Trajectory Prediction

Building on recent advances in world models, World Action Models (WAMs) jointly model video prediction and action generation. However, they typically represent videos in 2D pixel space, creating a representation gap with 3D space in which robotic actions are executed. Recent 3D approaches introduce 3D information, but fail to fully exploit the dynamics of 3D structures. In this work, we propose 4D-WAM, a model-agnostic training strategy that injects spatiotemporal knowledge from 3D trajectory fields into WAMs through representation alignment. To this end, we introduce two complementary objectives: 1) motion alignment, which aligns temporal feature variations across adjacent frames and encourages the model to build local 4D awareness during training, and 2) destination alignment, which guides the model to infer the final destination from the source frame by minimizing the gap between their attention-like similarity distributions. Together, these objectives provide both local motion supervision and long-horizon goal guidance, enabling WAMs to learn trajectory-level spatiotemporal representations. Extensive in-distribution and out-of-distribution experiments across different base models demonstrate the model's improvements in spatial understanding, execution precision, robustness, generalization, and versatility.

World-Action Models (WAMs) improve end-to-end autonomous driving by transferring video dynamics priors to action prediction, but existing methods incur costly test-time future imagination. We present SimWAM, a simple yet effective WAM that leverages future-video prediction as a training-time supervision signal. It co-trains a pretrained video expert and a lightweight action expert with joint flow matching. An isolated attention mask keeps action prediction independent of future frames, allowing trajectory prediction without explicit future-frame generation at inference. Since the two experts share no parameters and interact only through a unified attention interface, the video backbone could be replaced and the action expert scaled independently without modifying the learning objective or inference pipeline. We further apply reinforcement learning to optimize a compositional driving reward beyond trajectory imitation. Our SimWAM achieves 91.5 PDMS on NAVSIM, surpasses state-of-the-art WAM-based planners with substantially lower latency, and transfers zero-shot to nuScenes. These results position SimWAM as a simple yet solid baseline that could readily benefit from advances in video generation for efficient autonomous driving. The code and model weights are available at https://github.com/H-EmbodVis/SimWAM/.

World Action Models (WAMs) aim to construct a unified architecture capable of understanding world state evolution and guiding to generative motion planning. However, existing visual branches focus on predicting static visual observation, rather than reflecting potential transition information that captures the evolution of world states under motion interactions. This leads to representational entanglement between high-level physical condition evolution and low-level action trajectory generation within the Action Model, creating a structural bottleneck while weakening the predictive capability of world evolution modeling for action generation. We propose PILOT (Physical Inference for Latent Optimized Trajectories), whose core Representational Deduction (RD) bridges this gap by integrating motion thought-of-chain (CoT) guidance as a native model capability. Specifically, RD aims to encourage the action branch to explicitly model potential state transition tokens, which are retained as CoT in the reasoning space to guide fine-grained motion trajectory. Experiments demonstrate that RD not only significantly improves the success rate and generalization ability of WAMs in complex robotic manipulation tasks but also enhances the model's physical interpretability by decoupling high-level motion semantics from low-level trajectory details. Furthermore, the abundant state transition supervision signals introduced by RD effectively alleviate the sparse supervision in action generation, enabling it to serve as an efficient few-shot real-robot fine-tuning strategy and demonstrating superior scalability for migration to mainstream WAM architectures.

This paper presents a real-time Plan-and-Avoid (PAA framework for coordinating cooperative multi-agent airspace operations around a declared priority trajectory. The priority trajectory represents an aircraft flight plan that must be preserved because of constrained maneuverability, an emergency, a mission-critical task, or assigned operational priority. The framework predicts uncertainty-aware, well-clear separation violations with surrounding traffic and, when the priority plan alone cannot maintain separation, generates vehicle-constrained unilateral advisories that modify nearby aircraft trajectories to maintain well-clear separation for all traffic. The approach is applicable to any declared priority trajectory. This paper demonstrates the Plan component using a contingency landing planner to generate candidate priority trajectories. PAA then identifies nearby aircraft passing too close to this priority trajectory and issues Avoid resolution advisories to these aircraft. The framework is tested using real-world Automatic Dependent Surveillance-Broadcast (ADS-B) traffic from the Washington, D.C., airspace across more than 900 forced-landing cases, totaling over 140 hours of simulated flight. The PAA framework generates feasible cooperative advisories for all 575 unique conflict encounters, with a worst-case end-to-end response time of 5.7 s on a personal computer, including priority trajectory planning, advisory generation, and 1 s two-way datalink delay. In total, 93.5% of generated advisories satisfy the 35 s RTCA DO-365 Detect-and-Avoid temporal threshold. These results demonstrate low-latency coordination for preserving priority trajectories while maintaining well-clear separation through real-time automated advisory generation. Future work will quantify advisory-induced delays and their operational impacts.

Trajectory prediction has shifted toward structured formulations with explicit social modeling. However, existing methods inadequately distinguish the functional roles of social influence in trajectory planning. Observing that agents typically form motion plans by anticipating others' future behaviors before making local reactive adjustments, we identify social interactions as playing staged roles, namely planning precedes reaction. We propose INTraJ, a unified framework that decomposes social influence into two stages: a planning stage constructs reference trajectories using future social information, and a reaction stage recovers local adjustments from the residual between full-context prediction and the reference. INTraJ supports both multi-target and single-target paradigms. Extensive experiments on four standard benchmarks, including Argoverse 2, Argoverse 2-ped, ETH/UCY, and SDD, demonstrate consistent improvements, particularly in FDE and long-horizon consistency, with state-of-the-art performance achieved in several settings. INTraJ reframes trajectory prediction as a planning-driven two-stage process, validating that staged social modeling is critical for stable predictions. The code is publicly available at https://github.com/11isnotavailable/INTraJ.

As language models are increasingly used for tasks that require verifiable reasoning, reliably distinguishing sound reasoning from flawed reasoning has become an important practical problem. Recent trajectory-based methods seek this signal in layerwise residual-stream displacements, which capture how representations change while attenuating some stable, token-specific information. However, displacement omits the state from which an update originates, whereas restoring the full state risks reintroducing shortcut-prone information. We identify this trade-off and propose a three-stream detector that combines motion with two restricted views of location. A coarse region reader based on vector quantization and a fine direction reader over normalized multi-layer states. This design restores enough state context to interpret the motion without returning to full-state probing. On reasoning benchmarks unseen during training, our method improves selection accuracy by up to 12% over the displacement-only state of the art and 21% over single-layer probing baselines. Although trained only on reasoning benchmarks, it also reads factual completion and fact verification, ahead of every detector we compare against, which places the signal on correctness rather than on a kind of reasoning. Ablations further show that motion, region, and direction provide complementary signals. These results suggest that reasoning validity is better read from state-conditioned motion than from either static states or decontextualized trajectories alone.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

We study empirical risk minimization for learning non-linear dynamical systems whose transition dynamics may switch over time. Under stability assumptions, and i.i.d switching over a set of $K$ modes, we derive non-asymptotic bounds on the prediction risk expressed in terms of the metric entropy of the underlying function class. We instantiate our general result for Hölder and linear function classes, obtaining explicit convergence rates that depend on the effective sample size $Tp_i$, where $T$ is the trajectory length and $p_i$ is the probability of observing mode $i$. Numerical simulations support our theoretical findings. To the best of our knowledge, these results are the first non-asymptotic guarantees for learning switched nonlinear dynamical systems from a single trajectory.

Neural operators provide data-driven mappings for modeling dynamical systems. Extending them to families of systems typically requires explicit conditioning variables such as physical parameters, geometries, or boundary conditions. In many real-world settings, these quantities are unobserved. Here, we formulate neural operator discovery (NOD) as the problem of learning both shared solution operators and system-specific variation directly from heterogeneous trajectories without access to labeled governing factors. We introduce a factorized latent-conditioning formulation that jointly learns a neural operator and a low-dimensional latent representation through factorized prediction, trajectory-decoupled sampling, and dimension selection. Across diverse systems, the learned latent representation captures the intrinsic dimensionality of system variation and organizes system instances in a smooth and approximately invertible latent structure aligned with the underlying governing factors. This organization enables generalization to previously unseen system instances, including zero-shot extrapolation across regimes and stable long-horizon prediction. These results establish an interpretable paradigm for operator learning in the absence of explicit factor supervision.

Deciding whether a trajectory actually fulfills its instruction governs how we measure computer-use agents on long-horizon graphical-user-interface tasks and how we train them with reinforcement learning. This judgment has long relied on rule-based evaluation, which struggles to align with human intention and goes stale when an app updates or its online content drifts. Existing model-based judges attempt to address these problems but still leave a performance gap to the rule-based evaluation. We propose the \textbf{SeekJudge} framework, in which four role-specialized agents, a Condense, a Ground, a Seek and an Analyze agent, reach a verdict through a Seek--Analyze loop over the trajectory. A seed-calibrated distillation pipeline trains one specialized $9$B model to serve as the shared backbone for all four agents. Measured by downstream success rate on held-out RL test goals, SeekJudge is the first practical model-based reward to match or surpass native rule-based supervision in online RL. Beyond accuracy, SeekJudge provides step-level judgments, runs far cheaper than a closed-source large model, and keeps a small per-call context that scales to much longer trajectories. We further contribute a general architectural improvement to the reward server that speeds up judging in RL. Together these make model-based reward a practical drop-in for rule-based supervision in CUA reinforcement learning.

We consider the problem of learning from a single finite trajectory of an ergodic stochastic dynamical system. More precisely, we study discrete-time autonomous stochastic systems defining time-homogeneous Markov processes. We first focus on estimating the optimal one-step prediction function by nonlinear least squares, and derive high-probability guarantees measured with respect to the invariant measure of the process. These results make explicit how the non-independent and non-identically distributed nature of trajectory data modifies the classical statistical learning analysis. We then extend the framework to higher-order systems and finite-state spaces. Finally, we show that the same least squares and concentration arguments naturally extend to learning Koopman operators. Our approach combines tools from statistical learning theory and quantitative ergodic theory for Markov chains. It relies, in particular, on a concentration inequality for Hilbert-space-valued additive functionals of uniformly geometrically ergodic Markov chains.

Longitudinal studies often collect data at sparse, irregular, and unequally spaced time points. Such heterogeneity is often driven by subject-specific covariates, yet existing methods have been restricted to a scalar endpoint value, completely neglecting the underlying response trajectories. We propose a novel Longitudinal Random Forest (LRF) framework that leverages tree-based ensemble machine learning with adaptive node-wise longitudinal trajectory estimation. The LRF framework makes five methodological contributions. it captures each subject's individual response trajectory while simultaneously accommodating within-node correlation, between-node heterogeneity, and nonlinear and interactive covariate effects. It introduces a novel trajectory-based splitting criterion that maximizes trajectory separation while incorporating a size-weighted penalty; it provides two variants, Principal Analysis by Conditional Expectation (LRF-PACE) and adaptive linear mixed-effects models (LRF-adaptiveLMM), which employ nonparametric and semiparametric node-wise smoothers, respectively, while learning covariate effects in a data-driven manner. It provides a comprehensive interpretation of covariates using both the classical trajectory-based permutation variable importance measure (PVIM) and a newly proposed finite-way interaction frequency count, and it not only predicts entire trajectories for new subjects but also forecasts future trajectories for existing subjects. Extensive simulation studies demonstrate that LRF achieves superior performance over several competing methods, even under severe sparsity. The practical significance of the LRF framework lies in its ability to address five important clinical questions.

Rectified-flow-based diffusion transformers, particularly FLUX, have demonstrated outstanding performance in high-quality image generation. However, achieving fast and accurate inversion--transforming images back to latent noise for faithful reconstruction and editing--remains a challenging bottleneck due to the discretization errors of linear solvers. This paper introduces SlerpFlow, a straightforward yet highly effective zero-shot approach that unlocks the full potential of FLUX for high-fidelity inversion and editing. Unlike existing approaches (e.g., RF-Solver) that rely on complex numerical approximations such as high-order Taylor expansions to correct trajectory errors, we present a geometric view based on the Manifold Hypothesis: the empirically observed trajectory curvature is not a numerical artifact, but rather serves as a necessary "centripetal force" that constrains the flow to remain on the data manifold. Guided by this insight, SlerpFlow integrates Spherical Linear Interpolation (Slerp) to rectify flow velocity directions on the hypersphere, strictly adhering to the intrinsic curvature of the latent space. Crucially, by caching the corrected velocity for subsequent steps, SlerpFlow achieves high-precision inversion while maintaining the computational efficiency of a first-order Euler solver. Extensive experiments on FLUX-based reconstruction and editing tasks demonstrate that SlerpFlow improves reconstruction fidelity and achieves stronger semantic alignment in editing without requiring additional training. Code is available at https://github.com/0answer0/SlerpFlow.

The successful integration of mobile robots in human-centric environments requires navigation that is not only safe and efficient, but also predictable and aligned with social conventions, key precursors for human comfort and acceptance. While significant research addresses short-term human-aware planning, these methods often lack mechanisms for ensuring consistent and predictable behaviors across long horizons. Without socially aware long-term planners, local planners are overburdened, resulting in inefficient and locally reactive movements that undermine predictability. This paper introduces a partially decentralized framework that generates predictable and socially consistent multi-robot motion by decoupling global path planning from trajectory coordination. First, we propose a modified A* planner that embeds macroscopic social norms into the planner cost function. Planned paths are shared across mobile robots to collaboratively build a social graph of established routes, which enforces path consistency and reduces future planning effort. Second, we leverage the emergent structure of the socially constrained paths to formulate the multi-robot trajectory coordination problem as a mixed-integer convex program. The convex program enables efficient computation of conflict- free trajectories, scaling effectively to large fleets and supporting dynamic task assignment. Our results demonstrate that enforcing social consistency at the path planning stage produces predictable, socially compliant mobile robot paths and simplifies the otherwise complex problem of multi-robot coordination.

Long-form streaming speech-to-speech translation (S2ST) requires incremental, unbounded translation under strict latency constraints. Existing methods typically suffer from sentence-bounded supervision or demand massive paired-S2ST supervision. We introduce a training recipe enabling a speech language model for sentence-level and long-form streaming S2ST using only $\sim$2k hours of paired cross-lingual S2ST data, layered atop auxiliary supervision. Anchored by auxiliary multitask training, our approach remains robust even when the paired-S2ST budget itself is reduced by 90%. Our core contribution, joint text-code trajectory supervision, schedules target text and acoustic semantic codes as a unified commitment path, eliminating the need for separate, unstable speech-side emission controllers. Furthermore, our two-stream Thinker--Talker factorization significantly outperforms unified-decoder baselines by decoupling linguistic reasoning from dense acoustic prediction to mitigate modality interference. Finally, our system achieves highly competitive quality-latency trade-offs on RealSI and ACL60/60-dev, matching state-of-the-art, closed-source S2ST systems such as LiveInterpret~2.0 on ASR-BLEU.

Detecting staypoints from raw trajectory data is fundamental to numerous spatial computing applications. This process transforms raw numeric sequences of geolocations into semantically meaningful locations, such as homes, workplaces, or restaurants. Despite its importance for semantic trajectory analysis, staypoint detection lacks standard benchmarks, and existing algorithms have never been systematically evaluated. This gap persists because no publicly available datasets provide both raw individual trajectories and ground-truth staypoint annotations. This benchmark paper addresses this limitation with two key contributions: (1) we introduce 16 large-scale simulated datasets capturing thousands of agents with annotated staypoints across varying trajectory noise levels, and (2) we evaluate nine staypoint detection algorithms-including both state-of-the-art and novel methods-to analyze their robustness to noise. Our evaluation reveals that existing state-of-the-art algorithms perform poorly under realistic noise conditions. Conversely, our proposed unsupervised methods yield substantial improvements, while supervised approaches drastically outperform existing baselines. While these results are very promising, these datasets and methods are only meant as starting points for future research in staypoint detection.

Autonomous flight in cluttered environments requires a robot to build a geometric map of its surroundings and plan safe, dynamically feasible trajectories, all onboard and in real time. Conventional approaches treat mapping and planning as separate stages and often rely on binary occupancy for collision checking. We argue that these two stages should be co-designed around a single representation: a signed distance function (SDF). By encoding distance to the nearest obstacle, an SDF provides richer information for planning and trajectory optimization than occupancy alone. We develop an Octree REsidual Network (OREN) that pairs an explicit octree prior with an implicit neural residual to reconstruct SDFs online from point cloud observations with the efficiency of volumetric methods and the accuracy and differentiability of neural methods. In tandem, we develop Bubble$^\star$, a search-based planner that exploits the distance information to grow maximal collision-free balls, which we call bubbles, with formal guarantees of termination, completeness, and failure detection. Planning over a graph of bubbles significantly reduces collision checks compared to a grid-based A$^\star$ search and returns a bubble sequence that forms a safe corridor for trajectory optimization. We demonstrate the integrated OREN-Bubble$^\star$ approach onboard a quadrotor, navigating unseen indoor environments in real time under tight compute constraints. OREN improves SDF estimation by $22$% compared to baselines, while Bubble$^\star$ finds trajectories spanning $\approx 90$ m through a cluttered environment in $1$-$3$ sec., whereas baselines take up to $10$ sec. in the same environment.

Model-Agnostic Meta-Learning (MAML) is a widely used framework for reinforcement learning (RL) that enables efficient transfer by learning global policy parameters that can be rapidly adapted to new tasks. MAML training proceeds in two loops: an inner loop where the global parameters are adapted to task-specific parameters, and an outer loop where these task-specific parameters are evaluated and losses are back-propagated to improve the global parameters. Traditionally, the inner loop adaptation is performed by collecting trajectories from the task environment and applying gradient updates on the empirical expected return, which can be a costly operation. We note that it is the outer loop that drives the actual learning of global parameters, and therefore the inner loop adaptation mechanism need not be restricted to be gradient-based. This observation leads us to ask: Can we replace the inner loop trajectory collection and gradient update with a simpler, task-specific signal? In many practical settings, tasks are naturally accompanied by language instructions. Leveraging these instructions as a direct task-specific signal, we propose LA-MAML (Language Adapted MAML), which modifies the inner loop by adapting the global policy parameters in a single step through a learned embedding of the task instruction, replacing the inner loop trajectory collection and gradient-based updates. Experiments on the BabyAI benchmark demonstrate that LA-MAML achieves competitive or improved performance compared to baselines at a significantly lower per-iteration wall-clock training time. These results demonstrate that language instructions are an effective and efficient substitute for trajectory-based inner loop adaptation in meta RL.

Efficient, collision-free, and time-optimal motion planning is a fundamental requirement for autonomous forestry cranes operating under hydraulic pump-flow constraints. The Via-Point-based Stochastic Trajectory Optimization (VP-STO) algorithm has demonstrated near-time-optimal hybrid motion planning in this domain, but requires a fixed terminal joint configuration specified prior to optimization. For kinematically redundant manipulators such as forestry cranes, this pre-commitment to a single inverse kinematics solution restricts the planner's ability to exploit redundancy, particularly under the nonlinear, globally coupled pump-flow constraint where admissible joint velocities depend on their combined hydraulic demand. This paper presents TSC-VP-STO, a task-space-constrained extension of VP-STO that replaces the strict terminal joint-space constraint with a task-space constraint, jointly optimizing the trajectory and the redundant degrees of freedom of the terminal configuration. This enables the planner to adapt end configurations to the environment-dependent motion and hydraulic flow allocation, yielding more balanced pump utilization and shorter trajectory durations. We formalize the approach through a configuration space decomposition and derive a concrete reachability constraint for the forestry crane kinematics. Experimental evaluations across multiple planning targets and via-point configurations demonstrates a reduction on trajectory durations by 12-15% on average and improved pump-flow utilization compared to the baseline VP-STO. The practical applicability of TSC-VP-STO is validated through real-world deployment on a forestry crane, including a full log-loading cycle.

Supervised fine-tuning (SFT) of open-weight LLMs on expert agent trajectories has emerged as a prominent approach to building capable code agents without reliance on proprietary models. A central yet underexplored question is how trajectory quality and quantity jointly shape model performance. We present a systematic empirical study of trajectory data filtering for LoRA fine-tuning of Qwen2.5-Coder-7B-Instruct on the SWE-trajectory dataset (67,074 trajectories, of which 32,161 are resolved). We propose a two-axis quality scoring framework -- Efficiency and Style -- and evaluate it through 16 controlled experiments spanning strategy, scale, and ablation analyses. Since 7B-scale models attain near-zero SWE-bench resolve rates, we adopt cross-entropy (CE) loss on held-out trajectories as the primary metric, validated via first-action generation: CE loss and ROUGE-L are perfectly rank-correlated (Spearman $ρ$ = -1.00), with limited-sample evidence supporting but not conclusively establishing this proxy. Our results reveal a scale-dependent quality-quantity trade-off: at small scales, doubling the dataset (500 to 1,000) yields ~12.7% CE-loss reduction whereas the TopQ-Random gap stays <1% (Mann-Whitney p > 0.10); at 2,000 trajectories this same gap widens to 3.6% (p = 0.016). Ablation further identifies error-retry rate as the dominant sub-dimension, performing comparably to the full composite ($Δ$ < 0.2%). Together, these findings establish trajectory-level quality scoring as a viable but scale-sensitive lever for code-agent SFT and offer a proxy-validated evaluation protocol for the regime where end-to-end resolve rate is statistically infeasible.

Large language model agents solve tasks by generating trajectories that interleave planning, tool calls, and intermediate results. Current evaluation metrics reduce such a trajectory to a binary success flag, compare it against a reference by exact matching, or delegate judgment to another language model. A success flag cannot distinguish a sound solution from one that succeeds by luck, and says nothing about why a failed run went wrong. Exact matching penalizes plans that are valid but reordered or decomposed differently from the reference. We reframe trajectory evaluation as a distance between the agent's execution graph and a set of valid solution graphs, and instantiate it via an unbalanced fused Gromov-Wasserstein transport problem over attributed dependency graphs. The resulting score, termed OTAP (Optimal Transport for Agentic Planning), is a pseudo-metric that is provably invariant to dependency-preserving reorderings and has bounded sensitivity to redundant steps. Its unbalanced marginals handle missing or hallucinated steps without forcing a match, and its soft coupling accommodates variation in plan granularity. On controlled perturbations and three public benchmarks, OTAP separates valid from invalid trajectories in a regime where semantics-only metrics score below chance. Its advantage tracks the fidelity of the dependency graph: largest where edges follow from operator semantics, smallest where they are inferred from free text. Where a formal verifier exists, strict surface metrics predict validity better than OTAP does, which places OTAP in open-ended domains where no verifier is available.

This paper presents a method for user-driven robot Learning from Demonstration (LfD) that reduces user effort while ensuring compliant and precise reproduction. The method eliminates repeated teaching for the same task and enables real-time learning from a single demonstration. Demonstrated motions are reproduced with high precision, while impedance variations are learned in real time to provide both compliance and robustness against perturbations. This mitigates potential safety issues in Human-Robot Interaction (HRI) that arise from conventional time-indexed trajectories lacking compliance. The proposed approach integrates a three-dimensional (3D) Fast Diffeomorphic Matching (FDM) algorithm with a Dynamical System (DS)-based motion generator to achieve real-time single-shot demonstration learning and reproduction. An Extended Kalman Filter (EKF) framework compensates for reproduction errors and recovers from external interactions. Furthermore, an impedance parameterization function is incorporated to learn impedance variations from demonstrations and maintain surface contact for specific applications. The proposed approach is validated through comprehensive experiments on a 7 Degree-of-Freedom (DOF) KUKA LWR IV+ robot.

Many complex systems such as brain networks, financial markets, and gene-regulatory circuits are described not by a fixed graph but by one that changes over time. A standard way to summarise such structure at each instant is the sparse precision (inverse-covariance) matrix, and the time-varying graphical lasso (TVGL) turns a multivariate signal into a smooth chain of these matrices. We introduce TVGL-CFM, a single model that learns the distribution of such chains and can both generate new, realistic time-varying network trajectories for a given class and forecast how an observed trajectory will continue. Each precision matrix lives on a curved space of positive-definite matrices, but a log-Euclidean chart flattens an entire trajectory into an ordinary vector space, so a simple conditional flow-matching model can be trained and sampled there while every decoded matrix is guaranteed to be a valid precision matrix. For forecasting we start the flow not from noise but from a rough extrapolation of the recent history, so the model only has to learn a small correction. Across EEG motor-imagery, chaotic systems, and gene-expression data, TVGL-CFM generates trajectories that keep the class-discriminative structure of real data, and it forecasts future connectivity more accurately than raw-signal baselines. Generating the structured precision trajectory directly is therefore more faithful than generating raw signals and estimating connectivity afterwards.

This paper presents a new implementation of the NeoSLAM algorithm. The proposed version is a complete rewrite of NeoSLAM into a modular architecture using modern frameworks that, together, enable real-time execution with minimal discarding of input data. This work also provides a comparative evaluation between NeoSLAM and RatSLAM across three datasets under varying environmental conditions. The experimental results highlight differences in mapping consistency and trajectory reconstruction, demonstrating the effectiveness and practical applicability of the proposed ROS2-based implementation. The results indicate that the new NeoSLAM outperforms the original in terms of processing throughput for real-time applications and achieves comparable performance to RatSLAM in terms of map reconstruction across the evaluated datasets.