Tree Problem and the Simple Polygon Problem. Our method treats each problem instance as an image and trains a standard visual diffusion model that transforms Gaussian noise into an image representing a valid approximate solution that closely matches the exact one. The model learns to transform noisy geometric structures into correct configurations, effectively recasting geometric reasoning as image generation. Unlike prior work that necessitates specialized architectures and domain-specific adaptations when applying diffusion to parametric geometric representations, we employ a standard visual diffusion model that operates on the visual representation of the problem. This simplicity highlights a surprising bridge between generative modeling and geometric problem solving. Beyond the specific problems studied here, our results point toward a broader paradigm: operating in image space provides a general and practical framework for approximating notoriously hard problems, and opens the door to tackling a far wider class of challenging geometric tasks.

Abstract--The coordination of autonomous agents in dynamic environments is hampered by the semantic gap between high-level mission objectives and low-level planner inputs. T o address this, we introduce a framework centered on a Knowledge Graph (KG) that functions as an intelligent translation layer . The KG's two-plane architecture compiles declarative facts into per-agent, mission-aware "worldviews" and physics-aware traversal rules, decoupling mission semantics from a domain-agnostic planner . This allows complex, coordinated paths to be modified simply by changing facts in the KG. A case study involving Autonomous Underwater V ehicles (AUVs) in the Gulf of Mexico visually demonstrates the end-to-end process and quantitatively proves that different declarative policies produce distinct, high-performing outcomes. This work establishes the KG not merely as a data repository, but as a powerful, stateful orchestrator for creating adaptive and explainable autonomous systems. The effective coordination of autonomous agents, be they robotic vehicles, sensor networks, or even human teams, in dynamic, real-world environments presents a formidable challenge.

Neural networks have advanced combinatorial optimization, with Transformer-based solvers achieving near-optimal solutions on the Traveling Salesman Problem (TSP) in milliseconds. However, these models operate as black boxes, providing no insight into the geometric patterns they learn or the heuristics they employ during tour construction. We address this opacity by applying sparse autoencoders (SAEs), a mechanistic interpretability technique, to a Transformer-based TSP solver, representing the first application of activation-based interpretability methods to operations research models. We train a pointer network with reinforcement learning on 100-node instances, then fit an SAE to the encoder's residual stream to discover an overcomplete dictionary of interpretable features. Our analysis reveals that the solver naturally develops features mirroring fundamental TSP concepts: boundary detectors that activate on convex-hull nodes, cluster-sensitive features responding to locally dense regions, and separator features encoding geometric partitions. These findings provide the first model-internal account of what neural TSP solvers compute before node selection, demonstrate that geometric structure emerges without explicit supervision, and suggest pathways toward transparent hybrid systems that combine neural efficiency with algorithmic interpretability. Interactive feature explorer: https://reubennarad.github.io/TSP_interp

Computer vision can accelerate ecological research and conservation monitoring, yet adoption in ecology lags in part because of a lack of trust in black-box neural-network-based models. We seek to address this challenge by applying post-hoc explanations to provide evidence for predictions and document limitations that are important to field deployment. Using aerial imagery from Glacier Bay National Park, we train a Faster R-CNN to detect pinnipeds (harbor seals) and generate explanations via gradient-based class activation mapping (HiResCAM, LayerCAM), local interpretable model-agnostic explanations (LIME), and perturbation-based explanations. We assess explanations along three axes relevant to field use: (i) localization fidelity: whether high-attribution regions coincide with the animal rather than background context; (ii) faithfulness: whether deletion/insertion tests produce changes in detector confidence; and (iii) diagnostic utility: whether explanations reveal systematic failure modes. Explanations concentrate on seal torsos and contours rather than surrounding ice/rock, and removal of the seals reduces detection confidence, providing model-evidence for true positives. The analysis also uncovers recurrent error sources, including confusion between seals and black ice and rocks. We translate these findings into actionable next steps for model development, including more targeted data curation and augmentation. By pairing object detection with post-hoc explainability, we can move beyond "black-box" predictions toward auditable, decision-supporting tools for conservation monitoring.

Constructing comprehensive knowledge graphs requires the use of multiple ontologies in order to fully contextualize data into a domain. Ontology matching finds equivalences between concepts interconnecting ontologies and creating a cohesive semantic layer. While the simple pairwise state of the art is well established, simple equivalence mappings cannot provide full semantic integration of related but disjoint ontologies. Complex multi-ontology matching (CMOM) aligns one source entity to composite logical expressions of multiple target entities, establishing more nuanced equivalences and provenance along the ontological hierarchy. We present CMOMgen, the first end-to-end CMOM strategy that generates complete and semantically sound mappings, without establishing any restrictions on the number of target ontologies or entities. Retrieval-Augmented Generation selects relevant classes to compose the mapping and filters matching reference mappings to serve as examples, enhancing In-Context Learning. The strategy was evaluated in three biomedical tasks with partial reference alignments. CMOMgen outperforms baselines in class selection, demonstrating the impact of having a dedicated strategy. Our strategy also achieves a minimum of 63% in F1-score, outperforming all baselines and ablated versions in two out of three tasks and placing second in the third. Furthermore, a manual evaluation of non-reference mappings showed that 46% of the mappings achieve the maximum score, further substantiating its ability to construct semantically sound mappings.

Tracking human full-body motion using sparse wearable inertial measurement units (IMUs) overcomes the limitations of occlusion and instrumentation of the environment inherent in vision-based approaches. However, purely IMU-based tracking compromises translation estimates and accurate relative positioning between individuals, as inertial cues are inherently self-referential and provide no direct spatial reference for others. In this paper, we present a novel approach for robustly estimating body poses and global translation for multiple individuals by leveraging the distances between sparse wearable sensors - both on each individual and across multiple individuals. Our method Group Inertial Poser estimates these absolute distances between pairs of sensors from ultra-wideband ranging (UWB) and fuses them with inertial observations as input into structured state-space models to integrate temporal motion patterns for precise 3D pose estimation. Our novel two-step optimization further leverages the estimated distances for accurately tracking people's global trajectories through the world. We also introduce GIP-DB, the first IMU+UWB dataset for two-person tracking, which comprises 200 minutes of motion recordings from 14 participants. In our evaluation, Group Inertial Poser outperforms previous state-of-the-art methods in accuracy and robustness across synthetic and real-world data, showing the promise of IMU+UWB-based multi-human motion capture in the wild. Code, models, dataset: https://github.com/eth-siplab/GroupInertialPoser