Trajectory

Training LLM agents commonly relies on supervised fine-tuning from expert trajectories or online reinforcement learning over human-specified tasks with handcrafted verifiers. Though effective, both remain bottlenecked by externally specified tasks and supervision signals, limiting the scalability and diversity of agent training. We study an environment learning paradigm in which agents acquire interaction and manipulation capabilities solely through environment interaction, without externally specified tasks. We propose State2State, an environment-derived mid-training method that converts explored environment states into training objectives, challenging agents to reach a specified target state. By deriving tasks from environment exploration and verifying success through rule-based state matching, State2State provides scalable and verifiable training objectives without expert supervision or manual task design. Experiments on ALFWorld and ScienceWorld show that State2State improves agent performance as a standalone environment-learning stage in most settings. As initialization for downstream RL, it further improves final performance and learning efficiency, with promising evidence of cross-environment generalization.

Research agents increasingly conduct multi-round machine-learning experiments in industrial recommendation settings and retain the resulting trajectories to guide later decisions. Yet a completed trajectory is not automatically evidence: generated artifacts may be unsupported or incomplete, executed rounds may be invalid or confounded, and later modifications may obscure earlier findings. We study \textbf{trajectory-to-evidence conversion}, asking what a completed research process has actually established. We introduce an evidence-grounded framework that couples bounded verification of consequential artifacts with post-execution claim qualification. A context-isolated generate--verify--repair process checks artifacts for evidence violations and missing downstream requirements before release. After execution, validity and attribution checks consolidate evidence across rounds, qualify intervention-level claims as actionable repairs, diagnostic guards, or withheld findings, and preserve admitted claims as auditable records with explicit provenance and applicability boundaries. A hybrid LLM-assisted controller subsequently applies, defers, or rejects records based on available target evidence. Record audits characterize which claims survive qualification, while downstream diagnostics identify affirmative applicability judgment as a bottleneck for the tested controller. Across paper-to-target adaptations, later rounds often improve on the first, while final rounds frequently underperform an earlier best, exposing non-monotonic trajectory evolution. Candidates produced through the complete workflow also yielded positive online lifts relative to deployed baselines.

Privileged on-policy distillation provides dense supervision for multi-turn agents by allowing a synchronized teacher to re-score the student's response at every turn with access to training-only references, such as successful trajectories. In interactive environments, however, the student's preceding actions continually change the execution state. As the student takes different actions or completes subgoals in a different order, its rollout may reach states not covered by the reference, making the reference an unreliable source of guidance for the state actually reached. Applying privileged distillation indiscriminately therefore creates state--reference mismatch. This mismatch motivates a central objective: providing privileged reference guidance that remains compatible with the student's current execution state. We introduce State-Matched Routing and Contextualized Self-Distillation (SMRC-SD), which explicitly determines when and how a privileged trajectory should guide an on-policy student. At each turn, SMRC-SD verifies whether the student's current execution state matches a supported state along the reference trajectory. Distillation is applied only at matched states, filtering out turns for which the reference lacks locally compatible guidance. For each matched state, SMRC-SD further constructs state-conditioned teacher context from the successful trajectory, grounding supervision in the state actually reached. Across ALFWorld and WebShop, SMRC-SD consistently outperforms unconditional successful full-path distillation. With Qwen3-1.7B, it improves task success from $0.746$ to $0.865$ on ALFWorld and from $0.574$ to $0.693$ on WebShop. Controlled routing and context ablations support both selecting locally supported turns and constructing state-compatible teacher context as contributors to these gains. Code is available at https://github.com/liujunzhuo/SMRC-SD.

On-policy distillation (OPD) supervises student-visited trajectories, yet divergence-based rules cannot determine whether an erroneous prefix remains correctable. We formulate this decision as counterfactual recoverability and replay each error state through budget-matched teacher-continuation and rollback branches. Based on their relative success, states are categorized as recoverable, irreversible-but-avoidable, or ambiguous, and these labels guide whether training retains, rolls back, or conventionally supervises the corresponding trajectory. On AIME branch diagnostics, the mean continuation-minus-rollback effect is 0.185 for recoverable states and -1.000 for irreversible-but-avoidable states, demonstrating opposite intervention preferences. A branch-derived recoverability proxy achieves an AUC of 1.000, substantially outperforming divergence alone at 0.392. Across frozen evaluations, recoverability-aware control achieves the strongest recorded performance, reaching 0.578 success on held-out AIME2025 compared with 0.517 for the best baseline. It also improves AIME2024-2025 average@32 from 0.2656 to 0.3125 and GPQA-Diamond average@32 from 0.2702 to 0.3070. Component ablations further show that retaining teacher-correctable prefixes provides the largest individual contribution. These findings establish recoverability as an outcome-grounded decision variable for selective supervision in OPD.

On-policy training has emerged as a powerful post-training paradigm for improving the reasoning capabilities of large language models, and is often enhanced by golden trajectories from stronger expert models. However, when the expert fails on harder problems, existing trajectory-guided methods lose their main source of supervision, and these failed trajectories are typically discarded as negative samples. We argue that such failures, which we call Golden Negative Trajectories, can still provide valuable reasoning signals when treated not as demonstrations to imitate, but as flawed trajectories to reflect upon. We identify a Reflection Advantage: for hard problems, reflecting on a flawed trajectory can be easier and more effective than solving the problem directly from scratch. Motivated by this, we propose ReflectRL, a lightweight plug-and-play framework that learns from Golden Negative Trajectories during on-policy training. ReflectRL first uses these trajectories to elicit Reflective Reasoning, then applies Reflective-to-Direct Policy Transition to transfer the acquired reasoning behavior back to Direct Reasoning. Experiments across 9 benchmarks, 4 LLM backbones, and 4 on-policy training methods show that ReflectRL consistently improves reasoning performance with minimal overhead.

Trajectory inference is a fundamental problem in many scientific domains: given a collection of unpaired snapshots of observations at discrete time points, the goal is to generate smooth trajectories that best resemble and interpolate the data. Existing algorithms exhibit computational challenges: they either rely on preprocessing subroutines to enforce smoothness or on simulation-based training objectives, both of which can be expensive. In order to overcome these limitations, we propose a new algorithm called Acceleration Matching (\texttt{AM}). Our approach consists of lifting the original interpolation problem to phase space and then regressing onto an explicit conditional acceleration field that induces random, smooth trajectories that agree with the prescribed marginals. Importantly, our resulting training algorithm only requires positional data, avoids trajectory simulation during training, and is devoid of expensive preprocessing. We provide ample numerical evidence suggesting that \texttt{AM} is competitive with or superior to existing algorithms on several benchmark problems from the existing literature.

Forecasting precise future motion of surrounding agents is essential for reliable autonomous vehicles. However, as the demand for longer prediction horizons increases, existing endpoint-completion or iterative-refine methods increasingly struggle with weak guidance and compounding errors. To tackle the long-horizon prediction challenge, we propose Pivot-Centric Trajectory Prediction (PCTP). By introducing pivots'' and focusing on predicting pivot points along extended trajectories, we divide the long-term prediction task into short-term sub-tasks at various scales. Specifically, PCTP decouples the long-term trajectory predicting process into two processes: pivot prediction and pivot-based trajectory refinement. The pivot prediction process aims to utilize global map context and agent-to-agent interactions to identify these pivot points'', while the pivot-based trajectory refinement process focuses on local map details and refines the short-term trajectory based on predicted ``pivot points''. Compared with existing methods, PCTP provides more intermediate guidance while reducing compounding errors. Moreover, PCTP is a flexible approach that can be integrated into most state-of-the-art trajectory prediction models. Experimental results show that PCTP improves the prediction accuracy of leading models on both Argoverse I and Argoverse II datasets with minimal impact on model size. Specifically, PCTP combined with QCNet outperforms all published ensemble-free methods on the Argoverse II leaderboard at submission.

Image-goal visual navigation is a fundamental capability for embodied agents. Existing navigation policies efficiently predict waypoint trajectories but lack visual foresight, while navigation world models can anticipate future observations but often require costly planning rollouts. We present UniNav, a unified world-action model that generates future visual observations and continuous waypoint trajectories through a single diffusion process. Given history frames and a goal image, UniNav jointly denoises visual and waypoint tokens within a single transformer, unifying future prediction and action generation in a shared framework. To improve spatial grounding, we incorporate geometry-aware camera tokens. We also train on both trajectory-labeled navigation data and video-only data, enabling the model to benefit from diverse videos without waypoint annotations. Based on this unified framework, we introduce two variants: UniNav-Full jointly predicts interpretable future observations and their corresponding trajectories, while UniNav-Fast removes future-image tokens at inference for efficient trajectory prediction. Experiments on navigation benchmarks show that UniNav outperforms the strongest baseline in ATE across all datasets. With one-step inference, UniNav-Fast achieves a latency of 0.1s without a substantial accuracy drop. Code will be released.

Controllable local editing of 3D assets requires precise target localization and appropriate visual guidance. However, existing methods lack a simple yet accurate way to obtain 3D masks and struggle to achieve the desired edit while faithfully preserving the structure and appearance of non-target regions. To address these challenges, we present EditFlow3D, a training-free framework for local 3D editing. Given a source asset and an edit instruction, a VLM-driven workflow interprets the editing intent and automatically constructs a visual guidance image and a refined 3D editing mask, enabling localized editing in the native representation space of a pretrained 3D generative model. Specifically, mask-guided differential flow focuses the edit on the target region, while step-wise trajectory preservation maintains consistency between non-target regions and the source asset without directly replacing intermediate features. Since the existing Edit3D-Bench covers only a limited range of local editing categories, we further introduce EditFlow-Bench as a complementary benchmark encompassing a broader variety of structural and appearance edits, and evaluate EditFlow3D on both benchmarks. Quantitative results, qualitative comparisons, and a user study demonstrate that EditFlow3D achieves more accurate target-region editing and better preserves non-target regions than existing 3D editing methods.

This research proposes a constrained motion planning framework for robot manipulators in human-robot interaction (HRI). For a non-redundant manipulator with a fully specified end-effector pose, additional requirements such as collision avoidance and self-collision avoidance are difficult to handle as simple null-space secondary tasks. This limitation makes it challenging to generate feasible joint-space trajectories in HRI environments where safety and kinematic constraints must be considered simultaneously. To address this limitation, collision- and self-collision-aware trajectories are generated using Rapidly-exploring Random Tree (RRT) and RRT* algorithms, and the resulting dataset is used to train a diffusion model that generates constraint-satisfying trajectories through guided sampling. To reduce the inference time required for iterative diffusion sampling, consistency distillation is applied, and a joint-weighted jerk regularization term is incorporated into the loss function to promote smoother trajectories by penalizing abrupt changes in joint acceleration. Simulation results show that the consistency model generates 150 trajectory candidates in less than 100 ms, maintains a high episode success rate, and substantially reduces joint and end-effector jerk when jerk regularization is applied.

Text-to-image diffusion models can generate individual concepts well, but they often omit or merge concepts incorrectly with multiple concepts. We trace these failures to an early coordination bottleneck: before denoising begins, prompt-conditioned attention may allocate different concepts to strongly overlapping spatial support, which can keep their attention coupled as denoising proceeds. This observation motivates treating compositional generation as a boundary-condition problem rather than repeatedly controlling the evolving trajectory. To this end, we propose Rectify-then-Diffuse (RTD), a training-free framework that rectifies the initial allocation once before standard denoising. Firstly, we propose Soft-Overlap Disentanglement (SOD), which converts normalized overlap between pilot concept maps into a differentiable and layout-agnostic separation objective. Secondly, we introduce Isotropic Gradient Rectification (IGR), which normalizes the SOD gradient and applies a bounded latent displacement with a consistent scale across prompts and initializations. Extensive experiments show that RTD achieves state-of-the-art compositional fidelity and robust gains. On the AE-Bench object pair subset, RTD improves BLIP-VQA by 45.8% and ImageReward by 19.6% over CO3 while running 2.3$\times$ faster. Code will be released at https://github.com/Z-yiwei/rectify-then-diffuse

End-to-end driving requires a coherent understanding of future scenes, yet existing methods model these scenes using task-specific heads and output formats, with limited scalability. Can video generation instead provide a shared predictor? We introduce SUV, a unified end-to-end driving framework that casts future Scene Understanding as Video generation using a pretrained video foundation model. SUV models future appearance, semantics, relative depth, and instance-level dynamics as video streams with a shared video expert, without stream-specific visual prediction heads. Through joint video-action attention, the action expert attends to the latent representations of all future streams and generates the ego trajectory. Experiments show that SUV directly predicts all four future streams, while controlled ablations show that structured future supervision and direct future-stream access yield higher trajectory planning scores. With only a single front camera and no candidate-trajectory selection, SUV outperforms a broad set of recent state-of-the-art methods on both NAVSIM-v2 splits, achieving 91.0 EPDMS on navtest and 36.9 on navhard. On the long-tail WOD-E2E benchmark, SUV achieves a competitive RFS of 7.94.

Reinforcement learning (RL) has emerged as an effective method for enhancing the reasoning capabilities of large language models (LLMs). However, existing methods suffer from insufficient precision in feedback on generated answer trajectories and exhibit the phenomenon of problem difficulty drift. To address these challenges, we propose CVPO - Curriculum-guided Value-Variance Policy Optimization. At the response trajectory level, we find that token-level value-variance correlates with exploration intensity. Our theoretical analysis shows this variance bounds policy update magnitude. We then use the estimated trajectory value-variance to quantify the intrinsic randomness in generation. Based on this, we design a variance-aware advantage adjustment mechanism for different reward types. At the question level, we introduce a dynamic curriculum weighting method that adapts to question difficulty. This helps the model focus on tasks matched to its current ability during each training stage. Experimental results show our method outperforms strong value-based baselines like VAPO. It achieves better performance and stronger exploration, enabling more accurate and robust reasoning in language models across various math tasks.

A stable compression score can still select the worse model. In our dense study, a split-half reliable path-quadratic score predicted a 16.1% gain, while the selected endpoints were 6.0--7.7% worse than two controls. We ask what a compression statistic can justify when deployment cares about the worst supplied group. We treat each statistic as an information interface. Its observation leaves a fiber of compatible endpoint-risk tables, and only orders fixed across that fiber are identified. Cone and fiber identities quantify the remaining uncertainty, while matched observations reverse endpoint order for pooled moments, group-local moments, and reference-path curvature. Sequential composition adds one state variable: the slack from each group risk to the current maximum. This vector determines every unrestricted one-step response, and a margin condition keeps the active group fixed along paths with bounded relative drift. The experiments follow the same ladder. Across three dense LLMs, an early-preserving allocation reduces worst-group perplexity inflation by 12.6--20.9%; target-matched complete-menu selection improves over its references by 2.7--8.0%. Across all 16 routed layers of OLMoE, pooled endpoint refresh lowers held-out worst-group teacher KL by 15.8% over the best static score. A compute-matched hard-max trajectory ends 32.7% worse than pooled, and neither adaptive trajectory improves excess NLL. Local evidence can narrow a menu. Complete endpoints rank that menu, while multistep claims also require control of the evolving active face and future candidates.

We present a biconvex approach for minimum-time motion planning around convex obstacles that is guaranteed to converge, is anytime, and supports derivative constraints to arbitrary order. We jointly convexify the minimum-time objective and all derivative constraints through a change of variables, and handle collision avoidance via time-varying separating planes, reducing the problem to a biconvex program. This program is solved by alternating between computing maximum-margin separating planes and optimizing the trajectory. By only adding planes for obstacles that the current iterate collides with, the trajectory can jump around obstacles and escape local minima. The method is guaranteed to converge starting from a simple collision-free polygonal curve. In our experiments on drone navigation and dual-arm bin unloading, we find that the proposed method reliably produces high-quality trajectories with computation times comparable to state-of-the-art decomposition-based motion planners, while handling a larger class of problems and being substantially more robust to bad initialization. Project page:https://wernerpe.github.io/bmtp-website/

Existing active reconstruction systems with Gaussian-splatting maps select observations greedily, optimizing a single next-best-view (NBV) at each step and connecting the chosen views by short-horizon path planning. This greedy decoupling disregards the global structure of scene information, producing inefficient trajectories that waste sensing capacity in transit between selected views. In this work, we study active reconstruction as an ergodic coverage problem: the time-averaged spatial statistics of the sensor trajectory should match a target information distribution induced by the current map. Our approach derives this target distribution online from uncertainty and visibility, and calculates ergodic trajectories via a kernel-ergodic horizon planner with gradient flow and footprint depletion, closing the loop between mapping and trajectory optimization. We thoroughly evaluate TRACE on the Replica dataset against the Next-Best-View (NBV) baselines, improving PSNR by 1.5 dB. Code: https://github.com/spikelab-jhu/trace-active-reconstruction.

Long-horizon coding-agent trajectories are poorly matched to the credit units available to train on: a single action has no stable value, an episode label merges productive exploration with abandoned directions, and a fixed window cuts where the logging mechanics fall. We introduce collection-time semantic self-segmentation, in which a declarative contract has the acting agent expose its own boundaries while the trajectory is generated. Instantiated with falsifiable causal hypotheses, successive adoptions expose variable-length semantic phases, and no milestone vocabulary, gold patch, environment replay, teacher logits, or retrospective segmenter places a boundary. Because the agent names its conjecture, a reviewer can negate it by name, which lets our protocol manufacture wrong-cause-then-correction transitions that recorded work rarely contains; one collection then yields four supervised targets, including audit supervision from exactly the failed regions an episode label discards. We then ask what survives deleting the declaration. Given the cut points but not the hypothesis, a model attributes action blocks to their governing hypothesis at over twice chance, beating equal-length blocks over the same trajectories (paired sign test $p = 0.0002$), surviving a lexical control and collapsing under label permutation. Asked instead to place boundaries, a code-blind annotator matches 24 of 40 where random placement matches 11.5, while a mechanical test-event rule beats chance at neither end of a strict-to-permissive sweep. The segments are therefore coherent and not cheaply reproducible. Downstream, DPO on 2,551 phase-boundary pairs changes no decision on 91 adversarial held-out items, while four of 60 change on matched-construction items, all wrong to right, where two controls change none: with 1,825 pairs from one generator, the variable to vary next is corpus diversity, not the boundary.

Realistic and diverse trajectory generation is central to enabling higher levels of vehicle automation. While rule-based and classical learning-based methods may struggle to capture the complexity of traffic behavior, generative models have already demonstrated in other fields that they can handle a comparable level of complexity. In this paper, we build upon previous work on generative adversarial network (GAN)-based semantic bird's-eye-view traffic generation and extend the proposed framework in several key aspects. We improve the semantic representation, replace the trajectory extraction procedure with a graph-based association method, and systematically investigate increasingly larger fields of view. In addition, we introduce a quantitative evaluation framework to assess hallucinations and object permanence in generated videos. Our experiments demonstrate that the framework generalizes to larger and more complex traffic scenes while maintaining statistically realistic trajectories and coherent spatial relationships between traffic participants. Within 150GPU hours of training and with inference times below 20ms for scenes of up to 20s, our results demonstrate that video-based GANs remain an efficient and scalable approach for realistic trajectory generation, even in substantially larger traffic scenes, making them well suited for downstream tasks such as prediction, planning, and simulation in automated driving.

Agents built around large language models continually accumulate interaction trajectories during deployment, yet their behavior typically remains fixed. Beyond updating model weights, these trajectories can improve the agent harness that constructs context, mediates tools, validates actions, and recovers execution. We introduce Harness-R1, the first method, to our knowledge, that makes failure-conditioned, lifecycle-wide editing of an existing executable runtime a learned capability. It post-trains a dedicated harness engineer with online reinforcement learning so that its edits are optimized for the realized task success they produce, rather than proposed by a fixed editor. A separate 9B engineer converts batches of target-agent failures into validated executable patches; fresh same-batch reruns of the frozen target provide outcome rewards, so training updates only the engineer. Cold-start supervised fine-tuning initializes this editing policy, which is then trained online with group-relative policy optimization. Across WebShop, ALFWorld, and DBBench, Harness-R1 raises vanilla Qwen3.5-9B success from 44.3% to 53.6% (+9.3 percentage points). After direct target-agent fine-tuning, a target-specific engineer raises the average further from 59.2% to 64.2% (+5.0 points); because these gains hold both before and after fine-tuning the target, Harness-R1 points toward co-evolving the harness engineer and the target agent.

Agentic multimodal reasoning extends passive image understanding by allowing VLMs to actively acquire and refine visual evidence through visual tool interactions. Effective visual tool use requires three capabilities: grounding tool calls in visual context, composing tools across multiple steps, and adapting reasoning to tool-returned observations. However, existing approaches largely focus on grounding within fixed tool spaces and rigid invocation patterns, leaving composition and adaptation insufficiently addressed. We present VC-Tooler, which learns visual tool use as a compositional and adaptive capability. To this end, we first build a trajectory bank through a hierarchical synthesis pipeline covering three capability levels: single-tool grounding, multi-tool composition, and diverse tool contexts and interfaces. We then train the model in two stages: a supervised cold start that establishes these capabilities, followed by reinforcement learning that encourages accurate, efficient, and context-aware visual tool use. VC-Tooler achieves state-of-the-art performance among open-source models on both general-purpose and agentic benchmarks, including $95.8\%$ on V* and $35.3\%$ on VTC-Bench, and shows promising transfer under richer tool settings at inference time. Project page: https://w1zheng.github.io/VC-Tooler

Dynamic 3D scene reconstruction has achieved remarkable success under the assumption of strictly synchronized multi-camera inputs. However, in real-world scenarios, temporal asynchrony among capturing devices remains a critical challenge, leading to severe motion blur and geometric artifacts. Existing asynchronous reconstruction methods typically estimate temporal offsets through photometric supervision, but appearance matching provides weak temporal cues under large offsets and complex motions. We attribute this limitation to two major bottlenecks: texture-induced collapse, where low-texture regions provide nearly vanishing alignment signals, and deformation-induced coupling, where temporal errors are absorbed into distorted geometry or motion rather than being explicitly corrected. To address these issues, we propose ASTRA (Asynchronous Spatio-Temporal Reconstruction via Trajectory Alignment), a framework that introduces 2D motion trajectories as explicit, texture-agnostic supervision for asynchronous dynamic reconstruction. Instead of synchronizing cameras solely through rendered color residuals, ASTRA jointly optimizes temporal offsets and dynamic 3D representations by aligning the projected motion of reconstructed 3D points with observed 2D trajectories, while using dynamic and certainty masking to suppress unreliable trajectory constraints. Extensive experiments on different dynamic Gaussian Splatting backbones show that ASTRA preserves high-frequency spatial details and sustains strong robustness even under severe asynchrony with up to 25-frame offsets, achieving approximately 1.4 dB PSNR improvement, reducing temporal-offset MAE by 54.0%, and nearly quadrupling the synchronization success rate.

On-policy distillation (OPD) provides teacher supervision on states visited by the student, reducing the distribution gap between training and inference. However, in multi-turn agentic tasks, student deviations may accumulate over time, gradually moving the trajectory away from states where teacher guidance remains effective. Our quantitative analysis further shows that high-disagreement states offer promising opportunities for teacher guidance, but determining whether such guidance is beneficial requires examining its effect on subsequent student trajectories. We propose FutureBridge-OPD (FTB), which executes a short teacher bridge at a high disagreement state and uses the resulting student continuation to assess whether the bridge increases the density of positive distillation signals relative to the teacher. On ALFWorld, WebShop, and ScienceWorld, under the main Qwen3-32B teacher to Qwen3-1.7B student setting, FTB outperforms vanilla OPD and TCOD by an average of 16.6 and 7.6 points, respectively, and remains effective across student scales and teacher settings. Our code is publicly available at https://github.com/ChenChiShui/FutureBridge-OPD.

JEPA-style visual world models offer an effective paradigm for visual goal planning by predicting future latent representations. Existing methods typically learn local transition consistency through next-step representation prediction. However, in long-horizon tasks, accurate local prediction alone need not ensure sustained progress toward the goal. First, multi-step rollouts can remain locally plausible while drifting away from goal-relevant trajectories. Second, locally similar future states can correspond to substantially different long-term progress, making them difficult to distinguish in a latent space optimized mainly for local consistency. To address these challenges, we introduce goal-conditioned progress order, a relative ordering of states according to how they advance toward a given goal. This order exhibits an asymmetric, coarse-to-fine structure: early states retain broader future possibilities, while later states concentrate on more specific goal-relevant regions. Such a structure is well suited to hyperbolic geometry. Motivated by this observation, we propose ProWorld, a progress-aware hyperbolic visual world model. ProWorld leverages goal-conditioned progress order to organize visual latent-space dynamics, maintains directional progress within trajectories via hyperbolic entailment learning, and mitigates progress ambiguity among locally similar future states via hyperbolic future discrimination. Furthermore, we design a progress-aware planning objective that scores candidate rollouts by jointly considering proximity to the goal and sustained progress across intermediate states. Experiments on four visual goal-reaching tasks demonstrate that ProWorld achieves an average absolute success-rate gain of 9.67 over LeWM. The code will be released after the paper is accepted.

Geographic Information System (GIS) professionals rely on multi-step spatial analysis workflows to support decision-making in urban planning, disaster response, and environmental monitoring. The process is tedious, time-consuming, and error-prone. While recent large language model (LLM) agents equipped with external tools have the potential to automate geospatial analysis, their ability to perform realistic GIS workflows remains largely unexplored. Existing GIS agent benchmarking datasets are mostly drawn from textbooks, tutorials, or LLM-generated seeds and remain limited in size and trajectory depth. More importantly, none provides ground truth outputs. They therefore rely on surrogate signals such as code similarity, trajectory matching, or LLM and VLM judges, which can conflate workflow resemblance with task correctness. To address this gap, we introduce GISAgentBench, a benchmark of 349 multi-step GIS tasks curated from GIS Stack Exchange and instantiated on real public data across six selected geographic areas of interest. Each task ships with an executable reference trajectory and an exact ground truth output file, enabling strict, deterministic, tolerance-aware output matching beyond LLM judging. Evaluations of six LLM models reveal that realistic GIS workflows remain challenging: the best agent completes only 32.7% of tasks under strict tolerance-aware scoring, although most models produce outputs that are close to the ground truth.

This paper studies feedback Nash equilibrium (FBNE) seeking for multi-agent trajectory planning in nonlinear dynamical systems with unknown agents' objectives and state-dependent inter-agent coupling. While dynamic game theory provides a principled framework for such problems, existing approaches typically assume fully rational agents with known objectives or rely on fixed regularization, limiting their ability to capture bounded rationality and spatially varying interaction intensity in safety-critical settings. To this end, we propose a KL-regularized dynamic game with a state-dependent weight that adaptively balances optimality and behavioral priors. To infer unknown cost parameters from demonstrated behaviors, we develop a context-aware inverse game module based on maximum-entropy inverse reinforcement learning with physics-informed regularization, ensuring structural consistency with the forward game. We establish per-iteration well-posedness of the regularized local game and show that the adaptive weighting function remains Lipschitz continuous under bounded nominal-trajectory updates. Numerical simulations and multi-robot experiments on cooperative navigation and merging scenarios validate the effectiveness of the proposed framework.

Optimal trajectory generation for rigid-body motions on Lie groups can be formulated as a variational problem that minimizes energy functionals defined by Riemannian metrics. While closed-form solutions exist for special cases such as product metrics and rest-to-rest boundary conditions, solving the general problem with arbitrary boundary states and coupled rotational-translational metrics often requires computationally expensive numerical boundary value solvers. These limitations restrict the use of geometrically consistent trajectory generation in real-time robotic planning and control. This paper presents a learning-based framework for approximating higher-order smooth trajectories on SE(3) under general left-invariant Riemannian metrics. The method parameterizes body-twist trajectories using high-order polynomials and relies on a neural network to learn a subset of the polynomial coefficients and the trajectory duration. The remaining coefficients are analytically determined to enforce the boundary conditions. The training of the network is guided by losses derived from Euler-Lagrange optimality conditions, metric-weighted smoothness objectives, and feasibility constraints. The metric-conditioned framework enables generalization across diverse metric structures and motion conditions. Extensive numerical experiments demonstrate that the proposed approach generates smooth trajectories that closely approximate solutions from numerical optimization while achieving millisecond-level inference times. We demonstrate two practical applications of the proposed framework: real-time generation of diverse motion primitives with waypoint traversal, and refinement for quadrotor flight under dynamic conditions. These results suggest that learning-based motions with geometric structure can provide an efficient alternative to conventional optimization-based methods for trajectory generation on SE(3).

Autonomous agents are increasingly used to execute consequential tasks in environments governed by operational constraints, organizational policies, regulatory requirements, and technical standards. Their safety is therefore determined not by the correctness of individual actions, but by whether their overall behavior remains consistent with the rules and invariants of the systems in which they operate. As large language model (LLM)-based agents become more autonomous and increasingly delegate tasks across organizational boundaries, securing them evolves from a single challenge into a broad and interconnected landscape spanning the entire agentic stack. At the single-agent level, untrusted inputs through prompts, memory, retrieved knowledge, and tool interfaces create attack surfaces. In multi-agent settings, delegation and communication introduce challenges related to identity, trust, capability control, and decision transparency, while the underlying model routing and execution control plane remains vulnerable to manipulation and to unverified model provenance. Perhaps the most fundamental challenge is behavioral containment: sequences of individually permissible actions may collectively violate system-level constraints and safety invariants. At the broader level, supply-chain integrity, provenance, accountability, and end-to-end observability remain largely open problems. A common principle unifies these directions: security must become a verifiable property of the architectures, protocols, and runtimes that govern agent behavior, rather than an optional layer of guidance. Charting these challenges provides a roadmap toward trustworthy autonomous agent deployment.

Mobile manipulation requires a robot to coordinate base and arm motion under continuously changing viewpoints and contact conditions, within an action space far larger than that of fixed-base manipulation. Existing Vision-Language-Action (VLA) policies are limited in two respects. (i)They map observations directly to whole-body action chunks, searching this large action space without an explicit task-space motion plan, which makes coordinated base--arm prediction imprecise. (ii)They execute the predicted chunk open-loop, without checking whether the actions can realize the motion the policy intended, so control errors and unmodeled contacts accumulate into a gap between planned and realized motion. We present DreamTrajectory, a trajectory-guided framework for language-conditioned mobile manipulation that introduces one component for each limitation. Addressing(i), DreamTrajectory jointly predicts an intention-level end-effector trajectory and a whole-body action chunk in a single action expert, so that the trajectory explicitly guides base--arm action generation instead of remaining implicit. Addressing(ii), a lightweight trajectory world model predicts the trajectory that a candidate action chunk would induce, and a test-time search--predict--score procedure selects the candidate best aligned with the planned trajectory. On MS-HAB, trajectory guidance raises average success from 32.3% to 47.5% and test-time refinement further to 54.8%, with the largest gains on contact-rich articulated-object tasks. On three real-world mobile manipulation tasks, the corresponding average success rates are 63.3%, 81.7%, and 90.0%.

Despite recent progress in Vision-Language-Action (VLA) models for robotic manipulation, the action chunk remains a weakly structured interface. Existing work typically flatten each chunk into per-timestep controls, relying on implicit data learning that manifests as jagged motion and boundary discontinuities during physical execution. To address these limitations, we introduce Hermite trajectory priors, parameterizing the chunk trajectory as a piecewise cubic Hermite curve defined by endpoint positions and velocities to explicitly enforce smoothness and continuity. We instantiate this fixed operator across discrete autoregressive and continuous generative paradigms via three variants: (1) Hermite Tokens, which predict quantized boundary variables autoregressively; (2) Hermite Scaffold, which decomposes clean actions into a base scaffold and residuals; and (3) Hermite Regularization, which applies the prior strictly as an auxiliary training objective. Across simulation benchmarks and real-robot platforms, Hermite Regularization achieves superior performance among these three variants, improving π0.5 baseline success rates from 95.9% to 98.7% on LIBERO, 85.7% to 90.9% on LIBERO-plus, and 63.4% to 90.0% across four real-robot tasks without additional inference overhead. Trajectory analyses reveal that explicitly structuring trajectory priors serves most effectively as a learning inductive bias rather than a runtime constraint.

Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning, but standard LoRA produces a single deterministic model and does not directly support predictive uncertainty estimation. We introduce EulerLoRA, a stochastic extension of LoRA that generates multiple predictive trajectories by sampling structured variations along the rank-one components of shared low-rank adapters, while preserving the deterministic LoRA transformation in expectation. We evaluate EulerLoRA with vision transformers on CIFAR-10, CIFAR-100, and HAM10000, together with out-of-distribution detection on SVHN. Across these benchmarks, EulerLoRA achieves comparable or improved performance relative to strong LoRA-Ensemble baselines. Using two rank-20 adapters, EulerLoRA requires approximately 3 million trainable adapter parameters, compared with about 10 million for a rank-8, 16-adapter LoRA-Ensemble, corresponding to roughly 69% fewer trainable parameters. These results show that useful predictive diversity can be obtained from a small number of shared adapters.

A broad range of models face the mismatch where they are updated through trajectory losses but are evaluated by downstream task reward. Here, a trajectory is a training instance that induces a surrogate loss whose reduction might not track the model's decision utility update. Theoretically, we ask when one step of trajectory training reduces both population surrogate loss and decision risk, and how transfer accumulates along repeated updates. To formalize this, we first fix a checkpoint and a restricted update space, and define the reductions in population surrogate risk and decision risk induced by a trajectory as its learnability and decision utility, respectively. On this basis, our theory yields four main results. First, a one-step transfer bound separates their discrepancy into first-order gradient misalignment after nonnegative calibration and second-order curvature; and a pathwise extension accumulates the same terms over repeated updates. Second, when the accessible surrogate gradient is nonzero, universal first-order transfer over every accessible direction holds exactly when the accessible surrogate and decision gradients are positively collinear. Third, the calibration gap bounds the decision regret of learnability-based trajectory selection, while a candidate-difference refinement tightens this guarantee by retaining only directions that affect pairwise rankings. Finally, we establish an approximation--calibration trade-off across nested update spaces. Controlled gridworld and LLM post-training experiments yield results consistent with our predictions.

Trajectory similarity learning is fundamental to efficient trajectory retrieval under complex distance measures. Existing learning-based methods typically rely on embeddings trained to approximate trajectory distances or rankings, but they often lack guarantees with respect to the original distances, exhibit unstable performance across distance measures, and incur substantial training costs. We revisit trajectory similarity learning from a lower-bound representation perspective and propose LB-TrajRep, a unified lower-bound representation framework independent of deep neural embeddings. This framework constructs single-vector representations from a set of lower-bound components, enabling admissible and interpretable lower bounds for multiple classical trajectory distances, including Dynamic Time Warping (DTW), Hausdorff distance, and Discrete Fréchet Distance (DFD). Within this framework, we instantiate point-pivot components, which naturally support both metric and non-metric distances and remain compatible with standard vector-based retrieval pipelines. To improve ranking quality, we develop two data-driven pivot selection strategies that explicitly optimize lower-bound tightness and prioritize hard near-neighbor trajectory pairs, respectively. Extensive experiments on real-world trajectory datasets show that the proposed lower-bound representations are able to consistently outperform state-of-the-art neural trajectory embeddings across diverse distance measures, improving top-$k$ ranking accuracy by up to 20%--60% on the Hausdorff distance and DFD and by 15%--40% on DTW.

Large language model agents have shown strong capabilities in generating coherent and contextually appropriate responses, yet robust long-horizon dialogue remains limited by the lack of external memory that is traceable, updatable, and diagnostically transparent. Existing memory-augmented agents often store memories as isolated records or overwritable states, making it difficult to preserve how information originates, evolves, conflicts, or becomes obsolete over time. We propose TrajWiki, a trajectory-based memory framework for long-horizon conversational agents. Instead of treating memory as static entries, TrajWiki represents each memory as a source-grounded evolution trajectory, maintained through immutable episodic snapshots and claim-level operations such as ADD, REVISE, and DEPRECATE. To reduce fragmentation and retrieval cost, TrajWiki further introduces Memory Wiki, a persistent intermediate layer that incrementally compiles dialogue history into structured and interlinked wiki pages capturing salient entities, events, quantities, topics, and conflicts. At inference time, queries are routed hierarchically from relevant wiki pages to linked memory trajectories, then to corresponding snapshots and source messages for evidence-grounded answer synthesis. Experiments on LoCoMo and MedMT show that TrajWiki improves long-horizon dialogue performance across both open-source and closed-source LLM backbones, while providing greater interpretability and diagnostic visibility into memory evolution, retrieval failures, and answer generation.

Trajectory prediction of surrounding agents is a prerequisite for safe planning and decision making in autonomous driving. Without high-definition (HD) maps, sensor-derived bird's-eye-view (BEV) features provide no explicit lane topology or drivable-area priors, making it inherently difficult to ground each agent in its surrounding scene context. Moreover, physical feasibility remains difficult to capture through data-driven learning alone, as kinematic constraints on agent motion cannot be explicitly encoded without structured supervision. Existing map-free predictors extract scene context in an agent-agnostic manner through a single fusion step and treat physical constraints only as output-level penalties, leaving both challenges unaddressed. We propose SIPTraj, a map-free trajectory prediction framework that jointly addresses scene grounding and physical feasibility. SIPTraj introduces a Hierarchical Agent-Scene Encoder (HASE) progressively grounding each agent in agent-guided scene evidence and refining inter-agent relations within the scene-grounded space. To tackle physical infeasibility in predicted trajectories, we develop a Physics-Guided Iterative Decoder (PGID). It conditions decoding on instantaneous kinematic states, propagating physical supervision into internal representations rather than output trajectories alone. Extensive experiments on nuScenes and Argoverse 2 Sensor show that SIPTraj surpasses prior map-free predictors and strong map-based baselines without any HD map at inference. Our code will be released as open-source.

Deep research agents are often trained on expensive, environment-grounded tool-use trajectories that require repeated retrieval, document inspection, and report evaluation. We introduce Deep Research Pretraining (DRP), an offline framework that derives predictive navigation supervision from naturally occurring evidence structures. Given a citation-bearing or hyperlinked passage, DRP constructs a proxy research objective, recovers linked evidence and graph-related alternatives, and converts them into search-open-write trajectories. This teaches models what to search for, which documents to inspect, and how to synthesize evidence, without a live retrieval environment or executed policy rollout. We instantiate DRP on scholarly citation graphs (DRP-Paper) and Wikipedia hyperlinks (DRP-Web), continually pretrain separate Qwen3-14B-Base models on 1B tokens, and fine-tune them on controlled fractions of 13K agent trajectories. Across five independently sampled subsets at each low-data budget, both variants consistently outperform matched no-DRP models on DeepResearch Bench. With one quarter of the SFT data, DRP-Web even surpasses a fixed no-DRP full-data checkpoint, with gains transferring to ResearchQA, WebWalkerQA, and SimpleQA. Starting from matched low-data SFT checkpoints, the DRP-Web advantage also persists through subsequent agentic RL. Source-matched and evidence-mismatch controls indicate that these improvements arise from evidence-conditioned navigation rather than domain exposure or agent-format imitation. DRP thus provides a promising complementary approach to trajectory-based agent training.

Diffusion language models (DLMs) update many tokens in parallel, yet practical decoders often use a fixed denoising horizon. Many predictions stabilize early, but blockwise decoding continues until all positions are resolved, causing repeated dense forward passes. Existing accelerators often rely on learned filters, modified scores, dependency models, or cache-specific mechanisms. We ask whether native trajectory signals can identify residual positions likely to match the deterministic dense endpoint. We propose CORA-Diff, a training-free method that preserves the original transfer rule and applies confidence-and-persistence gating only to positions that rule leaves unresolved. Accepted tokens remain visible as context, and the block terminates once all positions are resolved. This requires no backbone change, learned acceptance model, or logit modification. Our theory explains why high-confidence, persistent predictions are more likely to match the fixed-horizon dense endpoint, and paired post-intervention trajectories provide direct empirical support. We select one operating point on a separate GSM8K calibration subset and freeze it for all evaluations. Under a matched Learn2PD-style LLaDA protocol, CORA-Diff has the lowest measured runtime in all eight task-length settings. Task scores match or exceed dense decoding in five settings, and the largest observed drop is 1.22 points. Its incremental speedups over EOS-aware dense decoding are 2.70x and 3.32x on GSM8K and HumanEval. It also reaches 13.14x under the fixed-horizon 1024/1024 mechanism-isolation protocol and transfers to Dream without retuning at 3.18x-3.53x. These results show that native confidence and persistence enable reliable residual acceptance, reducing repeated denoising computation while preserving task quality.

Existing autonomous-driving world models typically perform dense prediction of future videos, occupancy states, BEV representations, or agent motion. We argue that planning need not reconstruct the complete future world, but only focus on scene features that affect future ego action. Based on this perspective, we propose Auto-JEPA, an action-oriented latent world model that learns continuous future driving intent through joint-embedding prediction. Given visual observations, egomotion history, and navigation commands, Auto-JEPA predicts an intent embedding aligned with the latent representation of the future ego trajectory. The predicted intent retrieves executable trajectories from a fixed trajectory memory, which are then ranked by a scene-conditioned candidate selection module. Auto-JEPA keeps the visual encoder frozen, requires no explicit perception annotations, and uses no learned trajectory generator. By optimizing only task-specific modules for trajectory representation, intent prediction, and candidate selection, Auto-JEPA achieves 91.3 PDMS on NAVSIM v1 and 89.1 EPDMS on NAVSIM v2. Semantic occlusion experiments show that masking dynamic-agent regions induces an average intent change 2.97x that of equal-area random masking. Moreover, occluding vehicles that affect future driving substantially changes the predicted intent and selected trajectory, whereas both remain essentially unchanged when non-influential vehicles are occluded. These results show that future-intent prediction encourages the model to focus on planning-relevant visual features and supports high-quality planning without dense future-world modeling.

As AI companions increasingly mediate repeated social interaction, users may rely on a stable role and shared history, yet locally acceptable replies do not ensure that either persists. We study two observable long-horizon failures: 'persona collapse', the loss of a deployed role, boundaries, values, or style, and 'behavioral drift', the gradual or recurrent erosion of those properties. We introduce ANCHOR, a controlled synthetic audit that separately measures persona enactment and trajectory recall. The study contains 2,008 conversations spanning 27 personas, nine interaction schedules, three generated memory settings, and four evaluated models. The Identity Probe combines a sealed 102-item questionnaire with turn-level judgments, while the Trajectory Probe scores 110 calibrated counterfactual questions from 35 conversation banks. Our results show that no evaluated model and configuration reliably preserves either dimensions: trajectory accuracy averages only 44.4%, user-state recall remains near four-option chance, and no tested context condition or memory consistently resolves these failures. Questionnaire retention also varies by model and persona facet, disagrees with turn-level behavior, and is sensitive to evaluator choice. These results indicate that current systems do not yet reliably support long-horizon companion continuity and that audits must distinguish persona enactment, trajectory recall, evaluator provenance, and deployment context rather than collapse them into a single trust or stability score.

Checkpoint selection can improve an electroencephalography (EEG) emotion-recognition score without improving performance on other trials. We compared selection and scoring on disjoint trial pools along fixed training trajectories. A same-session SEED study comprised 300 trajectories from 15 participants, two models and five trial-role rotations. Another 276 trajectories extended the comparison to separate training, validation and target sessions in SEED, SEED-IV and SEED-V, with 15, 15 and 16 participants, respectively. Increasing the candidate set from five to 80 checkpoints raised the same-session dynamical graph convolutional neural network (DGCNN) selection-pool score by 6.24 percentage points, while the other-pool change was -1.24 (descriptive 95% participant-bootstrap interval -2.67 to 0.26). Under the cross-session design, DGCNN retained gains of 4.47 [1.79, 7.25], 4.27 [2.00, 6.53] and 2.75 [0.79, 4.78] points across the three datasets. Multilayer perceptron results varied across datasets. Common-time-range analysis and trial-level scoring supported the respective patterns. Both target pools supplied labels for symmetric checkpoint selection; these results concern retention across trials, not evaluation without target labels. Complete policy curves and executable reconstruction support reporting selected-score improvements alongside performance on other trials, rather than assuming a universal penalty for checkpoint search.

Large Language Model~(LLM)-based agents have demonstrated exceptional performance across a wide range of complex interactive tasks. However, they often struggle with long-horizon interactive tasks common in domains, such as embodied AI. The complexity and vast action spaces in these settings lead to compounding errors, where a single suboptimal action can derail an entire trajectory, causing the agent to exhaust its limited step budget on inefficient or unrecoverable paths. To overcome this without costly fine-tuning, we draw inspiration from software debugging, where execution logs are analyzed to preemptively catch errors. We propose \textit{Trajectory Graph Copilot}, a novel framework that acts as a ``copilot'' for LLM agents by diagnosing potential action errors before they are executed. At its core,\textit{Graph Debugger} models historical trajectories as a probabilistic graph and uses a Graph Neural Network to identify sequential action patterns that frequently lead to failure. Functioning as a proactive diagnostic sandbox, our method provides early warnings on potentially flawed actions, prompting the agent to self-correct. This pre-action error diagnosis prevents costly mistakes, significantly enhancing the agent's ability to complete long-horizon tasks successfully. The extensive experiments on four benchmarks with three LLM agents demonstrate a $14.69\%$ pass ratio improvement on average.

Long-term ship trajectory prediction is a fundamental capability for maritime safety and autonomous navigation. While recent Transformer-based architectures have improved forecasting horizons, they predominantly rely on historical kinematic states, treating vessel motion as an isolated system. In reality, maritime navigation is profoundly modulated by extrinsic factors like weather and constrained by static vessel characteristics. Existing multimodal approaches fundamentally model the joint distribution over states and contexts, treating environmental variables as peer features rather than encoding the directional physical dependence of vessel dynamics on environmental conditions. In this work, we propose the Conditional Informer, a novel encoder-decoder architecture that formulates trajectory prediction as a conditional generation task. We employ a dedicated Conditional Attention mechanism where the vessel state explicitly queries environmental contexts through cross-attention, encoding the physical prior that weather modulates - but is not generated by - vessel dynamics. Furthermore, to address the intermittency of real-world data, we introduce a Modality Masking training strategy to prevent catastrophic degradation during sensor fallback. Extensive experiments on AIS and ERA5 data demonstrate that our approach outperforms kinematic and concatenation-based baselines by 15.4% in prediction accuracy when context is available. Crucially, Modality Masking prevents shortcut learning, reducing fallback error by nearly an order of magnitude compared to unconstrained models.

Energy-Based Models (EBMs) provide an interpretable framework for generative modeling of scientific data, but poor Markov Chain Monte Carlo mixing often limits their reliability. We introduce a training algorithm based on Parallel Trajectory Tempering (PTT), which exploits the continuity of the optimization path to maintain equilibrium sampling throughout learning. This enables stable and fast training on highly multimodal and data-scarce scientific datasets. Combined with reservoir sampling and adaptive optimization, PTT has a computational cost comparable to Persistent Contrastive Divergence, making it a practical replacement for standard training methods. It also provides direct estimates of thermalization times, equilibrium samples from trained models, and accurate log-likelihoods at essentially no additional cost. Experiments on Restricted Boltzmann Machines show that PTT consistently outperforms existing EBM training approaches. On discrete tabular data, it also surpasses state-of-the-art deep generative models, yielding higher-quality samples and greater robustness to overfitting and limited data. Our results make equilibrium maximum-likelihood training of EBMs practical and computationally efficient.

Automatically generating cinematically expressive camera trajectories through 3D scenes from natural language descriptions is a challenging task of high practical value, with applications ranging from real-estate advertising to virtual tour creation. Existing methods either lack true 3D spatial awareness by relying on 2D image priors, or treat trajectory generation as a geometric path planning problem divorced from cinematographic semantics. We present CinemaTraj, a framework that reframes camera trajectory planning as a language-grounded spatial reasoning problem. Given a set of RGB-D images and a user prompt, CinemaTraj equips an LLM agent with a structured 3D scene graph: the agent decomposes the prompt into a sequence of atomic cinematographic movements (dolly, orbit, crane, pan, tilt, zoom, arc). Each movement is instantiated via a novel parametric trajectory representation that is both cinematographically expressive and optimizable for collision avoidance. The scene graph acts as a structured spatial prior, grounding the agent's reasoning in accurate geometric and semantic knowledge of the environment. CinemaTraj further generates synchronized voiceover and subtitles aligned with camera motion, producing narrated cinematic video outputs. We evaluate CinemaTraj on real-world ScanNet++ environments, and show that it produces prompt-faithful, collision-free trajectories with high cinematographic quality, outperforming existing approaches on prompt alignment, trajectory quality, and safety metrics.

This paper presents a radial basis function network (RBFN)-informed motion planning framework for safe and efficient urban autonomous driving. The proposed approach combines RBFN-based candidate trajectory generation with an analytic collision probability assessment and optimization-based trajectory refinement. The network learns jerk-minimal trajectories, enabling the MPC to operate within a reduced and dynamically consistent search space. Candidate motion primitives are selected based on an accurate probabilistic risk measure. This design decreases solver complexity while preserving safety and constraint satisfaction. The framework is evaluated in numerous urban driving scenarios. Results demonstrate improved risk awareness and fewer vehicle-limit violations compared to benchmark methods. The proposed approach integrates learning-based trajectories into optimization-based motion planning, thereby ensuring safety and interpretability.

Temporal logic (TL) provides a compositional language for the formulation of long horizon robotic tasks, but existing TL-conditioned trajectory generators can sidestep perception-to-symbol binding by encoding exact object geometry in the task graph. We introduce \emph{Vision-TL-Action}, which generates action trajectories from multi-view images, a coordinate-free TL syntax graph, and the robot initial state. TL-node tokens and spatial visual tokens are fused through bidirectional cross-attention, and the resulting representation conditions a flow-matching trajectory generator. Visual tokens are augmented only with normalized image-plane locations and camera-view identifiers, while a training-only predicate-to-region objective encourages grounding to referenced objects. Consistent with prior work in this domain, we evaluate the model using Success@$K$, the fraction of tasks for which at least one of K sampled trajectories satisfies the TL specification. On Panda task, our model achieves 67.45% Success@1024, compared with 59.11% for the oracle-state baseline. On AntMaze task, it achieves 96.35% Success@256, comparable to the oracle result of 96.88%. Resolution and intervention studies show that spatial detail depends on semantic grounding and predicate identity affects both attention and performance. These results demonstrate a direct mapping from visual observations and structured TL goals to action trajectories without requiring object geometry at inference. Code is available at https://github.com/AricLau07/vision-tl-action.

Digital pens are commonly used to write on digital devices, providing the handwriting trace and enhancing human-computer interation. This study focuses on a digital pen equipped with kinematic sensors, allowing users to write on any surface while simultaneously preserving a digital trajectory of handwriting. This technology holds significant potential as a valuable educational tool, particularly in classrooms where it can facilitate the process of learning to write. A major issue is based on the difference in captured signals between adults and children. For similar handwriting trace, we have large differences in sensor signals due to differences in speed and confidence in the handwriting gesture of children. To address this, we investigate a domain adaptation approach to build a unified intermediate feature representation aimed at facilitating the trajectory reconstruction. We demonstrate the interest of domain adaptation methods in leveraging existing knowledge for application in different contexts. Specifically, we compare our domain adaptation approach with two other methods: training the model from scratch and fine-tuning the model.

Handwriting with digital pens is a common way to facilitate human-computer interaction through the use of Online Handwriting (OH) trajectory reconstruction. In this work, we focus on a digital pen equipped with sensors from which one wants to reconstruct the OH trajectory. Such a pen allows to write on any surface and to get the digital trace, which can help learning to write, by writing on paper, and can be useful for many other applications such as collaborative meetings, etc. In this paper, we introduce a novel processing pipeline that maps the sensor signals of the pen to the corresponding OH trajectory. Notably, in order to tackle the difference of sampling rates between the pen and the tablet (which provides ground truth information), our preprocessing pipeline relies on Dynamic Time Warping to align the signals. We introduce a dedicated neural network architecture, inspired by a Temporal Convolutional Network, to reconstruct the online trajectory from the pen sensor signals. Finally, we also present a new benchmark dataset on which our method is evaluated both qualitatively and quantitatively, showing a notable improvement over its most notable competitor.

Inversion-based watermarking is a promising approach to authenticate diffusion-generated images, yet practical use is bottlenecked by inversion that is both slow and error-prone. While the primary challenge in the watermarking setting is robustness against external distortions, existing approaches over-optimize internal truncation error, and because that error scales with the sampler step size, they are inherently confined to high-NFE (number of function evaluations) regimes that cannot meet the dual demands of speed and robustness. In this work, we have two key observations: (i) the inversion trajectory has markedly lower curvature than the forward generation path does, making it highly compressible and amenable to low-NFE approximation; and (ii) in inversion for watermark verification, the trade-off between speed and truncation error is less critical, since external distortions dominate the error. A faster inverter provides a dual benefit: it is not only more efficient, but it also enables end-to-end adversarial training to directly target robustness, a task that is computationally prohibitive for the original, lengthy inversion trajectories. Building on this, we propose \textbf{FARI} (\textbf{F}ast \textbf{A}symmetric \textbf{R}obust \textbf{I}nversion), a one-step inversion framework paired with lightweight adversarial LoRA fine-tuning of the denoiser for watermark extraction. While consolidation slightly increases internal error, FARI delivers large gains in both speed and robustness: with approximately 20 minutes of fine-tuning on a single NVIDIA RTX A6000 GPU, it surpasses 50-step DDIM inversion on watermark-verification robustness while dramatically reducing inference time. Code and pretrained models are available at https://github.com/0xD009/FARI.

The use of digital pens for online handwriting trajectory reconstruction is a prevalent method for human-computer interaction. In this study, we focus on a digital pen equipped with sensors where we aim at reconstructing the online handwriting trajectory. This pen enables writing on any surface and preserving the digital trace of handwriting. This type of pen could be used as an aid to learning to write in classroom. In this paper, we propose a new approach learning to finely reconstruct the touching trajectories while precisely analyzing the hovering part in order to position the next touching trace correctly. This relies on a Mixture-Of-Experts (MOE) approach. The first expert is dedicated for the pencil touch, and is named touching expert model. The second one is dedicated for the hovering pen trajectory, and is named hovering expert model. We improve on the learning of each of these experts based on additional context or specific examples. In addition we introduce a novel public benchmark dataset, to enable future research and comparisons in the field of handwriting reconstruction. The results demonstrates a significant enhancement compared to its primary competitors.

Vision models do not form a representation at once; each block revises it. We ask whether the resulting computation path contains evidence that the final representation discards, and whether that evidence improves OOD detection and image classification on clean and shifted data. Unlike approaches that treat intermediate layers as separate snapshots, we retain sample identity across depth and study the transformations connecting successive states. We separate class-coherent transport from input-specific innovation, and coordinate movement from relational reorganization. Across supervised, self-supervised, vision--language, hierarchical, and convolutional encoders, these paths show strong sample-specific continuity and architecture-specific depth profiles that recur across datasets. They are also practically useful. An ID-only transition-surprise score complements strong final-state detectors, reducing FPR95 in 131/152 non-saturated comparisons on a balanced OpenOOD grid; gains are largest for visually disruptive and semantically far shifts, and remain positive on near-OOD for most detectors. Frozen update probes improve 71/72 clean model--dataset cases, while shifted-data gains vary with architecture and corruption type. Computation paths therefore provide a broadly useful reliability signal whose value is determined jointly by model organization and the shift encountered.

Sonomyography (SMG) enables continuous device control via ultrasound-measured muscle deformation signals, but existing SMG interfaces generally require substantial user- and sensor-location-specific training data and provide only one proportional signal or task-specific classification. We present a real-time, sensor-placement-agnostic SMG control system based on sparse optical flow tracking that enables continuous 1-DOF control after minimal calibration (3 pose definitions). We also present a preliminary expansion of this method that augments this algorithm with a short computer-aided calibration to enable 2-DOF control. We evaluate both 1- and 2-DOF systems' performance for a preliminary cohort of 3 cervical spinal cord injury survivors and 6 uninjured individuals across 6 sensor placements spanning the arm, neck, and upper torso. As assessed by a cursor trajectory tracking task, all participants achieved continuous 1-DOF control at all tested sensor locations (even those that relied on passive tissue motions), with all participants achieving <5.5% tracking error using at least one placement (and many <4% across many). All participants were also able to modulate 2D cursor position via the 2-DOF system, with varying levels of control authority, and several were able to complete a 2D drawing task, constituting the first (to our knowledge) demonstration of location-agnostic multi-DOF continuous SMG-based control. These results highlight the promise of SMG to enable rapidly calibratable, high-dimensional, sensor-placement-agnostic device control by users with tetraplegia, and also illuminate key challenges in both signal processing and practical system deployment. To enable further development by scientific and user communities, developed algorithms have been open-sourced as part of the OpenMyoControl project on SimTK (simtk.org/projects/openmyocontrol).

Modeling and forecasting nonlinear dynamics under distribution shifts is essential for robust decision-making in real-world systems. In this work, we propose MetaKoopman, a Bayesian meta-learning framework for modeling nonlinear dynamics through linear latent representations. MetaKoopman learns a Matrix Normal-Inverse Wishart (MNIW) prior over the Koopman operator, enabling closed-form Bayesian updates conditioned on recent trajectory segments. Moreover, it provides a closed-form posterior predictive distribution over future state trajectories, capturing both epistemic and aleatoric uncertainty in the learned dynamics. We evaluate MetaKoopman on a full-scale autonomous truck and trailer system across a wide range of adverse winter scenarios, including snow, ice, and mixed-friction conditions, as well as in simulated control tasks with diverse distribution shifts. MetaKoopman consistently outperforms prior approaches in multi-step prediction accuracy, uncertainty calibration, and robustness to distributional shifts. Field experiments further demonstrate its effectiveness in dynamically feasible motion planning, particularly during evasive maneuvers and operation at the limits of traction. Project website: https://mahmoud-selim.github.io/MetaKoopman/

Many time-series forecasts depend not only on prior observations but also on actions specified during the forecast period. In intensive care units (ICUs), future vital signs and laboratory values are influenced by treatments such as vasopressors. However, models that predict the full future sequence all at once make little use of these treatments, whereas autoregressive models can accumulate errors. We introduce DRIFT, a hybrid framework in which a direct model produces the primary forecast and a recursive, action-conditioned model contributes constrained corrections. We evaluate DRIFT on 6,046 admissions from MIMIC-IV and 8,345 admissions from eICU-CRD. Averaged across the 8-, 24-, and 48-hour forecast endpoints, DRIFT reduces mean absolute error for mean arterial pressure (MAP) by 0.673% relative to an action-conditioned Temporal Fusion Transformer (TFT-action) on MIMIC-IV and achieves the lowest corresponding error among the compared models on eICU-CRD. Although the overall accuracy improvement is modest, a MIMIC-IV audit restricted to windows in which the supplied treatment sequence was altered showed that DRIFT achieved lower observed-target MAP error than TFT-action at 8 and 24 hours. Treatment-sequence alteration increased DRIFT's MAP error by 0.21-0.26 mmHg more than it increased TFT-action's error, with prediction changes occurring primarily after the supplied paths diverged. In a separate robustness experiment, the MAP advantage persisted under three shared checkpoint-selection rules emphasizing overall endpoint error, MAP error, or both equally.

Skills have become an important abstraction for enabling large language model (LLM) agents to reuse past experience in long-horizon interactive tasks. However, existing trajectory-to-skill methods often produce flat collections of high-level textual skills that are stored and retrieved independently, leaving skill relations underutilized and maintaining a gap between high-level skills and executable actions. In this paper, we propose HiSkill, a hierarchical skill graph framework that organizes interaction trajectories into a directed graph with skill nodes, AtomicOp nodes, and typed edges. Specifically, the graph connects reusable high-level skills with executable action templates, while also capturing decomposition, temporal transition, compatibility, support, and recovery relations among them. At inference time, HiSkill retrieves a compact task-relevant subgraph and performs subgraph-guided task execution, where a symbolic task state, an active skill, and the retrieved subgraph guide the LLM agent to switch skills, select AtomicOps, and ground executable actions iteratively. Experiments on three interactive environments show that HiSkill outperforms state-of-the-art baselines while reducing inference token consumption, demonstrating the effectiveness of bridging high-level skills and executable action grounding through a hierarchical skill graph. Our data and code is available at https://github.com/BUPT-GAMMA/HiSkill.

Understanding disease trajectories from longitudinal clinical data remains challenging due to complex temporal dynamics and heterogeneous patient cohorts. Here, we present a contrastive representation learning framework that models multivariate disease trajectories as temporal graphs and learns representations using contrastive graph neural networks. Nodes represent patient observations over time, while edges capture temporal continuity and structural similarity between trajectories. Structure-aware random walks guide contrastive learning to generate embeddings that preserve temporal context and trajectory topology. The resulting representations enable robust clustering of patients with similar disease progression patterns and reveal latent structure in longitudinal data.

Agent skills package reusable procedures that improve downstream performance. Their lightweight, portable form enables marketplace monetization and private deployment behind cloud-hosted agent interfaces, giving providers incentives to keep high-value skills proprietary. Yet hiding the artifacts does not conceal their behavioral effects, which remain observable in execution trajectories and form a behavioral side channel. We define this exposure as Skill Leakage: reconstructing proprietary skills from trajectories elicited by benign queries, without reference answers or success labels. We introduce SigLeak, a black-box framework that exploits recurring skill signatures in agent behavior. It constructs diverse, decision-rich diagnostic tasks, contrasts matched skill-enabled and skill-disabled trajectories, and iteratively refines a reconstructed skill from the isolated patterns. Across five scenarios, three model families, and three agent frameworks, SigLeak outperforms or matches three baselines in nearly every setting. It raises the success rate by 6.88 percentage points over the skill-disabled reference on average and achieves the highest overall SkillSim, our metric for coarse- and fine-grained semantic similarity. These results show that benign execution trajectories can expose proprietary procedural knowledge. The code is available at https://anonymous.4open.science/r/SigLeak-D1DB.

Understanding how computational effort is allocated across individual chain-of-thought (CoT) reasoning steps remains an open challenge: existing interpretability methods rely on output-level signals or collapse processing depth into a single trajectory-level scalar, leaving step-wise effort opaque. We propose Step-Aware Reasoning Energy (SARE), a geometric framework that quantifies effort at the granularity of individual CoT steps via Centered Kernel Alignment (CKA) between Gram matrices of token hidden states across adjacent transformer layers, capturing inter-token relational structure without requiring eigenvector alignment or cluster correspondence. SARE further contextualizes this energy within reasoning's semantic progression by modeling CoT trajectories as transitions among latent semantic states. Across six reasoning benchmarks and three open-weight LLMs, we find that reasoning energy is highly non-uniform across step types, exhibiting phase-like transitions invisible to trajectory-level metrics; incorrect trajectories show systematically lower energy at critical reasoning junctions; and SARE-based features match or outperform output-based confidence baselines in most settings, indicating that internal geometric dynamics encode predictive information beyond surface-level signals.

Trajectory data collected in real-world settings is frequently incomplete due to sensor failure, communication loss, or occlusion. We address the task of \emph{trajectory inpainting}: reconstructing contiguous missing segments from observed context. We propose a Temporal Convolutional Network (TCN) with symmetric dilation that relaxes the standard causality constraint, allowing each time step to draw on both past and future observations, a property that is essential for inpainting, but absent from forecasting-oriented architectures. The model is trained with a composite loss that combines weighted mean squared error, boundary--continuity penalties, and a smoothness regularizer. Trained on a synthetic dataset of $1,000$ (train), $200$ (validation), and $300$ (test) two-dimensional trajectories with randomly placed 20% masked segments, the model achieves good R$^{2}$, MSE and MAE metrics.

While on-policy distillation (OPD) effectively addresses sparse rewards and exposure bias in large language model post-training, its extension to flow models remains underexplored. To this end, we propose Flow Continuous Trajectory Supervision (FlowCTS), which matches subsequent student and reference trajectories initialized from the same student-visited state. Using the integral relation between trajectories and velocity fields, we derive a temporally weighted velocity-matching upper bound and discretize it into practical objectives parameterized by the number of supervision steps. Under a multi-reference setup, single-state FlowCTS-OPD outperforms vanilla KL-based OPD with faster convergence. FlowCTS-OPD improves GenEval from 0.90 to 0.93, OCR from 0.90 to 0.92, and PickScore from 22.75 to 23.06, while outperforming a mixed-reward RL baseline across all target metrics. Further analysis reveals a clear temporal supervision mismatch in vanilla KL-based OPD arising from its auxiliary SDE transition kernels. Beyond on-policy setting,FlowCTS also consistently outperforms vanilla SFT , particularly on OCR, while increasing supervision steps exhibit a trade-off between richer trajectory information and greater optimization difficulty.

Using large language models (LLMs) to assist psychological counseling is an important task in the field of natural language processing. The construction of high-quality psychological support dialogue corpora serves as a critical foundation for training counseling-oriented conversational models. However, existing data generation approaches generally suffer from several limitations, including emotionally stable seekers, limited variation in emotional dynamics, and a high degree of compliance with counselors' guidance. These issues result in LLM that lack the capability to effectively respond to emotionally unstable scenarios. In addition, counselor responses are typically driven by problem-solving objectives, thereby overlooking the role of emotion-focused interaction, which are essential in psychological counseling. To address these gaps, we propose EmoTrace, a multi-turn dialogue corpus generation framework centered on modeling seekers' emotional trajectories. we construct seekers' cognitive profile and introduce a seeker module with emotional schemas and an associated activation mechanism, a counselor module, and an emotional trajectory control module, thereby enhancing the layering of the seeker's emotional expression and the counselor's targeted empathic expression. Experimental results demonstrate that the proposed method outperforms existing approaches in terms of emotional richness and empathy quality.