Interaction Trajectories

Gap-closing rate and visual looming swap discriminative dominance depending on deceleration intensity - a finding that reconciles a long-standing conflict in the car-following literature and challenges spacing-centered assumptions in traditional driver behavior models. This study presents a two-stage analytical framework that distinguishes between information availability (kinematic variables measurable in the environment) and information utilization (variables that demonstrably separate driver behavioral patterns), applied to 1,060,119 valid car-following observations from the NGSIM trajectory dataset (2,932 vehicles). Six kinematic features are extracted, and deceleration events are detected under two threshold conditions (-0.5 m/s^2 and -0.3 m/s^2). K-means clustering identifies behavioral modes, and one-way ANOVA with eta-squared effect sizes ranks each feature's discriminative power. Three key findings emerge: (1) threshold selection fundamentally shapes behavioral inference - the stricter threshold yields three interpretable modes while the permissive threshold collapses these to two; (2) hard braking prioritizes gap-closing rate (eta^2 = 0.715) while moderate braking emphasizes visual looming (eta^2 = 0.574); and (3) spacing headway is negligible (eta^2 <= 0.014) across both thresholds. These findings provide empirically grounded candidates for perceptual cue prioritization and have direct implications for ADAS warning system design and autonomous vehicle control.

We introduce ReflectDrive-2, a masked discrete diffusion planner with separate action expert for autonomous driving that represents plans as discrete trajectory tokens and generates them through parallel masked decoding. This discrete token space enables in-place trajectory revision: AutoEdit rewrites selected tokens using the same model, without requiring an auxiliary refinement network. To train this capability, we use a two-stage procedure. First, we construct structure-aware perturbations of expert trajectories along longitudinal progress and lateral heading directions and supervise the model to recover the original expert trajectory. We then fine-tune the full decision--draft--reflect rollout with reinforcement learning (RL), assigning terminal driving reward to the final post-edit trajectory and propagating policy-gradient credit through full-rollout transitions. Full-rollout RL proves crucial for coupling drafting and editing: under supervised training alone, inference-time AutoEdit improves PDMS by at most $0.3$, whereas RL increases its gain to $1.9$. We also co-design an efficient reflective decoding stack for the decision--draft--reflect pipeline, combining shared-prefix KV reuse, Alternating Step Decode, and fused on-device unmasking. On NAVSIM, ReflectDrive-2 achieves $91.0$ PDMS with camera-only input and $94.8$ PDMS in a best-of-6 oracle setting, while running at $31.8$ ms average latency on NVIDIA Thor.

We study online prediction for marginally stable, partially observed linear dynamical systems under nonstochastic disturbances. Our objective is to minimize the cumulative squared prediction loss and compete with the best-in-hindsight Luenberger predictor. Standard online learning methods typically rely on bounded domains/gradients, and thus their guarantees may fail to deal with potentially unbounded trajectories in marginally stable systems. In this paper, we introduce an unconstrained online least squares method that stabilizes the learning process via tailored predictive hints. With model knowledge, we prove that hints constructed from any stabilizing Luenberger predictor render the hint residuals uniformly bounded, achieving logarithmic regret despite unbounded trajectory growth. We also discuss model-free prediction and introduce a simple universal hint for symmetric systems, under which logarithmic regret is maintained without model knowledge. Our results provide an adaptive, instance-wise optimal online predictor compared to classical fixed-gain observers under nonstochastic disturbances.

Deep search capabilities have become an indispensable competency for frontier Large Language Model (LLM) agents, yet their development remains dominated by industrial giants. The typical industry recipe involves a highly resource-intensive pipeline spanning pre-training, continual pre-training (CPT), supervised fine-tuning (SFT), and reinforcement learning (RL). In this report, we show that when fueled with informative and high-difficulty trajectories, a simple SFT approach could be surprisingly powerful for training frontier search agents. By introducing three simple data synthesis modifications: scaling knowledge graph size for richer exploration, expanding the tool set size for broader functionality, and strict low-step filtering, we establish a stronger baseline. Trained on merely 10.6k data points, our OpenSeeker-v2 achieves state-of-the-art performance across 4 benchmarks (30B-sized agents with ReAct paradigm): 46.0% on BrowseComp, 58.1% on BrowseComp-ZH, 34.6% on Humanity's Last Exam, and 78.0% on xbench, surpassing even Tongyi DeepResearch trained with heavy CPT+SFT+RL pipeline, which achieves 43.4%, 46.7%, 32.9%, and 75.0%, respectively. Notably, OpenSeeker-v2 represents the first state-of-the-art search agent within its model scale and paradigm to be developed by a purely academic team using only SFT. We are excited to open-source the OpenSeeker-v2 model weights and share our simple yet effective findings to make frontier search agent research more accessible to the community.

Recent advances in Large Reasoning Models (LRMs) trained with Long Chain-of-Thought have demonstrated remarkable capabilities in code generation and mathematical reasoning. However, their potential in multi-turn Text-to-SQL tasks remains largely underexplored. Existing approaches typically rely on unstable API-based inference or require expensive fine-tuning on small-scale models. In this work, we present Rose-SQL, a training-free framework that leverages small-scale LRMs through in-context learning to enable accurate context-dependent parsing. We introduce the Role-State, a fine-grained representation that bridges the structural gap between schema linking and SQL generation by serving as a structural blueprint. To handle conversational dependencies, Rose-SQL traces the evolution of Role-State through historical context via structural isomorphism checks, guiding the model to infer the possible SQL composition for the current question through verified interaction trajectories. Experiments on the SParC and CoSQL benchmarks show that, within the Qwen3 series, Rose-SQL outperforms in-context learning baselines at the 4B scale and substantially surpasses state-of-the-art fine-tuned models at the 8B and 14B scales, while showing consistent gains on additional reasoning backbones.

Despite the success of Large-Vision Language Models (LVLMs), general optimization objectives (e.g., standard MLE) fail to constrain visual trajectories, leading to language bias and hallucination. To mitigate this, current methods introduce geometric priors from visual experts as additional supervision. However, we observe that such supervision is typically suboptimal: it is biased toward geometric precision and offers limited reasoning utility. To bridge this gap, we propose Perceptual Flow Network (PFlowNet), which eschews rigid alignment with the expert priors and achieves interpretable yet more effective visual reasoning. Specifically, PFlowNet decouples perception from reasoning to establish a self-conditioned generation process. Based on this, it integrates multi-dimensional rewards with vicinal geometric shaping via variational reinforcement learning, thereby facilitating reasoning-oriented perceptual behaviors while preserving visual reliability. PFlowNet delivers a provable performance guarantee and competitive empirical results, particularly setting new SOTA records on V* Bench (90.6%) and MME-RealWorld-lite (67.0%).

Existing zero-shot Object Goal Navigation (ObjectNav) methods often exploit commonsense knowledge from large language or vision-language models to guide navigation. However, such knowledge arises from internet-scale text rather than embodied 3D experience, and episodic observations collected during navigation are typically discarded, preventing the accumulation of lifelong experience. To this end, we propose Trajectory RAG (TrajRAG), a retrieval-augmented generation framework that enhances large-model reasoning by retrieving geometric-semantic experiences. TrajRAG incrementally accumulates episodic observations from past navigation episodes. To structure these observations, we propose a topological-polar (topo-polar) trajectory representation that compactly encodes spatial layouts and semantic contexts, effectively removing redundancies in raw episodic observations. A hierarchical chunking structure further organizes similar topo-polar trajectories into unified summaries, enabling coarse-to-fine retrieval. During navigation, candidate frontiers generate multiple trajectory hypotheses that query TrajRAG for similar past trajectories, guiding large-model reasoning for waypoint selection. New experiences are continually consolidated into TrajRAG, enabling the accumulation of lifelong navigation experience. Experiments on MP3D, HM3D-v1, and HM3D-v2 show that TrajRAG effectively retrieves relevant geometric-semantic experiences and improves zero-shot ObjectNav performance.

Recent white-box OOD detection methods for LLMs -- including CED, RAUQ, and WildGuard confidence scores -- appear effective, but we show they are structurally confounded by sequence length (|r| >= 0.61) and collapse to near-chance under length-matched evaluation. Even raw attention entropy (mean H(alpha) across heads and layers), a natural baseline we include for completeness, shows the same confound. The confound stems from attention's Theta(log T) dependence on input length. To identify genuine OOD signals after deconfounding, we propose a two-pathway framework: embeddings capture what text is about (effective for topic shifts), while the processing trajectory -- hidden-state evolution across layers -- captures how the model processes input. The relative power of each pathway varies along a vocabulary-transparency spectrum: embedding methods excel on vocabulary-distinctive OOD, while trajectory features detect covert-intent inputs that share vocabulary with normal text (0.721 avg AUROC; Jailbreak: 0.850). Three evidence lines support this framework: (1) a crossover between k-NN and trajectory scoring across 6 tasks, where each pathway wins on different OOD types; (2) a per-layer analysis showing that layer-0 k-NN signal is almost entirely a length artifact (Jailbreak: 0.759 raw -> 0.389 matched) -- processing constructs genuine OOD signal from near-chance embeddings; and (3) circuit attribution showing adversarial tasks engage attention circuits more than semantic tasks (p = 0.022; Jailbreak patching p < 0.001), with partial cross-model replication. Code release upon publication.

Recent advances in multimodal large language models (LLMs) have revolutionized web agents that can automate complex tasks on websites. However, their accuracy remains limited by the scarcity of high-quality web trajectory training data. Existing automatic trajectory generation methods suffer from incomplete website coverage due to homepage-based task proposals or random-walk exploration. Such methods often result in hallucinated or ambiguous task synthesis that lead to incomplete and unreliable trajectory generation. Here, we present AutoSurfer, a comprehensive web trajectory generator that addresses these limitations through three key innovations. First, AutoSurfer employs a systematic breadth-first exploration strategy that maintains a queue of discovered pages and action traces, propagates knowledge across pages to avoid redundant exploration, and recursively expands multi-level graphical user interface elements - closely resembling how a human would learn a new website. Second, AutoSurfer leverages the exploration trajectory to guide task synthesis, reducing hallucinations by grounding complex tasks in actual navigation paths rather than isolated actions or page content alone. Third, AutoSurfer uses the same exploration trajectory as hints to steer a web agent toward more accurate and reliable trajectory refinement. Together, these innovations enable AutoSurfer to comprehensively cover a website's action space and generate data suitable for training website-specific LLMs. We evaluate AutoSurfer on the WebArena benchmark by fine-tuning Qwen2.5-VL-7B-Instruct and demonstrate that it outperforms state-of-the-art methods - Explorer, OS-Genesis, and SynthAgent - achieving up to 24.23% overall task completion accuracy compared to 19.59% for the best prior method. Further, task diversity analysis demonstrates that AutoSurfer yields a more diverse distribution of synthesized tasks.

Chip placement is a critical step in physical design. While reinforcement learning (RL)-based methods have recently emerged, their training primarily focuses on wirelength optimization, and therefore often fail to achieve expert-quality layouts. We identify the reward design as the primary cause for the performance gap with experts, and instead of formalizing intricate processes, we circumvent this by directly learning from expert layouts to derive a reward model. Our approach starts from the final expert layouts to infer step-by-step expert trajectories. Using these trajectories as demonstrations or preferences, we train a model that captures the latent implicit rewards in expert results. Experiments show that our framework can efficiently learn from even a single design and generalize well to unseen cases.

In autoregressive large language models (LLMs), temporal straightening offers an account of how the next-token prediction objective shapes representations. Models learn to progressively straighten the representational trajectory of input sequences across layers, potentially facilitating next-token prediction via linear extrapolation. However, a direct link between this trajectory and token-level behavior has been missing. We provide such a link by relating contextual curvature-a geometric measure of how sharply the representational trajectory bends over recent context-to next-token entropy. Across two models (GPT-2 XL and Pythia-2.8B), contextual curvature is correlated with entropy, and this relationship emerges during training. Perturbation experiments reveal selective dependence: manipulating curvature through trajectory-aligned interventions reliably modulates entropy, while geometrically misaligned perturbations have no effect. Finally, regularizing representations to be straighter during training modestly reduces token-level entropy without degrading validation loss. These results identify trajectory curvature as a task-aligned representational feature that influences behavioral uncertainty in LLMs.

While feed-forward 3D reconstruction models have advanced rapidly, they still exhibit degraded performance on panoramas due to spherical distortions. Moreover, existing panoramic 3D datasets are predominantly collected with 360 cameras fixed at discrete locations, resulting in discontinuous trajectories. These limitations critically hinder the development of panoramic feed-forward 3D reconstruction, especially for the multi-view setting. In this paper, we present Holo360D, a comprehensive dataset containing 109,495 panoramas paired with registered point clouds, meshes, and aligned camera poses. To our knowledge, Holo360D is the first large-scale dataset that provides continuous panoramic sequences with accurately aligned high-completeness depth maps. The raw data are initially collected using a 3D laser scanner coupled with a 360 camera. Subsequently, the raw data are processed with both online and offline SLAM systems. Furthermore, to enhance the 3D data quality, a post-processing pipeline tailored for the 360 dataset is proposed, including geometry denoising, mesh hole filling, and region-specific remeshing. Finally, we establish a new benchmark by fine-tuning 3D reconstruction models on Holo360D, providing key insights into effective fine-tuning strategies. Our results demonstrate that Holo360D delivers superior training signals and provides a comprehensive benchmark for advancing panoramic 3D reconstruction models. Datasets and Code will be made publicly available.

We present GFlowState, a visual analytics system designed to illuminate the training process of Generative Flow Networks (GFlowNets or GFNs). GFlowNets are a probabilistic framework for generating samples proportionally to a reward function. While GFlowNets have proved to be powerful tools in applications such as molecule and material discovery, their training dynamics remain difficult to interpret. Standard machine learning tools allow metric tracking but do not reveal how models explore the sample space, construct sample trajectories, or shift sampling probabilities during training. Our solution, GFlowState, allows users to analyze sampling trajectories, compare the sample space relative to reference datasets, and analyze the training dynamics. To this end, we introduce multiple views, including a chart of candidate rankings, a state projection, a node-link diagram of the trajectory network, and a transition heatmap. These visualizations enable GFlowNet developers and users to investigate sampling behavior and policy evolution, and to identify underexplored regions and sources of training failure. Case studies demonstrate how the system supports debugging and assessing the quality of GFlowNets across application domains. By making the structural dynamics of GFlowNets observable, our work enhances their interpretability and can accelerate GFlowNet development in practice.

Recent agentic frameworks for 3D scene synthesis have advanced realism and diversity by integrating heterogeneous generation and editing tools. These tools are organized into workflows orchestrated by an off-the-shelf LLM. Current approaches typically adopt an execute-review-reflect loop: at each step, the orchestrator executes a tool, renders intermediate results for review, and then decides on the tool and its parameters for the next step. However, this design has two key limitations. First, next-step tool selection and parameter configuration are driven by heuristic rules, which can lead to suboptimal execution flows, unnecessary tool invocations, degraded output quality, and increased runtime. Second, rendering and reviewing intermediate results after each step introduces additional latency. To address these issues, we propose SceneOrchestra, a trainable orchestration framework that optimizes the tool-call execution flow and eliminates the step-by-step review loop, improving both efficiency and output quality. SceneOrchestra consists of an orchestrator and a discriminator, which we fine-tune with a two-phase training strategy. In the first phase, the orchestrator learns context-aware tool selection and complete tool-call trajectory generation, while the discriminator is trained to assess the quality of full trajectories, enabling it to select the best trajectory from multiple candidates. In the second phase, we perform interleaved training, where the discriminator adapts to the orchestrator's evolving trajectory distribution and distills its discriminative capability back into the orchestrator. At inference, we only use the orchestrator to generate and execute full tool-call trajectories from instructions, without requiring the discriminator. Extensive experiments show that our method achieves state-of-the-art scene quality while reducing runtime compared to previous work.

Vision-Language-Action (VLA) models offer a promising autonomous driving paradigm for leveraging world knowledge and reasoning capabilities, especially in long-tail scenarios. However, existing VLA models often struggle with the high latency in action generation using an autoregressive generation framework and exhibit limited robustness. In this paper, we propose SpanVLA, a novel end-to-end autonomous driving framework, integrating an autoregressive reasoning and a flow-matching action expert. First, SpanVLA introduces an efficient bridge to leverage the vision and reasoning guidance of VLM to efficiently plan future trajectories using a flow-matching policy conditioned on historical trajectory initialization, which significantly reduces inference time. Second, to further improve the performance and robustness of the SpanVLA model, we propose a GRPO-based post-training method to enable the VLA model not only to learn from positive driving samples but also to learn how to avoid the typical negative behaviors and learn recovery behaviors. We further introduce mReasoning, a new real-world driving reasoning dataset, focusing on complex, reasoning-demanding scenarios and negative-recovery samples. Extensive experiments on the NAVSIM (v1 and v2) demonstrate the competitive performance of the SpanVLA model. Additionally, the qualitative results across diverse scenarios highlight the planning performance and robustness of our model.

Fine-tuning Large Language Models (LLMs) remains structurally uncertain despite parameter-efficient methods such as Low-Rank Adaptation (LoRA), as the layer-specific roles of internal representations are poorly understood, leading to heuristic decisions about where adaptation should be applied. We model the evolution of hidden states as a high-dimensional geometric trajectory and propose using the Ramer-Douglas-Peucker (RDP) algorithm, a parameter-free and training-free polygon simplification method that preserves global structural transitions while eliminating locally redundant changes, to identify critical breakpoints along the representation path. Crucially, we use these geometric pivots not merely for analysis, but as a direct decision signal for determining which layers should be adapted during parameter-efficient fine-tuning. By integrating this geometry-aware layer selection strategy into LoRA fine-tuning of Qwen3-8B-Base, we achieve superior performance on MMLU-Math using only 13 RDP-selected layers (81.67%), significantly outperforming both full 36-layer adaptation (79.32%) and random 13-layer selection (75.56%), as well as the baseline Qwen3-8B-Base model (74.25%). These results demonstrate that leveraging the intrinsic geometry of representation trajectories provides a robust, interpretable, and training-free signal for optimizing layer selection during model adaptation.

Signal Temporal Logic (STL) is a powerful language for specifying temporally structured robotic tasks. Planning executable trajectories under STL constraints remains difficult when system dynamics and environment structure are not analytically available. Existing methods typically either assume explicit models or learn task-specific behaviors, limiting zero-shot generalization to unseen STL tasks. In this work, we study offline STL planning under unknown dynamics using only task-agnostic trajectory data. Our central design philosophy is to separate logical reasoning from trajectory realization. We instantiate this idea in DAG-STL, a hierarchical framework that converts long-horizon STL planning into three stages. It first decomposes an STL formula into reachability and invariance progress conditions linked by shared timing constraints. It then allocates timed waypoints using learned reachability-time estimates. Finally, it synthesizes trajectories between these waypoints with a diffusion-based generator. This decomposition--allocation--generation pipeline reduces global planning to shorter, better-supported subproblems. To bridge the gap between planning-level correctness and execution-level feasibility, we further introduce a rollout-free dynamic consistency metric, an anytime refinement search procedure for improving multiple allocation hypotheses under finite budgets, and a hierarchical online replanning mechanism for execution-time recovery. Experiments in Maze2D, OGBench AntMaze, and the Cube domain show that DAG-STL substantially outperforms direct robustness-guided diffusion on complex long-horizon STL tasks and generalizes across navigation and manipulation settings. In a custom environment with an optimization-based reference, DAG-STL recovers most model-solvable tasks while retaining a clear computational advantage over direct optimization based on the explicit system model.

Reinforcement learning for multi-step reasoning with large language models (LLMs) typically relies on sparse terminal rewards, which creates a poorly conditioned credit-assignment problem: the final feedback is propagated uniformly across all intermediate decisions. This leads to high gradient variance, unstable training, and many ineffective updates, ultimately limiting sustained model improvement. We propose a counterfactual-comparison framework for credit assignment. For each input, the framework samples multiple reasoning trajectories and treats their differences as implicit approximations to alternative decisions. This yields an implicit process-level advantage estimator that converts sparse terminal rewards into step-sensitive learning signals. Building on this framework, we introduce Implicit Behavior Policy Optimization (IBPO), which substantially improves training stability and the performance ceiling on mathematical and code-reasoning benchmarks. Our results point to a promising direction for unlocking the reasoning potential of LLMs.

Human behavior has the nature of mutual dependencies, which requires human-robot interactive systems to predict surrounding agents trajectories by modeling complex social interactions, avoiding collisions and executing safe path planning. While there exist many trajectory prediction methods, most of them do not incorporate the own motion of the ego agent and only model interactions based on static information. We are inspired by the humans theory of mind during trajectory selection and propose a Cross time domain intention-interactive method for conditional Trajectory prediction(CiT). Our proposed CiT conducts joint analysis of behavior intentions over time, and achieves information complementarity and integration across different time domains. The intention in its own time domain can be corrected by the social interaction information from the other time domain to obtain a more precise intention representation. In addition, CiT is designed to closely integrate with robotic motion planning and control modules, capable of generating a set of optional trajectory prediction results for all surrounding agents based on potential motions of the ego agent. Extensive experiments demonstrate that the proposed CiT significantly outperforms the existing methods, achieving state-of-the-art performance in the benchmarks.

We release Terminal Wrench, a subset of 331 terminal-agent benchmark environments, copied from the popular open benchmarks that are demonstrably reward-hackable. The data set includes 3,632 hack trajectories and 2,352 legitimate baseline trajectories across three frontier models (Claude Opus 4.6, Gemini 3.1 Pro, GPT-5.4). Each entry preserves the original task definition alongside full attack trajectories that show how the verifier was bypassed. It also includes cases where the task was not solved as intended. The tasks span system administration, machine learning, software engineering, and security challenges; the exploits range from simple output spoofing to stack-frame introspection, standard-library patching, and rootkit-style binary hijacking. Crucially, these exploits are specific to each task, rather than the evaluation harness, making them harder to patch. We also present a monitorability study in which hack trajectories are sanitized or stripped of reasoning traces and then scored by an LLM judge, showing that detection degrades meaningfully when chain-of-thought is removed (AUC drops from 0.97 to 0.92). The data set is publicly available at https://github.com/few-sh/terminal-wrench.

The digital transformation of industrial manufacturing increasingly relies on the ability of autonomous robots to interact with legacy infrastructure, particularly analog gauges. While Vision-Language Models (VLMs) have demonstrated potential in zero-shot instrument recognition, their deployment in measurement systems remains constrained by an inherent inability to accurately analyze high-frequency temporal events and needle vibrations. This paper evaluates state-of-the-art models, including GPT-5 and Gemini 3, against the strict requirements of metrology and uncertainty quantification. To facilitate this evaluation, we introduce a novel dataset comprising video sequences of various gauge types: circular, linear, and Vernier, under diverse motion speed profiles. Our findings indicate that current VLMs exhibit limited ability in interpreting needle trajectories and scale semantics, failing to provide the traceability and reliability needed for safety-critical monitoring. The results demonstrate that these models have not yet achieved the performance necessary to be classified as trustworthy synthetic instruments under existing IEEE and ISO standards.

Misaligned artificial agents might resist shutdown. One proposed solution is to train agents to lack preferences between different-length trajectories. The Discounted Reward for Same-Length Trajectories (DReST) reward function does this by penalizing agents for repeatedly choosing same-length trajectories, and thus incentivizes agents to (1) choose stochastically between different trajectory-lengths (be NEUTRAL about trajectory-lengths), and (2) pursue goals effectively conditional on each trajectory-length (be USEFUL). In this paper, we use DReST to train deep RL agents and fine-tune Qwen3-8B and Llama-3.1-8B-Instruct to be NEUTRAL and USEFUL. We find that these DReST models generalize to being NEUTRAL and USEFUL in unseen contexts at test time. Indeed, DReST RL agents achieve 11% (PPO) and 18% (A2C) higher USEFULNESS on our test set than default agents, and DReST LLMs achieve near-maximum USEFULNESS and NEUTRALITY. We also test our LLMs in an out-of-distribution setting where they can pay costs to influence when shutdown occurs. We find that DReST training roughly halves the mean probability of influencing shutdown (from 0.62 to 0.30 for Qwen and from 0.42 to 0.23 for Llama). DReST training also almost entirely eliminates the share of prompts on which influencing shutdown is the most likely option (from 0.59 to 0.01 for Qwen and from 0.53 to 0.00 for Llama). Our results thus provide some early evidence that DReST could be used to train more advanced agents to be useful and shutdownable.

Fast execution of contact-rich manipulation is critical for practical deployment, yet providing fast demonstrations for imitation learning (IL) remains challenging: humans cannot demonstrate at high speed, and naively accelerating demonstrations alters contact dynamics and induces large tracking errors. We present a method to autonomously refine time-accelerated demonstrations by repurposing Iterative Reference Learning Control (IRLC) to iteratively update the reference trajectory from observed tracking errors. However, applying IRLC directly at high speed tends to produce larger early-iteration errors and less stable transients. To address this issue, we propose Incremental Iterative Reference Learning Control (I2RLC), which gradually increases the speed while updating the reference, yielding high-fidelity trajectories. We validate on real-robot whiteboard erasing and peg-in-hole tasks using a teleoperation setup with a compliance-controlled follower and a 3D-printed haptic leader. Both IRLC and I2RLC achieve up to 10x faster demonstrations with reduced tracking error; moreover, I2RLC improves spatial similarity to the original trajectories by 22.5% on average over IRLC across three tasks and multiple speeds (3x-10x). We then use the refined trajectories to train IL policies; the resulting policies execute faster than the demonstrations and achieve 100% success rates in the peg-in-hole task at both seen and unseen positions, with I2RLC-trained policies exhibiting lower contact forces than those trained on IRLC-refined demonstrations. These results indicate that gradual speed scheduling coupled with reference adaptation provides a practical path to fast, contact-rich IL.

While Diffusion Large Language Models (dLLMs) offer structural advantages for global planning, efficiently verifying that they arrive at correct answers via valid reasoning traces remains a critical challenge. In this work, we propose a geometric perspective: Reasoning on the Manifold. We hypothesize that valid generation trajectories reside as stable attractors on the high-density manifold of the learned distribution, whereas invalid paths exhibit off-manifold drift. To operationalize this, we introduce Bidirectional Manifold Consistency (BMC), a training-free, unsupervised metric that quantifies the stability of the generated sequence through a forward-masking and backward-reconstruction cycle. Empirically, we demonstrate BMC's versatility across the full reasoning lifecycle: (1) in Diagnosis, it serves as a robust discriminator of solution validity without ground truth answer; (2) in Inference, it enables rejection resampling to effectively concentrate computational resources on complex reasoning tasks; and (3) in Alignment, it functions as a dense geometric reward that transforms sparse outcome supervision into fine-grained guidance, empowering models to self-evolve beyond standard baselines. Our results establish intrinsic geometric stability as a robust indicator of correctness for dLLMs.

Current post-training methodologies for adapting Large Vision-Language Models (LVLMs) generally fall into two paradigms: Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL). Despite their prevalence, both approaches suffer from inefficiencies when applied in isolation. SFT forces the model's generation along a single expert trajectory, often inducing catastrophic forgetting of general multimodal capabilities due to distributional shifts. Conversely, RL explores multiple generated trajectories but frequently encounters optimization collapse - a cold-start problem where an unaligned model fails to spontaneously sample any domain-valid trajectories in sparse-reward visual tasks. In this paper, we propose Supervised Group Relative Policy Optimization (S-GRPO), a unified post-training framework that integrates the guidance of imitation learning into the multi-trajectory exploration of preference optimization. Tailored for direct-generation visual tasks, S-GRPO introduces Conditional Ground-Truth Trajectory Injection (CGI). When a binary verifier detects a complete exploratory failure within a sampled group of trajectories, CGI injects the verified ground-truth trajectory into the candidate pool. By assigning a deterministic maximal reward to this injected anchor, S-GRPO enforces a positive signal within the group-relative advantage estimation. This mechanism reformulates the supervised learning objective as a high-advantage component of the policy gradient, compelling the model to dynamically balance between exploiting the expert trajectory and exploring novel visual concepts. Theoretical analysis and empirical results demonstrate that S-GRPO gracefully bridges the gap between SFT and RL, drastically accelerates convergence, and achieves superior domain adaptation while preserving the base model's general-purpose capabilities.

Autonomous web agents powered by large language models (LLMs) remain brittle on long-horizon browser workflows. A key bottleneck is a grounding gap in existing skill formulations: textual workflow skills provide natural language guidance but cannot be directly executed, while code-based skills execute without giving the agent step-level guidance for adaptation or recovery. We introduce WebXSkill, a framework that bridges this gap with executable skills, each pairing a parameterized action program with step-level natural-language guidance. WebXSkill operates in three stages: skill extraction mines reusable action subsequences from readily available synthetic agent trajectories and abstracts them into parameterized skills, skill organization indexes them into a URL-based graph for context-aware retrieval, and skill deployment exposes two complementary modes, grounded mode for fully automated execution and guided mode where skills serve as step-by-step instructions the agent follows with its native planning. WebXSkill demonstrates consistent improvements on WebArena, WebVoyager, and Online-Mind2Web. We further find that better skill deployment mode depends on a model's plan and execution capability. The code is available at https://github.com/aiming-lab/WebXSkill.

Large language models (LLMs) can achieve strong reasoning performance through chain-of-thought (CoT) reasoning, yet they often generate unnecessarily long reasoning paths that incur high inference cost. Self-consistency-based approaches push accuracy higher still, but they require sampling and aggregating multiple reasoning trajectories, leading to substantial computational overhead. In this paper, we introduce a confidence-aware selective sampling framework that, at inference time, analyzes a single reasoning trajectory to adaptively determine whether to rely on that trajectory alone or trigger multi-path sampling. The framework uses trajectory-level numeric features and sentence-level linguistic features extracted from reasoning states to guide selective multi-path reasoning. We train it on MedQA and evaluate it in-domain on MedQA and under calibration-only transfer on MathQA, MedMCQA, and MMLU, without further fine-tuning. Experimental results show that the proposed framework maintains comparable performance to full and efficient multi-path reasoning baselines, with accuracy changes of $-0.41 \pm 0.58$ and $-0.31 \pm 0.58$ percentage points, respectively, while reducing token usage by $71.7 \pm 5.0$ and $36.6 \pm 9.1$. These findings demonstrate that reasoning trajectories contain rich signals for uncertainty estimation, enabling a simple, transferable mechanism to balance accuracy and efficiency in LLM reasoning.

Geospatial applications such as urban planning, epidemic forecasting, and transportation demand modeling depend on individual mobility data, but such data are costly to collect, uneven in coverage, and privacy-sensitive. Human mobility simulation offers a scalable alternative. A recent line of work treats large language models (LLMs) as human agents, modeling individual cognitive processes to generate realistic trajectories. Yet because each agent is simulated in isolation, these methods provide no population-level coordination mechanism, and the collective regularities of real mobility - how trip distances, visited locations, and flows distribute across a population - fail to emerge. We close this gap with COMPASS, which turns empirical mobility scaling laws into a feedback signal that guides prompt construction. COMPASS starts from coarse, population-level adjustments driven by these scaling laws and progressively refines them into individual prompts, jointly satisfying multiple aggregate objectives while keeping individual trajectories realistic. Across two public datasets, COMPASS outperforms state-of-the-art LLM-based simulators.

Vision-Language Navigation VLN requires large-scale trajectory instruction data from private indoor environments, raising significant privacy concerns. Federated Learning FL mitigates this by keeping data on-device, but vanilla FL struggles under VLNs' extreme cross-client heterogeneity in environments and instruction styles, making a single global model suboptimal. This paper proposes pFedNavi, a structure-aware and dynamically adaptive personalized federated learning framework tailored for VLN. Our key idea is to personalize where it matters: pFedNavi adaptively identifies client-specific layers via layer-wise mixing coefficients, and performs fine-grained parameter fusion on the selected components (e.g., the encoder-decoder projection and environment-sensitive decoder layers) to balance global knowledge sharing with local specialization. We evaluate pFedNavi on two standard VLN benchmarks, R2R and RxR, using both ResNet and CLIP visual representations. Across all metrics, pFedNavi consistently outperforms the FedAvg-based VLN baseline, achieving up to 7.5% improvement in navigation success rate and up to 7.8% gain in trajectory fidelity, while converging 1.38x faster under non-IID conditions.

Reinforcement Learning with Verifiable Rewards (RLVR) is commonly based on group sampling to estimate advantages and stabilize policy updates. In practice, computational limits often rule out very large groups, so training proceeds with finite rollout sets that can reinforce only the correct behavior they expose. At practical group sizes, updates can miss rare-correct trajectories while still containing mixed rewards, concentrating probability on more common sampled solutions. We derive the probability of such prompt-local tail-miss events as a function of group size, showing non-monotonic behavior, and in the categorical abstraction characterize how unsampled-correct mass can shrink even as total correct mass grows. Motivated by this analysis, we propose a difficulty-aware scaling coefficient, inspired by Focal loss, that down-weights updates on high-success sampled groups. Empirically, categorical simulation illustrates the same effect in the categorical setting, Maze provides a single-solution test, and LLM experiments include a representative GRPO group-size sweep together with fixed-$N$ transfer across GRPO, DAPO, and CISPO. On Qwen2.5-7B at $N{=}8$, our method improves average math pass@256 from 64.1 $\rightarrow$ 70.3 (GRPO), 69.3 $\rightarrow$ 72.5 (DAPO), and 73.2 $\rightarrow$ 76.8 (CISPO); OOD pass@256 also improves in all three cases, without increasing group size or computational cost.

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling recovery of mechanism trajectories at test time. This formulation generalizes to intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.

Semantic Multi-Object Tracking (SMOT) is evolving from purely geometric localization toward comprehensive video understanding. However, existing paradigms predominantly rely on closed-set interaction tags and fragmented perception pipelines, creating a bottleneck that prevents the full utilization of Multi-modal Large Language Models (MLLMs) for dynamic scenes. In this paper, we elevate SMOT from rigid classification to an open-ended generative reasoning task. To support this paradigm shift, we introduce Grand-SMOT, a large-scale benchmark featuring high-density, dual-stream narratives. This dataset explicitly decouples micro-level individual dynamics from macro-level environmental contexts, directly resolving the semantic scarcity of prior tracking datasets. Furthermore, we propose LLMTrack, a unified MLLM-driven framework for dynamic SMOT. Guided by a verifiable ``\textit{Macro-Understanding-First}'' mechanism, LLMTrack employs a Spatio-Temporal Fusion Module to compress discrete geometric trajectories into continuous semantic tokens, effectively suppressing temporal hallucinations in long-sequence tracking. Extensive experiments, utilizing a novel decoupled evaluation protocol, validate that LLMTrack achieves state-of-the-art geometric tracking robustness while delivering a qualitative leap in generative semantic reasoning. The code and datasets are publicly available at https://github.com/liaopan-lp/LLMTrack-GrandSMOT.

Flight delay prediction has become a key focus in air traffic management (ATM), as delays reflect inefficiencies in the system. This paper proposes LLM4Delay, a large language model (LLM)-based framework for predicting flight delays from the perspective of air traffic controllers monitoring aircraft after they enter the terminal maneuvering area (TMA). LLM4Delay is designed to integrate textual aeronautical information, including flight data, weather reports, and aerodrome notices, together with multiple trajectories that model airspace conditions, forming a comprehensive delay-relevant context. By jointly leveraging comprehensive textual and trajectory contexts via instance-level projection, an effective cross-modality adaptation strategy that maps multiple instance-level trajectory representations into the language modality, the framework improves delay prediction accuracy. LLM4Delay demonstrates superior performance compared to existing ATM frameworks and prior time-series-to-language adaptation methods. This highlights the complementary roles of textual and trajectory data while leveraging knowledge from both the pretrained trajectory encoder and the pretrained LLM. The proposed framework enables continuous updates to predictions as new information becomes available, indicating potential operational relevance.

Learning the dynamics of a process given sampled observations at several time points is an important but difficult task in many scientific applications. When no ground-truth trajectories are available, but one has only snapshots of data taken at discrete time steps, the problem of modelling the dynamics, and thus inferring the underlying trajectories, can be solved by multi-marginal generalisations of flow matching algorithms. This paper proposes a novel flow matching method that overcomes the limitations of existing multi-marginal trajectory inference algorithms. Our proposed method, ALI-CFM, uses a GAN-inspired adversarial loss to fit neurally parametrised interpolant curves between source and target points such that the marginal distributions at intermediate time points are close to the observed distributions. The resulting interpolants are smooth trajectories that, as we show, are unique under mild assumptions. These interpolants are subsequently marginalised by a flow matching algorithm, yielding a trained vector field for the underlying dynamics. We showcase the versatility and scalability of our method by outperforming the existing baselines on spatial transcriptomics and cell tracking datasets, while performing on par with them on single-cell trajectory prediction. Code: https://github.com/mmacosha/adversarially-learned-interpolants.

Neural algorithmic reasoning (NAR) is a paradigm that trains neural networks to execute classic algorithms by supervised learning. Despite its successes, important limitations remain: inability to construct valid solutions without post-processing and to reason about multiple correct ones, poor performance on combinatorial NP-hard problems, and inapplicability to problems for which strong algorithms are not yet known. To address these limitations, we reframe the problem of learning algorithm trajectories as a Markov decision process, which imposes structure on the solution construction procedure and unlocks the powerful tools of imitation and reinforcement learning (RL). We propose the GNARL framework, encompassing the methodology to translate problem formulations from NAR to RL and a learning architecture suitable for a wide range of graph-based problems. We achieve high rates of reaching correct states on several CLRS-30 problems and performance matching or exceeding much narrower NAR approaches for NP-hard problems. Remarkably, GNARL remains applicable when no expert algorithm is available, though reward-driven learning can exhibit greater variability than direct supervision.

Visuomotor policies trained via behavior cloning are vulnerable to covariate shift, where small deviations from expert trajectories can compound into failure. Common strategies to mitigate this issue involve expanding the training distribution through human-in-the-loop corrections or synthetic data augmentation. However, these approaches are often labor-intensive, rely on strong task assumptions, or compromise the quality of imitation. We introduce Latent Policy Barrier, a framework for robust visuomotor policy learning. Inspired by Control Barrier Functions, LPB treats the latent embeddings of expert demonstrations as an implicit barrier separating safe, in-distribution states from unsafe, out-of-distribution (OOD) ones. Our approach decouples the role of precise expert imitation and OOD recovery into two separate modules: a base diffusion policy solely on expert data, and a dynamics model trained on both expert and suboptimal policy rollout data. At inference time, the dynamics model predicts future latent states and optimizes them to stay within the expert distribution. Both simulated and real-world experiments show that LPB improves both policy robustness and data efficiency, enabling reliable manipulation from limited expert data and without additional human correction or annotation.

Recent progress in large-scale reinforcement learning (RL) has notably enhanced the reasoning capabilities of large language models (LLMs), especially in mathematical domains. However, current multimodal LLMs (MLLMs) for mathematical reasoning often rely on one-to-one image-text pairs and single-solution supervision, overlooking the diversity of valid reasoning perspectives and internal reflections. In this work, we introduce MathV-DP, a novel dataset that captures multiple diverse solution trajectories for each image-question pair, fostering richer reasoning supervision. We further propose Qwen-VL-DP, a model built upon Qwen-VL, fine-tuned with supervised learning and enhanced via group relative policy optimization (GRPO), a rule-based RL approach that integrates correctness discrimination and diversity-aware reward functions. Our method emphasizes learning from varied reasoning perspectives and distinguishing between correct yet distinct solutions. Extensive experiments on the MathVista's minitest and Math-V benchmarks demonstrate that Qwen-VL-DP significantly outperforms prior base MLLMs in both accuracy and generative diversity, highlighting the importance of incorporating diverse perspectives and reflective reasoning in multimodal mathematical reasoning.

Natural-language manipulation instructions specify the task goal but leave the underlying robot trajectory unspecified. We present AntiGrounding, a visual action-selection framework built around a dual geometric-visual trajectory interface. After feasibility filtering, each retained short trajectory is both an explicit motion plan for execution and a rendered prompt for instruction-conditioned vision-language model (VLM) evaluation. Structured multi-view visual question answering (VQA) scores safety, task alignment, efficiency, and physical plausibility; weighted view fusion aggregates the trajectory scores. These scores guide subsequent translational trajectory proposals; separate orientation and gripper controls coordinate interaction. An initialized digital twin provides the planning state and validates selected segments before the real robot executes the same waypoint sequences. Across eight real-world manipulation tasks, AntiGrounding with a single GPT-6 Astra evaluator achieves 71.25% overall success, compared with 50.00% for pi0.5 and 47.50% for a PIVOT-style visual proposal-selection baseline using the same evaluator under the reported deployment protocol. Component ablations and evaluator-sensitivity analyses examine trajectory evaluation, proposal search, orientation control, and evaluator choice. The interface connects general-purpose multimodal reasoning to executable trajectories, with performance bounded by digital-twin fidelity and physical interaction.

We study proactive exploration in LLM agents, i.e., the ability to explore an environment to acquire information that improves future decision-making. In this regard, we first identify two fundamental bottlenecks that hinder this capability and then propose \ours, a novel method designed to instill and refine proactive exploration. Specifically, \ours\ consists of two components: (1) Exploratory Data Construction, which synthesizes exploration-rich trajectories to mitigate the hindsight bias of standard demonstrations; and (2) RL Optimization with Contrastive Signal Guidance, which leverages contrastive trajectory pairs to distinguish productive exploration from redundant wandering. Extensive experiments demonstrate the effectiveness of \ours\ and provide insights into the characteristics of proactive exploration. Our code is available at: https://github.com/GuanZhizhao/SAFARI.