Trajectory Prediction

Action chunking is widely used for action generation and execution in Vision-Language-Action (VLA) policies, yet existing approaches commonly use a fixed action horizon. During a rollout, different task stages may require different levels of action continuity, control precision, and closed-loop feedback, making a fixed horizon unable to accommodate changing control requirements. We propose \textbf{GeoAAC}, a geometry-based adaptive action chunking method for flow-based VLA policies that adjusts the action horizon according to the reliability of the current action prediction. We show that the geometry of Flow Matching denoising trajectories provides process-level information for characterizing prediction reliability, with geometric variation across action prefixes remaining positively correlated with predictive uncertainty. GeoAAC uses this prefix-wise geometry to construct a horizon-wise geometric profile and adaptively determine the action horizon from a single generation without additional training. Experiments with GR00T N1.5 and π0.5 on LIBERO, LIBERO-Pro, RoboCasa365, and real-world manipulation tasks show consistent improvements over fixed-action-horizon baselines and existing adaptive methods, including up to 8.7 percentage points in simulation and an increase in average real-world success rate from 53.3% to 74.4%.

The paper presents a numerical approach for the end-effector trajectory smoothing of a parallel robot designed for minimally invasive pancreatic surgery. The approach is tailored for real-time master-slave control architecture and uses a 3D space mouse for command input for velocity control. The trajectory smoothing is achieved by generating S-curves in the end-effector velocity fields, thus controlling the accelerations, which in turn reduces tissue trauma in the minimally invasive procedures. Real-time control is enabled by segmenting the S-curves based on the command inputs from the 3D space mouse. A special case is considered where the acceleration time is constant for all command inputs. Numeric results demonstrate stable transitions (without abrupt changes) in both the end-effector parameter space and in the active joints parameters, thereby validating the proposed approach. Further work aims to test the approach on an experimental model and integrate it into AI-based training modules.

Occlusion creates fundamental uncertainty in autonomous driving. Existing methods often propagate frame-wise hypotheses or optimize ego behavior against prescribed hidden-agent predictions, leaving the worst history-consistent interaction unexplored. We introduce History-Conditioned Minimax Trajectory Search (HC-MTS), which combines temporal occlusion reasoning with response-aware search. First, HC-MTS constructs finite hidden-state modes, each certified by a backward witness satisfying multi-frame visibility, occupancy, semantic-map support, and class-specific kinematic constraints. It then solves a bilevel minimax problem: an inner finite oracle maximizes the ego driving score over destination attainment and ride comfort, while the outer search selects the legal hidden-vehicle trajectory that minimizes this best-response value. Across eight Waymo Open Motion Dataset scenarios, increasing the visibility-memory horizon from K=1 to K=20 reduces the mean per-scenario vehicle, pedestrian, and total retained hidden-seed counts by 18.12%, 21.67%, and 18.45%, respectively. HC-MTS identifies six avoidable counterexamples, while no legal collision-producing attacker is found in the remaining two scenes within the finite search budget.

Gromov--Wasserstein optimal transport (GW-OT) extends classical optimal transport by introducing structure-aware transport cost. This is particularly relevant for spatial transcriptomics, where dynamical reconstruction should preserve tissue structure in addition to matching expression patterns. While static formulations have been widely used for such structure-aware alignment, a general dynamic formulation for reconstructing continuous trajectories is still missing. We introduce Travelling Pair Dynamical Alignment and Trajectory Estimation (TP-DATE), a theoretical and computational framework to generalize GW-OT dynamically in a simulation-free manner. We formulate a broad class of static and dynamic Quadratic-form OT (QOT) through path actions and prove the static dynamic equivalence. We further develop travelling-pair flow matching, which allows interacting conditional paths and marginalizes their interactions into a single vector field. On synthetic and real spatial transcriptomics data, TP-DATE better preserves spatial structure and improves continuous 3D dynamics reconstruction.

Reinforcement learning for LLM agents involves two distinct optimization di- mensions: how environment feedback is exploited within a trajectory, and how complete trajectories are aggregated across a batch. We formulate these dimen- sions as Intra-Trajectory Feedback Attribution and Inter-Trajectory Objec- tive Aggregation, and introduce BATON (Bayesian Attribution and Trajectory Objective Normalization), a dual-axis policy optimization framework. BATON instantiates the first axis with Bayesian Feedback Attribution, which constructs a feedback-conditioned posterior over sampled actions, and the second with Trajec- tory Mass Normalization (TMN), which assigns equal optimization mass to com- plete trajectories. Experiments with GRPO and GiGPO on ALFWorld, WebShop, and SearchQA show that both axes provide independent gains and that their combi- nation consistently achieves the strongest overall performance across model scales.

Predicting the future trajectories of surrounding vehicles in autonomous driving is important for collision risk assessment and safe ego-vehicle path planning. Conventional neural network-based trajectory predictors typically achieve strong prediction performance by exploiting agent history, dynamic scene graphs, and semantic maps. However, in specific motion regimes such as acceleration, deceleration, and turning, these predictors may fail to reflect physically feasible trajectories. To address this issue, this study proposes a framework that fuses the output of Trajectron++, a neural network-based trajectory predictor, with extended Kalman filter (EKF)-based multiple trajectory candidates at a late stage. On the nuScenes dataset, the proposed method reduces the average displacement error and final displacement error of the Trajectron++ robot baseline by 13.7% and 14.6%, respectively, without modifying the baseline architecture. These results indicate that EKF-based trajectory candidates can effectively complement neural trajectory prediction through learned fusion.

Historians have reconstructed the twentieth-century transformation of general relativity and gravitation (GRG) at the field level and through individual careers, but connecting these scales requires a way to compare researchers with the changing field over time. We develop such a comparison, setting a researcher's publications and references against GRG field literature from the same, earlier, and later two-year periods. Building on Own Vocabulary and Embedding Density Estimation from our earlier two-case study (arXiv:2501.00391), we extend the analysis to the fifty most-published authors in a NASA/ADS corpus of about 180,000 GRG records (1911 to 2000) and add two citation-based measures, Referenced Vocabulary and Citation Identity. The four measures compare an author's written language, cited literature, semantic neighbourhood, and cited-authority configuration with the surrounding field. The earlier cases suggested that closer field-vocabulary alignment accompanies a denser semantic neighbourhood. Across the fifty authors this holds only partially. Written and cited vocabularies tend to move together, usually resembling later GRG literature as the field turned towards astrophysical and cosmological research. Semantic neighbourhoods more often lie where the field's publications were concentrated in earlier periods, while co-citation patterns follow no single temporal direction, and the two citation measures frequently place the same researcher differently despite drawing on identical reference lists. Individual trajectories can thus combine vocabulary tied to later field states with older semantic or citation structures, and these divergent cases mark patterns for closer historical investigation. The approach transfers to other fields with defensible corpus boundaries and adequate coverage of texts, references, and disambiguated author identities.

We present a hierarchical UAV navigation framework that aligns natural-language intent with dynamically feasible flight behaviors in cluttered indoor environments. To bridge the gap between abstract semantics and low-level control, we employ a parallelized ensemble of six behavior-conditioned Model Predictive Path Integral (MPPI) planners. Crucially, by designing mode-specific guiding costs and sampling biases, we induce distinct trajectory modes that converge to unique behavioral means, yielding a compact set of intentionally diverse candidates rather than mere stochastic variations. We project these 3D candidates onto the onboard first-person-view RGB stream, turning language grounding into a visual action selection problem. A pretrained vision--language model (VLM) asynchronously selects the candidate index given the overlaid FPV image and a natural-language prompt, while MPPI replans at 20Hz and a PID-based low-level controller tracks the selected trajectory. We implement the full pipeline in NVIDIA Isaac Sim and on a real-world quadrotor platform equipped with LiDAR and RGB sensing. Experiments in both simulation and real-world flights show semantically meaningful behavior diversity, robust language alignment despite VLM latency, and safe, repeatable flight across all modes, achieving 100% task success in our evaluated scenarios.

Multi-turn agent trajectories often contain redundant rounds (failed tool calls, parallel sub-queries, verification-only steps) that inflate both training and inference cost. We propose viewing each trajectory as a \emph{round-level dependency DAG} that exposes which rounds are globally load-bearing for the final answer, and fine-tune agents on trajectories refined through this DAG. Given an LLM-annotated DAG, these edits are deterministic and interpretable, with optional rephrasing. Models trained on these refined trajectories consistently outperform those trained on the original trajectories at lower inference cost. Specifically, across four multi-modal QA benchmarks, our refinements improve downstream accuracy by up to $1.7$,pp over vanilla SFT (and $5.7$,pp over an LLM-deletion baseline) while reducing per-sample inference messages by up to approximately $40\%$ and inference tokens by up to approximately $48\%$, translating to substantial savings in compute and serving cost. Code is available.

Policies for robotic manipulation are produced by training on large teleoperated datasets. These datasets typically consist of free-space trajectories, making them difficult to transfer to test-time environments with obstacles. Previous methods for closing this gap have largely fallen into two groups. Dataset augmentation addresses it at training time but needs obstacle geometry in advance, whereas steering an existing checkpoint at inference time avoids that requirement but is limited in flexibility. Our method draws from both areas without inheriting either drawback. DetAug applies an obstacle-blind augmentation scheme to the transit phases of a free-space dataset, leaving object interactions untouched, and records the augmentation parameters as an explicit conditioning label. At inference it samples a batch of labels and executes the trajectory with the lowest collision cost. On the SafeLIBERO benchmark DetAug achieves a collision-free success rate more than 20pp above the next best method, and selecting over the label space outperforms guidance on the same policy by 26pp. On real hardware, inference-time steering methods collapse on tasks requiring large detours, while DetAug matches or exceeds an obstacle-conditioned baseline without ever seeing obstacles in training.

Many real-world processes exhibit long-range dependence, where the current state depends on a slowly decaying trace of past states rather than on the most recent state alone. This paper studies system identification for discrete-time fractional-order linear time-invariant systems from a single observed trajectory of length $t$, a setting that captures such non-Markovian dynamics through the Grünwald--Letnikov difference operator. Unlike Markovian systems, fractional-order systems couple estimation across the entire history, making both statistical analysis and practical identification more challenging. We propose \emph{Fractional-Order Ordinary-Least-Squares Grid-Search (FO-GS)}, a simple two-stage estimator that exploits the diagonal structure of the fractional-difference operator to decouple the identification problem row-wise. Under the stability assumption, we establish high-probability, non-asymptotic error bounds for estimating both the fractional order and the system matrix in the heterogeneous setting, with both estimation errors scaling as $\mathcal{O}(t^{-1/2})$. Through experiments, we show that \emph{FO-GS} outperforms existing baselines in recovering both the fractional order and the underlying system dynamics.

Accurate seafloor mapping is essential for marine science, archaeology, and environmental monitoring. However, integrating data from different sensors, such as side-scan sonar and optical cameras, collected across separate survey sessions, remains challenging due to positioning drift and sensor offsets. This paper presents a multi-session, multimodal underwater mapping framework based on factor graph optimization. The method jointly optimizes vehicle trajectories, 3D landmark positions, sensor extrinsics, and per-session global alignment transformations. By combining rigid inter-session corrections with local trajectory deformations, it compensates for both inter-session offsets and intra-session distortions from accumulated navigation errors. The proposed methodology was validated on real-world datasets collected along the Catalan coast. Results show measurable improvements in map consistency over both unoptimized and rigid-alignment baselines across all metrics, including Pixel Accuracy and mean Intersection over Union. The method achieves a 3.4% improvement in pixel accuracy over the unoptimized baseline, corresponding to improved semantic labelling across approximately 14700 $\text{m}^2$ of mapped area. Qualitative results further show consistent co-registration between sonar and optical maps, even in the presence of significant trajectory distortions and inter-session misalignments. These findings demonstrate the potential of the proposed framework to generate coherent multimodal seafloor maps from heterogeneous underwater surveys.

Solomonoff induction frames prediction as a mixture over computable hypotheses, typically leading to identification of the true environment. In a finite meta-reinforcement learning setting with nested constraint families, in our previous work, we observe a different regime: a value-mixture (VM) agent achieves near-optimal, zero-collision navigation without identifying the true environment, a phenomenon we call Free Inference. This regime persists up to a sharp density threshold, beyond which performance degrades and posterior-mode selection (PMS) becomes preferable. We formalize this behavior via the Free Inference dimension dFI(S,N), a combinatorial measure of the environmental complexity a VM agent can handle while preserving trajectory coherence. We prove dFI is strictly smaller than the VC-dimension and relates to the Natarajan dimension up to a path-length factor, capturing the cost of non-decomposable loss. A PAC-style relaxation yields generalization bounds driven by dFI^(epsilon,delta). We also define a complementary PMS identification dimension and show that a hybrid strategy---averaging until the first collision, then switching to selection---is optimal, with links to Littlestone-type dimensions supported by grid-world experiments.

Real-time multi-object tracking systems remain highly vulnerable to full and long-term occlusion, where targets temporarily or completely disappear from the camera's field of view. Conventional trackers may terminate trajectories prematurely, resulting in identity loss and reduced situational awareness in applications such as defense and surveillance. This work proposes an occlusion-robust target tracking framework that maintains target identity and trajectory continuity through the integration of YOLOv11n object detection, Kalman Filter motion prediction, and occlusion-aware appearance-based re-identification. The framework consists of three stages: object detection, position estimation during occlusion, and identity recovery after target reappearance. Six Re-Identification (Re-ID) architectures were evaluated within the same tracking framework under identical conditions, with the Occlusion-Aware Mask Network (OAMN) achieving the best overall performance and therefore selected for the final pipeline. The framework was benchmarked against OccluTrack on the public OVIS dataset, achieving relative improvements of 18.1 percent in Multiple Object Tracking Accuracy (MOTA) and 25.1 percent in Identity F1 Score (IDF1), while reducing identity switches by 12.8 percent. On a custom military dataset simulating surveillance and battlefield-like environments with long-term occlusion, the framework achieved a MOTA of 0.734 and an IDF1 of 0.729, corresponding to relative improvements of 14.2 percent and 5.8 percent over OccluTrack. The system demonstrated strong tracking continuity, robust identity preservation, and reliable trajectory estimation under challenging occlusion conditions, highlighting its effectiveness for defense-related surveillance applications requiring continuous target tracking during visibility loss.

In this work, we propose a structured methodology for the system identification of underwater vehicles through the design of optimal excitation trajectories. To this end, the trajectories are parameterized using Bezier curves, which ensure smooth and differentiable motion profiles while facilitating the enforcement of constraints through appropriate manipulation of the control points. An optimization problem is formulated to determine a dynamically feasible excitation trajectory that respects safety limits and maximizes the quality of the collected data, thereby enabling reliable estimation of the vehicle's dynamic parameters using least squares. The proposed methodology is experimentally validated in a laboratory water tank, where the dynamic parameters, identified from the optimized trajectory, are evaluated by predicting the vehicle's velocity through forward simulation on previously unseen trajectories.

Safe local planning requires forecasting surrounding-agent motion and evaluating candidate-specific risks, since identical agent motion can pose different risks to different ego trajectories. We present CorrRisk-WM, a planning-oriented partial world model coupling environment evolution with supervised intrusion and near-miss prediction over bounded candidate-trajectory corridors. A latent environment model recursively predicts agent states and updates agent-agent and agent-map interactions. Each candidate queries the evolving environment through footprint- aware geometry and learned agent-corridor representations. A lightweight recurrent risk module uses temporal context to estimate per-slice hazards; survival aggregation yields first-entry and horizon-level event probabilities. On 29,176 scenarios from 100 Waymo validation shards, CorrRisk-WM achieves intrusion average precision (AP) of 0.8567 and 1-m near-miss first-entry AP of 0.8671. In baseline comparisons, it attains the highest near-miss AP at all three distance thresholds and the lowest observed open-loop collision rate (4.88%), with route progress of 15.35 m. Across three seeds, removing dynamic environment modeling or candidate-conditioned geometric interaction reduces mean intrusion AP from 0.8590 to 0.7624 and 0.7252, respectively. These results support coupling environment evolution with candidate-conditioned geometric reasoning for risk prediction and safety-oriented candidate selection.

Diffusion models generate images through an iterative diffusion process, and recent studies have demonstrated that the intermediate feature maps produced during this process contain rich visual representations, leading to their adoption across a variety of downstream tasks. However, most existing approaches are limited to either using a single feature map at a specific timestep or aggregating feature maps across multiple timesteps. We observe that intermediate representations in the diffusion process form meaningful trajectories along the time axis. In particular, the representation of each spatial patch evolves progressively throughout the generative process, encoding semantics that are difficult to capture from static snapshots alone. This observation motivates the need to treat diffusion representations as temporally structured trajectories rather than static snapshots. To this end, we propose Diffusion Trajectory Modeling (DTM), a framework that interprets the temporal evolution of each spatial patch as a trajectory and leverages it for semantic correspondence. By effectively modeling patch-wise trajectories generated across multiple timesteps, DTM captures correspondence cues that prior methods are not designed to capture. We further demonstrate empirically that spatially corresponding patches form similar trajectory patterns throughout the diffusion process, suggesting that the temporal axis of diffusion carries semantic information. Experiments on SPair-71k, SPair-U and AP-10K show that DTM achieves strong performance, presenting a new perspective for exploiting diffusion representations from a trajectory-centric viewpoint.

Trajectory curvature constraints are inherent in practical multi-robot systems due to the limited turning capabilities of the robots. Without properly accounting for these constraints, robots may fail to accomplish assigned tasks, and their trajectories may diverge from the intended paths. This paper proposes a distributed safe cooperative vector field approach for multi-robot systems subject to trajectory curvature constraints. The proposed approach is composed of a cooperative vector field and a safety-oriented collision avoidance vector field, aiming to address the problems of cooperative motion and safe collision avoidance in multi-robot path-following tasks. A safety-oriented collision avoidance vector field with adaptively adjustable reactive boundary is developed to accommodate the kinematic curvature constraints of robots, thereby ensuring the physical feasibility of collision avoidance maneuvers. The proposed vector field requires only a single virtual variable from each neighboring robot to achieve cooperative motion and ensure both obstacle avoidance and inter-robot collision avoidance. The effectiveness of the proposed approach is validated through both simulations and real-world experiments on an actual multi-robot platform.

Diffusion Policy (DP) is a powerful Learning from Demonstration (LfD) method for robotic manipulation, yet it suffers from discontinuous and non-smooth trajectories. Spline-based action representations promote smooth motion within individual action chunks, but existing spline-based methods neither guarantee cross-chunk $C^2$ continuity nor account for the group structure of $\mathrm{SE}(3)$. We therefore propose LieSpline-DP, a Lie-group B-spline diffusion policy that generates end-effector trajectories directly on $\mathrm{SE}(3)$ and couples consecutive plans by sharing their boundary control poses, ensuring $C^2$ continuity throughout the entire planned trajectory. Across three real-robot tasks, LieSpline-DP produces lower trajectory jerk and higher task success rates than the DP baseline. The gains are particularly pronounced in real-world tasks involving liquids and flexible objects: in our real-robot experiments, LieSpline-DP achieved a 100% success rate on both pouring and bucket hooking, whereas the DP baseline achieved only 10% and 30%, respectively.

This paper presents a battery-aware predictive trajectory-planning and control framework for multirotors operating under spatially localized disturbances. Candidate trajectories are evaluated through closed-loop vehicle--motor--battery propagation, allowing disturbance-induced control demand, electrical energy, battery evolution, and terminal-voltage-dependent actuator capability to enter the planning process. % A reduced-order battery model is numerically benchmarked against an independently implemented Simscape equivalent-circuit reference, with a power NRMSE of $0.64\%$ and a cumulative-energy discrepancy below $0.7\%$. % In a $150$-s, $640$-m mission containing three disturbance regions, the selected trajectory reduces electrical energy consumption by $7.46\%$ and position-tracking RMSE by approximately $72\%$ relative to the disturbance-aware fixed-reference baseline. % Planner ablations show that battery-dependent terms are nonbinding at nominal SOC but alter the selected trajectory under a depleted-battery stress condition. % Execution with multiple feedback controllers further demonstrates that controller selection changes the tradeoff among tracking accuracy, energy consumption, and actuator utilization. % The results demonstrate the benefit of accounting for predicted closed-loop energetic and battery--actuator consequences during trajectory selection.

Autonomous driving requires more than recognizing what is present in a scene: a planner must determine how road structure, surrounding agents, and their motion states should influence a future maneuver. Existing learning-based planners can capture these influences through latent scene features and trajectory decoders, but the relationship between environmental factors and candidate actions often remains implicit. This limits the ability to inspect, diagnose, or refine how scene context affects the safety of a predicted trajectory. Classical safety fields provide an explicit spatial representation of this relationship, but their risk shapes and relative weights are prescribed in advance and do not adapt to each scene. We introduce READ, a framework that learns an explicit, planning-aligned risk representation from complementary geometric and behavioral constraints. READ instantiates this representation as a continuous spatiotemporal field, enabling differentiable queries along candidate trajectories. The learned field connects scene understanding with action selection by encouraging predicted trajectories to align with low-risk regions, while retaining a differentiable interface for trajectory evaluation and refinement. READ integrates with both end-to-end planners and Vision-Language-Action models. Experiments on NAVSIM show consistent gains across matched end-to-end backbones and strong performance in a VLA setting; READ also achieves competitive results on NAVSIM v2. These results establish learned spatial risk as an explicit, adaptable representation for safe planning.

Dynamically feasible trajectory optimization for rigid-body systems is naturally formulated on the special Euclidean group SE(3) but is challenging when dynamics are available only as black-box computations without derivatives. This paper formulates the Trajectory Bundle Method (TBM) for motion planning implicitly on SE(3). Bundles are constructed in the Lie algebra and propagated through nonlinear rigid-body dynamics using exponential and logarithmic maps, enabling derivative-free planning of non-Euclidean trajectories. We show that Euclidean TBM interpolation error is bounded quadratically by bundle diameter and extend this result to SE(3), where the bound additionally depends on a local Lipschitz constant of the Log map. Numerical experiments corroborate these bounds. Finally, we demonstrate SE(3) TBM by optimizing an acrobatic, collision-free fixed-wing maneuver through a rotated aperture without explicit models or derivatives of the vehicle dynamics, aerodynamics, or collision model.

Transfer learning explores how to leverage knowledge from various tasks or domains (sources) to enhance predictive performance in related tasks or domains (targets). Typically, transfer learning research is segmented into several isolated sub-areas (such as domain generalisation, domain adaptation, or multi-domain learning), each making distinct assumptions about target data availability, namely how much data and how many labels are available at training time. However, in many real-world applications, data availability is not fixed but evolves over time, as instances and labels are progressively collected from a new domain. Each of the classical settings then describes only a snapshot of a trajectory that a deployed system must traverse in full. We formalise this trajectory as a transfer learning problem in its own right, Transfer Learning for Evolving Domains (TrED), specified by a data availability process fixed by the environment, a learning protocol that the method is free to choose, and an evaluation criterion that scores the whole trajectory of models rather than a single one. Within this formalism, the classical settings are recovered as regimes that a learner may pass through, rather than as separate problems that TrED concatenates. We then examine the transfer learning literature to identify mechanisms that are promising building blocks for a solution, and find that most methods are tailored to a single regime and that even the strongest existing candidates do not yet optimise the whole trajectory. We argue that TrED is a well-posed and unsolved problem, and an important direction for future research.

In field robotics, acquiring independent large-scale reference trajectories more accurate than the evaluated estimates remains an open challenge. The domain is widely reliant on Absolute Trajectory Error (ATE) and Relative Pose Error (RPE), computed with automated tools, that rest on assumptions and evaluation parameters rarely made explicit. When unreported, the errors can be misleading and hinder fair comparisons. This paper introduces a trajectory-evaluation protocol for standardized and reliable accuracy assessment in state estimation, localization, and Simultaneous Localization And Mapping (SLAM). The approach combines a novel temporal alignment method based on curvature signals with an error metric normalized by travelled distance. We explicitly account for temporal synchronization, sampling alignment, and extrinsic calibration, quantifying their influence through a sensitivity analysis. The proposed protocol contributes to more rigorous, reproducible, and standardized trajectory evaluation.

Large language model agents are increasingly deployed for long-horizon task execution, raising a central granularity question for trajectory evaluation: whole-trajectory verification is too coarse to capture concrete failures and their associated evidence in long trajectories, while atomic-step scoring is too fine-grained, noise-sensitive, and computationally expensive. This granularity gap makes a single-reference trajectory paradigm inadequate for assessing the rich space of valid agent execution paths and delays timely feedback and early stopping in long-horizon tasks. To address these issues, we propose DynSTEER, a dynamic stage-wise framework for agent trajectory evaluation. DynSTEER bridges the granularity gap through stage-wise dynamic evaluation that segments rollouts at key execution nodes and adapts its multi-tier review strategy based on stage-level results; it compiles a path-tolerant milestone graph from public task views to preserve diverse legal paths without reference leakage; and it supports terminating unrecoverable agent executions to curb resource waste. Experiments show that DynSTEER improves evaluation discriminability by 85.2% over native evaluation, separates all model pairs with statistical significance, and saves 45.41% of execution steps on failed rollouts.

The pedestrian crossing intention task involves predicting whether pedestrians are likely to cross the road from the point of view of an autonomous vehicle. We introduce TrajFusionNet+, a novel transformer-based model for pedestrian crossing intention prediction. TrajFusionNet+ combines sequential and visual representations of pedestrian trajectory with a graph-based representation of the scene context in order to predict pedestrian crossing intention. The proposed architecture builds upon our previous model, TrajFusionNet, and comprises three branches: a Sequence Attention Module (SAM), which processes a sequential representation of past and predicted pedestrian trajectories; a Visual Attention Module (VAM), which utilizes a visual representation of the pedestrian trajectories by overlaying observed and predicted bounding boxes onto scene images; and a Graph Attention Module (GAM), which extracts pedestrian-centric graphs from segmented scene images and captures the relational dependencies between pedestrians and traffic elements. TrajFusionNet+ achieves improved state-of-the-art performance on the two most widely used pedestrian crossing intention datasets, PIE and JAAD. Furthermore, we introduce a new evaluation protocol in which models are trained jointly on the PIE and JAAD datasets but evaluated separately on each. Under this setting, TrajFusionNet+ demonstrates superior generalization compared to existing approaches.

This paper presents a coordinated trajectory generation and tracking control framework for a tail-sitter unmanned aerial vehicle (UAV), which does not require aerodynamic priors identified for a specific airframe while addressing the challenge of flight control under highly nonlinear aerodynamics across the full flight envelope. The core innovation lies in employing phase-specific aerodynamic modeling strategies for planning and tracking, tailored to their distinct functional characteristics, without requiring airframe-specific aerodynamic priors. Specifically, the phi-theory model under coordinated flight is employed to derive an analytic differential flatness mapping, and a simplified but locally accurate model is established for predictive control to enable real-time aerodynamic parameter estimation. The proposed framework is evaluated extensively through both simulation and challenging real-world flight tests under mild wind conditions, showing high-precision tracking and adaptability across the tested aerodynamic conditions. To the best of our knowledge, this is the first real-world demonstration of accurate trajectory tracking over tested flight regimes spanning the full envelope of a tail-sitter UAV without relying on aerodynamic identification campaigns. The source code of our framework is available at: https://github.com/SYSU-HILAB/AP-PnC.

LLM agents for sequential decision tasks are often post-trained with trajectory-level outcome labels, but such labels provide little supervision for preserving multiple successful branches from the same decision state. We study this problem as successful strategy coverage: how broadly a model realizes distinct successful strategies under a fixed rollout budget. We present Direct Diversity Optimization (DDO), an offline post-training method that combines Divergence-Tree Collection (DTC) with the Reference-Relative Target-Odds Objective (RTO). DTC constructs state-aligned branch sets rooted at shared decision states, and RTO trains the model to match reference-relative targets over successful alternatives. DDO achieves the strongest task success and successful strategy coverage among the compared post-training methods across BabyAI, BabaIsAI, and WebShop. It also achieves the highest recovery rate after local action replacement and higher task success and coverage than successful-only imitation and decoding-time diversification controls.

Machine-learning systems are built almost exclusively on a few large Python-orchestrated frameworks, and they inherit those stacks' engineering costs: environments of hundreds of version-coupled packages, separate export toolchains for deployment, and the split between the language research is written in and the language products ship in. We report on the construction and verification of numbat, a machine-learning stack written in one general-purpose language (Zig) with no third-party runtime dependencies. The stack spans tensor computation, automatic differentiation, neural-network modules, mixed precision, multi-GPU training, data loading and monitoring; an SDK exposes it behind a stable, additively versioned C ABI of over 1,400 entry points, with bindings for six languages; and its clinical domain planes encode regulatory requirements as executable acceptance gates rather than documentation. Verifying such a stack is the harder half of building it: a defective training run rarely fails, it converges quietly to a slightly worse model. We treat a widely used reference implementation as an executable specification and verify against it at five levels, from operator gradient checks to an automated trajectory gate against a same-machine reference run - the arrangement our companion study formalizes as a trajectory-level differential oracle. The protocol surfaced ten silent recipe divergences, which we catalog with mechanisms and symptoms. As the acceptance test, we train a 25.9M-parameter detector of the YOLOv8m class from random initialization on COCO 2017 for the full 500-epoch schedule: the exported weights score 0.4956 mAP50-95 under the official protocol, scored by the reference stack's own validator (published endpoint 0.502), with single-GPU step time at parity on identical hardware. Weights, per-epoch metrics and the full run manifest are released.

Chain-of-thought reasoning provides a structured computation between a model's input and final answer. Yet it is often evaluated through endpoint accuracy, which ignores the path taken to reach that answer. An emerging line of work addresses this limitation using entropy profiles, which track how uncertainty evolves over the reasoning process but do not reveal which competing hypotheses account for that uncertainty. We introduce answer-distribution trajectories, a stochastic-dynamics-inspired representation that tracks the model's full predictive distribution over answers as reasoning unfolds. As a strictly finer representation than endpoint and entropy summaries, answer-distribution trajectories enable us to characterize a trace through a dynamical reasoning profile spanning exploration, revision, motion, and commitment, and to distinguish different dynamical mechanisms of reasoning success and failure. Across sixteen open-weight language models and four reasoning benchmarks, we show that traces with the same endpoint and similar entropy profiles can exhibit substantially different reasoning dynamics. We further find substantial variation in these dynamics both within and across models and tasks, with different objectives favoring different dynamical profiles. Additionally, we show that training and inference choices systematically reshape these profiles. Our results suggest that answer-distribution trajectories provide a rich framework for analysing and evaluating the dynamics of LLM reasoning.

A dense retriever encodes a question as one vector, but the question arrives one word at a time. We read 2,144 held-out headlines from Thu Vien Phap Luat (Vietnamese legal library) word by word with Nemotron-3-Embed 8B/1B and Qwen3-Embedding 8B/0.6B, encoding 65,444 prefixes against 20,034 articles, plus every prefix of 3,438 sub-questions from 1,112 multi-question headlines and of 168 answers. (i) The gold article becomes rank 1 after a median of 6-7 content words in every encoder, before the interrogative frame is read, and stays there to the end in 78-85% of cases. (ii) In a multi-question headline the lock is inside the first sub-question 94-98% of the time; the second leaves rank unchanged in 89-95%; encoded alone, the second reaches rank 1 in 42-58% vs 91-96% for the first, at the same lock word (95-97% identical). (iii) Numbers, dates and instrument identifiers move the embedding twice as far as content words and four times as far as interrogative words; 72-78% of steps move toward the gold article, and the closing interrogative frame moves against that direction in 95-99% of headlines. (iv) Rank/cosine clustering yields six archetypes (instant, typical, unstable, late, never-locking) that differ by legal area and form (chi-squared p < 1e-8): real-estate and litigation headlines never lock on a number; environmental and accounting headlines do so a third of the time. (v) An answer read word by word retrieves its article after 8-16 words and addresses the sub-questions in order asked in 83-89% of cases. (vi) A word's step keeps a consistent direction across headlines (cosine 0.25-0.33; 0.44-0.60 for numbers); a preceding question rotates that step by about 60 degrees and a greeting by about 30 degrees; steps shrink as i^{-0.8}; and a two-question headline is within 12-17 degrees of a linear mix of its two questions. We call this a context-modulated additive walk.

The transition from human-centric assistance to Autonomous Software Engineering (ASE) agents has enabled the resolution of complex real-world SE tasks. However, the trial-and-error nature of these agents generates lengthy interaction trajectories, creating severe bottlenecks in terms of context window limits and cost. While context compression offers a potential remedy, prior approaches suffer from static pruning strategies and granularity mismatches, often failing to preserve the semantic dependencies and syntactic details crucial for SE tasks. To strictly preserve critical task evidence while reducing context length, we introduce AttnCompress, a dynamic attention-guided trajectory compression framework. Unlike existing approaches, AttnCompress bridges the gap between semantic integrity and dynamic adaptability through three key mechanisms: (1) structure-aware segmentation via perplexity (PPL) spikes to preserve the syntactic structure of code and logs; (2) relevance estimation using proxy attention weights to quantify the precise relevance of historical blocks to the agent's current reasoning; and (3) a dynamic rolling window to re-evaluate and recall historical context as the task evolves. Extensive evaluation on SWE-Bench-Verified and Multi-SWE-Bench demonstrates that AttnCompress achieves a pass rate of 53.17%, outperforming prior state-of-the-art baselines while reducing token consumption by 21.6% and total costs by 33.6%. The framework proves to be model-agnostic and generalizes effectively across diverse programming languages.

Voice phishing (vishing) unfolds in real time; by the time a call has ended and post-hoc classification is possible, the harm has already been done. The more actionable question is which concrete harm (Information Gathering or Financial Exploitation) an ongoing call is tactically progressing toward. We present Vishing-Tactics-Bench, a benchmark grounded in Endsley's situation-awareness (SA) framework that recasts vishing defense from after-the-fact fraud classification to harm projection: predicting at each turn whether the call will reach either terminal harm. We adapt MITRE ATT&CK to vishing as a 6-tactic taxonomy (Vishing-Tactics) and label 35,340 scammer utterances across 5,645 synthetic Chinese calls. We define Exploitation Trajectory Forecasting, a survival-style protocol over the two terminal harms with three metrics: AP@k, C-index, and divergence error. Baselines ranging from a Markov heuristic to fine-tuned LLMs show that the tactical trajectory serves as an interpretable representation of the call's tactical state, supporting harm-specific forecasting, which can then be used for the downstream application of intervention selection; a stratified lead-time analysis at a tight false-alarm budget further identifies at what point in a call the trajectory signal yields early warning.

As terminal-based code agents become prevalent, agent trajectories have accumulated at scale, while realistic, executable environments remain scarce. However, environments are what agent post-training actually requires: each can be re-queried into many verifiable tasks and provides execution feedback, whereas a trajectory is a single frozen demonstration. Rather than generating environments from scratch, we observe that the tool-execution history in existing trajectories exposes the structure and contents of the environments in which they ran, making it possible to reconstruct those environments from the trajectories themselves. Thus, we introduce Terminal-Universe, a framework which turns each trajectory into a reusable environment and explores it for synthesizing new tasks and continued interactions. Specifically, Terminal-Universe replays the file operations recorded in a trajectory to restore each file before the agent modified it, yielding a partial workspace; a completion agent then supplies the missing files and dependencies. On this recovered workspace, we both reconstruct the original intent task and synthesize entirely new ones. Besides, we also scale the tasks along two complementary axes: breadth and depth. For breadth, we mine directional dependency relations between related environments and synthesize cross-workspace queries spanning multiple codebases, as developers routinely do in real-world development. For depth, we extend the initial single-turn query into a multi-round session that captures iterative user feedback and requirement refinement via a user agent. Applied to public terminal agent trajectories, Terminal-Universe produces 37.3k task-sufficient environments. Supervised fine-tuning of Qwen3.5-27B on this corpus improves single-round performance on Terminal-Bench 2.1 by 11.9 points and multi-round performance on EvoCode-Bench v2 MT@4 by 13.8 points.

Agent evaluations report a tool-call rate read off the serving stack. That number can be zero while the model is emitting well-formed calls: the interface censors the trajectory before anything downstream sees it. On BFCL v4's own data, executor and scorer, holding weights, cases, decoding and seeds fixed and changing only the serving adapter, the same model scores 0.00 or 0.96 / 0.19. A 2x2 over chat template and parser locates the effect exactly: both main effects are exactly zero and all of it sits in the interaction -- no component is defective, and repairing one side of the contract buys precisely nothing. On tau-bench's 115 interactive retail tasks the same swap moves server-parsed calls from 0 to 636 and tasks reaching any tool execution from 0 to 103. Our probe reproduces the funnel across a 21x scale range of Qwen2.5-Coder: the server parses 0/100 at every size while well-formed emitted calls rise to 80/100 at 32B (~72 after calibration against an adjudicated gold standard). Under a matched envelope, across a comparable scale span, the silent fraction stays at 0-2, a prediction committed to the repository before the run. Llama-3.1-8B's 23% rate of calling the task function itself as a tool falls to 0 under one strict:true flag. The mismatch reaches inside the training loop, and its consequence is scale-dependent: in verl's AgentLoop at 7B, 45 of 115 generations carry a complete call; 0 are accepted, 0 execute, 0 return an observation. At 1.5B the same zero is over-determined, so we report the two scales separately. At evaluation time, repairing the adapter restores the mechanism but not a significant outcome gain: parsing 0->84, rescues 0->9, pass rate 53->62 (n.s.). We release a 98-line preflight check that catches every silent failure here. The observed tool-call rate is not a property of the model alone; it is a property of the model-interface stack that measures it.

AI agents increasingly gather evidence, invoke tools, apply constraints, and produce decisions that people or software may commit to action. A final output alone cannot show which evidence, tool state, rule, authorization, or action path produced it. We present DNative-Twin, a graph-native digital twin that records a committed agentic decision as a typed trajectory and re-executes its decision mechanism under declared conditions. The graph links the state observed by the agent, the path it followed, and the authority behind the resulting action. The twin synchronizes this information, replays the mechanism in isolation, and compares it under controlled changes. We instantiate the framework in enterprise decision processes using three public process logs and controlled replay suites. The experiments identify a specific failure: graph structure localizes represented changes but cannot determine the consequence of an unobserved tool state. In a three-condition controlled experiment with 300 injected instances, unresolved-divergence recall increased from 0 to 0.667 when replay-contract state was added and to 1.0 when verification results were also available; the held-out set contained no critical-class instance. Across 500--5,000 BPI 2020 cases, median end-to-end time increased from 0.794 to 8.889 seconds on the reported platform. These results separate the roles of graph structure, replay context, and verification evidence in reviewing a decision mechanism.

A reasoning model can improve from its own on-policy experience, but this inner loop is fragile: terminal verifiers provide reliable yet sparse supervision, while dense same-model guidance can reinforce false confidence or overconcentrate learning on a narrow solution mode. We introduce FlowBalance, a verifier-grounded self-improvement method that learns a normalized distribution over complete responses. For each on-policy trajectory, a frozen training-time view of the same policy uses privileged context to produce token-level log-probability gains, which are aggregated into a trajectory-level self-guidance score. FlowBalance calibrates this score with the verifier-derived group advantage: guidance is retained on positive-advantage trajectories, reversed on negative-advantage trajectories, and disabled when the rollout group provides no outcome preference. The resulting energy exponentially reweights a reference policy, and profiled trajectory balance fits the normalized target with one log-partition estimate per rollout group. This realizes outcome-calibrated self-guidance via trajectory balance, without a separate token-level imitation loss. Our analysis establishes within-group contrast preservation, a minimum-change reverse-KL characterization, monotonic verifier control of target reward, and an exact correction against false-positive self-guidance on rejected responses. On mathematical reasoning, FlowBalance improves average performance over FlowRL on both Qwen3-4B and Qwen3-8B, while also improving training speed and stability, avoiding direct OPSD's response-length collapse, and exhibiting higher correct-strategy diversity in a controlled AIME24 diagnostic.

Many current end-to-end driving policies emit a pool of candidate trajectories and select one, which makes selection a separable component: a scorer can be retrained while the planner, its backbone, and its trajectory generator all stay frozen. However, many strong planners concentrate their proposals around safe mode, providing limited supervision near decision boundaries. In this work, we design a training dataset that provides more informative supervision for the scorer. In particular, we construct two generators that perturb the logged human trajectory along the two axes a vehicle can be displaced: laterally toward the drivable boundary and longitudinally toward a leading vehicle. The designed dataset produces more informative positive and negative samples than the base planner's proposal pool. We attach a transformer-based scorer to two frozen generative planners, DiffusionDrive and MeanFuser, and train it on the NAVSIM navtrain dataset. The results of the experiments show that we achieve 90.1 EPDMS on DiffusionDrive and 90.4 EPDMS on MeanFuser when using ResNet-34, with 0.4 and 0.3 EPDMS respectively, from the designed training dataset.

Estimation of the absolute pose of an object is an essential task for various robotic applications. Recently, incorporating gravity direction as prior information has emerged as a popular approach to simplify absolute pose estimation. However, developing a robust and efficient algorithm to solve this challenging problem remains a difficult question due to large amounts of mismatches. In addition, obtaining an accurate pose solution from selected inlier correspondences with gravity prior is still a research gap. In this paper, we propose a novel transformation strategy that exploits geometric relations derived from the gravity prior. Through transformation decoupling, the original 6 degrees of freedom (DoF) absolute pose estimation problem is simplified into a 4-DoFs problem: 1-DoF for the rotation angle and 3-DoFs for translation, significantly improving the efficiency. For the 1-DoF rotation angle, we apply a one-dimensional global voting algorithm for optimal estimation. Once the optimal rotation is obtained, the mismatched correspondences are preliminarily filtered, and translation estimation, a linear problem, can be easily solved. Furthermore, to obtain accurate pose results, we introduce a novel pose refinement algorithm to enhance the accuracy of both rotation and translation. Extensive experiments on synthetic data and three publicly available real-world datasets (TUM RGB-D, ETH3D, and RobotCar) demonstrate that the proposed method achieves stronger performance compared to existing state-of-the-art (SOTA) approaches. To further validate our method, we integrated it into ORB-SLAM2. The results on the KITTI dataset show it effectively reduces drift and improves trajectory alignment during relocalization. The source code will be released upon acceptance.

Most trajectory forecasting models are trained on clean annotated histories, and are often evaluated under the same idealized assumption, although practical deployments rely on trajectories produced by imperfect multi-object trackers. The real-world observations exhibit localization jitter, missed or unstable detections, and data-association ambiguity, which are usually either ignored or removed through denoising. This paper instead treats tracking-derived reliability cues as an informative signal to be propagated to the predictor. We propose a plug-in uncertainty-aware formulation in which each observed state is encoded as an uncertain state representation, modeled by a Gaussian distribution whose covariance combines detection-level localization uncertainty and association-level ambiguity through the law of total variance. Existing backbones are adapted with minimal architectural changes: input trajectories are represented as Gaussian observations, and predicted trajectories are produced as Gaussian forecasts rather than deterministic coordinates. To train predictors that remain robust under structured observation noise, we combine temporally correlated Ornstein-Uhlenbeck perturbations with response-based knowledge distillation from a teacher trained on clean trajectories. Experiments on Oxford Town Centre and VIRAT using real tracker outputs, together with a complementary ETH/UCY pseudo-detection protocol, show that the proposed formulation improves displacement accuracy and the reliability-sharpness trade-off of probabilistic forecasts.

Trajectory data is getting more vital for training large language models for boosting the agentic abilities. Unlike the verifiable domains such as coding or mathematics, scaling trajectory data for open-ended tasks is much more difficult because these tasks lack singular ground truth and are costly to annotate or verify. In this paper, we propose RetroGen, a self-improving framework of retrospective process supervision. Our key observation is that although expert trajectories are scarce, high-quality final artifacts such as literature reviews, analyst reports and legal judgments, are abundant in pre-training data and can be viewed as compressed traces of the evidence-seeking processes that produced them. RetroGen reconstructs candidate latent trajectories from expert artifacts, verifies them against both the artifact and supporting evidence, and trains models on their own successful reconstruction data, without requiring trajectory data from stronger models. Experiments show that RetroGen improves grounding, faithful synthesis, and long-form evidence-seeking agent tasks.

Natural-language instructions enable flexible control of synthesized speech, yet emotional TTS systems primarily model a single utterance-level affect, leaving multi-emotion control underexplored. We study two complementary multi-emotion TTS tasks: emotion trajectory, which spans several ordered affective stages, and emotion blending, in which multiple emotions coexist throughout an utterance. These tasks expose a supervision mismatch: supervised fine-tuning (SFT) does not explicitly evaluate emotion features, while single-emotion rewards provide neither structure-aware feedback for trajectory completion nor pair-aware feedback for blending. We introduce HybridEmo, a post-training framework that initializes both tasks with SFT and then aligns the speech-token policy through Group Relative Policy Optimization using a sample-aware hybrid reward. For trajectory samples, segment-aligned consistency combines average and weakest-stage evidence to preserve the correctness and completeness of prescribed stages. For blending samples, a GMM-based reward combines frame-level support from the union of target-emotion anchors in an offline emotion space with an utterance-level weaker-target margin. Both branches share an ASR reward and are routed within a unified policy. On MultiEmo-Test, HybridEmo significantly improves trajectory correctness and blending intensity, without a noticeable degradation in speaker similarity. Human evaluation prefers HybridEmo to CosyVoice 3 and EmoVoice-0.5B, with nearly balanced preferences against Qwen3-TTS.

Planners on graphs of convex sets return trajectories that are collision-free by construction, provided the convex regions are collision-free. The region generator only promises that property probabilistically, and no planner in the family verifies it. We report the first measurement of what the gap costs. On a scaled 14-DOF bimanual library, $3.2\%$ of interface samples are in collision, and a search-based GCS planner (\gcsstar) turns that volume error into a $62\%$ answer error: $18$ of $29$ pick-and-place queries return trajectories that drive the arms through the shelves, up to $91$,mm deep, reported as successes. Repairing the library does not work; a ten times stricter acceptance contract, sums-of-squares certified regions, and uniform margins each destroy the connectivity planning needs before they deliver soundness. We instead build a planner that certifies its answers. It samples the overlaps and shared faces of the decomposition, prunes with an admissible informed bound, and verifies the one candidate each search round proposes, continuously, by a chain of clearance certificate balls with no resolution parameter; failures are repaired with local in-region detours, and the convex polish is re-verified. Head-to-head on all $29$ task queries it delivers zero invalid answers against $21$ for the reference, reaches its first certified answer in $0.11$,s against $1.59$,s for the reference's unverified one, and reproduces the reference optimum exactly on every query whose reference answer is physically valid.

Longitudinal cohort studies produce repeated data that enable the assessment of time-varying association patterns between exposures and health outcomes. Classical linear mixed-effects models (LMMs) can accommodate a large variety of association patterns while accounting for the irregularly spaced, partially observed measurement. But they require the analyst to pre-specify the functional form linking the exposure history to the outcome. We propose the Neural ODE-LMM, which embeds a Neural Ordinary Differential Equation (Neural ODE) within the linear mixed-effects framework: a learned vector field encodes covariate trajectories into a continuous-time latent state that drives both the fixed- and random-effect design, while preserving the standard LMM observation model. This retains classical likelihood-based inference while learning complex, potentially cumulative, covariate effects flexibly. All parameters are estimated by maximising a penalised marginal likelihood. To quantify covariate effects, we introduce contrasts of counterfactual predictions that compare the expected outcome under alternative covariate trajectories with variance estimated via the delta method. In simulations, the model recovers both instantaneous and cumulative-burden effects without prior specification of the functional form. Applied to the Trois-Cités (3C) cohort, a population-based study of 7{,}324 participants, the method reveals trajectory-dependent associations of BMI and fasting glucose with cognitive decline.

We present a training-free method for multi-modal trajectory prediction that achieves comparable accuracy to a 57M-parameter transformer while requiring no GPU and zero learned parameters. The method builds a transition table of historical state-to-next position pairs and retrieves neighbors using a product kernel over spatial proximity, bearing, speed, and temporal context. Two inference modes operate over this shared representation: diversity-penalized sampling produces trajectories covering distinct plausible routes, while beam search finds the highest-likelihood path. On the TrAISformer benchmark (Danish Maritime AIS), our method achieves competitive accuracy at full data availability and dramatically outperforms the transformer in data-scarce regimes---remaining stable down to 10% of training data where TrAISformer degrades catastrophically. This enables deployment in new geographic regions from an order of magnitude less historical data.

Retrieval can identify a past trajectory that may matter, yet it does not specify how an acting agent should use that trajectory after users, entities, constraints, or environment state have changed. We identify this post-retrieval reuse step as a distinct bottleneck for long-horizon trajectory memory and formulate an evaluation framework that holds candidate retrieval, target state, model, decoding, and tool budget fixed while varying the support delivered to the agent. We instantiate the framework with query-conditioned reuse (QCR), a deliberately simple target-bound note that records a reusable procedure, bindings to recover, applicability conditions, and verification requirements. QCR serves to test the reuse hypothesis rather than to claim a universally preferred memory format. Across 2,391 target instances in WebArena, WorkArena, and AppWorld, QCR reaches 62.3% average Success, 10.7 points above Full Trajectory, while using 48.9% fewer online tokens. Summary reranking selects a reusable memory for 94.8% of targets, placing end-task Success within 1.8 points of an oracle reusable selector. Analyses by trajectory length and source--target binding shift show that direct trajectory injection loses much of its utility as traces grow longer or source-specific values change, whereas target-bound support preserves a larger share of the measured gain. The resulting framework separates retrieval quality from the problem of turning retrieved experience into safe, useful support for a new task.

Deep search agents operate over trajectories spanning dozens of steps, yet standard reinforcement learning provides only a single outcome reward per trajectory, which is far too sparse for effective credit assignment. On-policy self-distillation (OPSD) addresses this by using the model's own logits as dense token-level teachers, but extending it to search agents introduces a fundamental tension: the teacher, having access to privileged information such as the correct answer, produces a distribution that differs systematically from the student's exploration-based reasoning, and naive distillation causes the student to inherit this information asymmetry rather than learn better search strategies. We resolve this tension through two contributions. First, we construct Evidence Anchors, which are concise, step-level evidence snippets extracted from the web, as privileged information that captures key reasoning steps without revealing the entire answer path. Second, we propose Step-Level Self-Distilled Policy Optimization (SSPO), which converts teacher-student disagreement into step-level advantage weights within GRPO, applied exclusively to incorrect trajectories. This design decouples what to update from how much to update: the outcome reward determines the direction of policy change, while the teacher modulates its magnitude at each step. Correct trajectories are left untouched, preserving their diversity. On Qwen3-8B, SSPO consistently outperforms GRPO across BrowseComp, GAIA, and FRAMES, surpassing or matching GRPO trained with twice as many gradient steps while adding only about 5 percent overhead per step from a single additional forward pass.

Contact-implicit trajectory optimization avoids prescribing contact sequences, but yields mathematical programs with complementarity constraints (MPCCs) whose degeneracy challenges conventional primal--dual solvers. Existing contact-specific methods improve robustness to this degeneracy but do not leverage a stagewise optimal-control factorization and primal--dual consistency, while structure-exploiting optimal-control solvers are not designed for complementarity constraints. We show that these capabilities can be combined in a single primal--dual method. ContactIPM identifies complementary inequality pairs, embeds them through a barrier-coupled elastic interior relaxation, eliminates slack and dual variables stagewise, and solves the reduced Newton system using a Riccati recursion. A fixed multi-phase MPCC recovery schedule provides four continuation and restart attempts from naive initializations, while termination is gated by the unrelaxed physical complementarity residual. We compare ContactIPM with two contact-specific MPCC solvers, CRISP and IMPACT, using matched benchmark conditions and common post-solve acceptance criteria. On four fixed CRISP benchmark cases, ContactIPM is $2.17$--$8.87\times$ faster over 20 paired timing repetitions per case and achieves higher success on the Push Box and Push-T robustness suites. Against IMPACT, ContactIPM is $2.96\times$ faster on Push T and $4.91\times$ faster on Cart Transport, but $4.46\times$ slower on Push Box. In 50 closed-loop Push Box rollouts spanning model mismatch, measurement noise, initial-pose errors, and state resets,

Uncertainty quantification (UQ) methods for language models are typically evaluated on single-turn outputs, where uncertainty is attached to one generated answer. For LLM agents, however, the unit of observation is an interactive trajectory, where the model can ask clarifying questions, call tools, update state, and make intermediate decisions whose errors propagate to the final outcome. We study whether three common families of single-turn UQ methods transfer to this setting. Across five LLMs and four multi-turn tool-use datasets from BFCL-v4 and $τ^2$-bench, we evaluate white-box scorers based on action-token probabilities, black-box consistency scorers based on resampled trajectories, and reflexive scorers based on model self-assessment of the trajectory. We find that transfer is often useful but uneven. Token-probability scores are highly sensitive to the choice of aggregator used across turns, reflexive scores provide the strongest low-cost baseline in most evaluated settings, and black-box self-consistency is often the strongest UQ family, with trajectory-equivalence and action-set consistency typically ranking highest among its variants. These results suggest that UQ methods developed for single generations should be revalidated at the trajectory level, with careful attention to the consistency measurement, aggregator choice, and computational budget.

Hamilton-Jacobi (HJ) reachability provides a mathematically rigorous framework for safe control of dynamical systems, but its practical application is bottlenecked by the computational complexity of solving Hamilton-Jacobi-Isaacs variational inequality PDEs in high dimensions. Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to classical mesh-based solvers, yet their performance is highly sensitive to the choice of collocation sampling. In order to learn accurate safety value functions, existing PINNs-based HJ reachability solvers must rely on complex training pipelines and auxiliary supervision. In this work, we propose STEER2REACH (S2R), a PINNs-based HJ reachability solver that requires minimal modification on top of standard PINNs training. S2R's key contribution is a lightweight, low-overhead adaptive collocation sampling distribution constructed by steering forward trajectories using a combination of the optimal control and disturbance signals induced by the current value function, with injected stochastic exploration noise. We demonstrate that despite its simplicity, S2R achieves competitive--and in some cases improved--performance on safety metrics while reducing relative L2 error across a range of reachability benchmarks compared with SoTA MPC-guided HJ reachability solvers, all without requiring multi-stage training or MPC-based supervision.

Robust traffic simulators are crucial for developing and testing autonomous vehicles to reduce the costly, labor-intensive real-world data collection process and the need for physical presence on the road. However, existing simulators require agents' initial states to generate trajectories, which limits scalability and diversity due to restrictions on the given initial states. While data-driven agent initialization has been widely studied, the generated initial states are not interpretable in terms of why the agents are initialized at those specific locations. Given known initial states, trajectory generation is also a challenging problem, as the model must learn the variability of the destination and how agents should reach it over time. In this paper, we propose TrafficDiffuser, a top-down traffic scenario generation framework that generates high-level traffic scenarios, defined by initial and goal state pairs, by jointly modeling them. The high-level scenario generation makes initial states better interpretable and reduces trajectory generation into as simple as an infilling problem. We demonstrate how the generated high-level traffic scenarios can be used, including constraining based on different trajectory modes and integrating them with existing trajectory generation models. We conduct extensive experiments on the Argoverse 2 motion prediction dataset to evaluate how well the generated outputs capture real-world distributions. In addition to generating goal states, TrafficDiffuser outperforms the next-best approach for agent initialization, reducing speed distribution distance by 55.3% and the off-road rate by 2.8%.

We study the approximation of dynamical systems by semi-autonomous neural ordinary differential equations (SA-NODEs) over long time horizons. For a single network trained on the whole horizon, the available error bound deteriorates double exponentially in the horizon length. We develop two training strategies that avoid this barrier, each built on a reset of the state. The model predictive strategy partitions the horizon adaptively and restarts every window from observed data: when training meets a prescribed tolerance on every window, the composite model meets it uniformly in time, with a parameter budget linear in the horizon for targets with a bounded, uniformly regular reachable tube. The Floquet strategy addresses autonomous targets with a stable limit cycle and uses no data at deployment: a certified contraction of the learned return map confines the error to linear growth in the number of elapsed periods. For the time-periodic architecture we deploy, the scalar certificate degenerates; we prove instead a uniform-in-time orbital guarantee whose hypotheses are measured on the trained model, and an obstruction showing that, for an exactly periodic learned field, small one-period error and a contracting stroboscopic map cannot hold at once. Numerical experiments on four benchmarks confirm the predicted error laws and measure the hypotheses of every guarantee.

Failure attribution in LLM-based multi-agent systems (MAS) aims to answer who caused failures, when they occurred, and why by identifying responsible targets including faulty agents, erroneous steps, and failure modes. Existing methods have primarily focused on developing dedicated models for specific attribution targets, with limited attention to the evidential dependencies among them. Despite these attribution targets are different, they rely on common diagnostic evidence from MAS trajectories, including task constraints, agent roles, behavioral histories and inter-agent interactions. This commonality motivates us to develop a unified representation model that aggregates the trajectory evidence into individual agent and step representations, which can subsequently be adapted to different attribution targets. Accordingly, we propose ASCon, a direction-aware reciprocal \textbf{A}gent--\textbf{S}tep \textbf{Con}textualization model for multiple failure attribution targets. ASCon introduces direction-aware graph attention to model execution context, masked step-to-agent attention to construct behavior-aware agent representations, and agent-conditioned step contextualization to incorporate agent context back into step representations. The resulting contextualized representations enable different attribution targets through lightweight target-specific heads. Experiments show that ASCon can improve faulty-agent detection by 5.83%+ in micro-accuracy, faulty-step detection by 10.63%+ in micro-accuracy, and failure-mode detection by 14.73%+ in Macro-F1. Meanwhile, it can also substantially enhance the LLM-based methods' attribution capabilities in out-of-domain scenarios.

We present a scalable framework for unsupervised clustering of maritime trajectories derived from terabyte-scale Automatic Identification System (AIS) archives. Variable-length trajectories are encoded with a custom BERT-based model trained via masked token modeling and clustered using CURE hierarchical clustering, producing physically interpretable trajectory groups without requiring a predefined number of clusters. An intrinsic unsupervised anomaly detection method based on reconstruction loss and clustering noise assignment identifies irregular navigation patterns. The framework is demonstrated on a national-scale AIS dataset comprising billions of messages spanning one year, yielding stable trajectory clusters and a clear separation between nominal and anomalous vessel behavior.

In motion planning algorithms for tethered mobile robots, the entanglement state of the tether is a critical aspect to consider during the planning phase. This is particularly important in case of a slack tether, where the shape of the tether is not determined solely by the geometry of the environment and the location of the obstacles, but also by the dynamics of the tether, by the trajectory followed by the robot, and possibly by exogenous forces. In this scenario, preventing entanglement requires planning a robot trajectory that accounts for the entanglement definition and for the dynamics of the robot and of the tether. In this work, we propose a motion planning algorithm for tethered mobile robots with a slack tether that computes dynamically feasible entanglement-free trajectories to navigate through an environment with static obstacles. By considering the entanglement state during all the stages of the planning pipeline, we are able to compute safer trajectories that avoid entanglement during the motion of the robot. We achieve this through a three-step pipeline, which includes (i) the construction of a topological model of the entanglement-free configuration space of the tethered robot, (ii) the generation of a set of candidate paths using this model, and (iii) the computation of a dynamically feasible entanglement-free trajectory by solving a homotopy-constrained trajectory generation problem. The resulting trajectory can then be executed to lead the robot to its target location, while maintaining the tether in an entanglement-free configuration. We demonstrate the benefits of this algorithm in simulations, where we show how the planning algorithm avoids violations of the entanglement constraints, resulting in safer and more reliable trajectories.

Collision avoidance systems are commonly used to avoid fragmentation events occurring in Low-Earth Orbit (LEO) and Geosynchronous Equatorial Orbit (GEO). However, these events have been growing in frequency as orbital congestion worsens with the launch of megaconstellations. Consequently, conjunction alerts and collision risks are becoming increasingly common. Current practices, which are commonly manual or rule-based, have difficulty scaling to these worsening dynamic environments. To address this intensifying situation, we propose a reinforcement-learning policy for autonomous collision avoidance, trained via Proximal Policy Optimization (PPO) along with an open-source, high-fidelity astrodynamics simulator for training and evaluation. In 1,000 deterministic GEO episodes, our agent achieves a 97.5% collision avoidance success rate, outperforming traditional controllers such as a rule-based baseline (20.7% success) and an impulsive delta-v planner baseline (27.5% success). To achieve these results, we designed a simulator to train and evaluate our agent, using real-world and simulated debris. We simulate Newtonian two-body dynamics using Sun/Moon third-body perturbations, fuel-dependent thrust, and configurable debris fields. The agent is trained with curriculum learning and shaped rewards oriented toward encouraging survival, adequate projected miss distance, and delta-v conservation. Finally, our evaluation consisted of a fully deterministic pipeline, including shared seeds, per-episode logs, and telemetry exports. Our work is a publicly available framework at https://purl.org/sat-trajectory-avoidance

Trajectory-User Linking (TUL) aims to identify the owner of an anonymous trajectory from a set of candidate users, providing a basis for user mobility analysis and personalized location-aware services. Existing methods often learn Point of Interest (POI), temporal, and semantic features independently, make limited use of structural knowledge shared across trajectories, and compress structural and sequential information before classification. To address these issues, we propose Multi-Relational Knowledge Graph Enhanced Embedding for Trajectory-User Linking (MakeTUL), which, to the best of our knowledge, is the first attempt to introduce knowledge graph representation learning into TUL. MakeTUL organizes visit-time, POI-category, and transfer-speed information as typed relations in a multi-relational mobility knowledge graph, allowing heterogeneous mobility semantics to jointly constrain the learned embeddings. The resulting POI representations are further enriched with high-order co-occurrence patterns extracted from the trajectory collection, providing structural prior knowledge for sparse and overlapping trajectories. By integrating these prior-enhanced representations with temporal, category, and transfer information, the trajectory sequence learning module captures ordered mobility patterns, while a dual-branch classification layer preserves and combines global structural evidence and sequential evidence at the decision level.

Digital-twin calibration requires interaction data that is expensive to collect. We study two acquisition decisions: which trajectories to generate, and when to spend a limited budget on privileged parameter measurements. Our framework couples an excitation-oriented reinforcement learning controller, a recurrent parameter estimator with predictive uncertainty, and a budgeted query policy. In Pendulum, a Random Forest diagnostic recovers gravity only weakly from task-oriented trajectories and does not recover mass or length, while a GRU trained on excitation-oriented trajectories reaches a mean absolute error of 0.0066 with no queries. We then withdraw continuous oracle access partway through an episode, so that the twin must run on the estimator's output for the remainder. The estimator-plus-policy pipeline achieves a terminal error of 0.0092 under a three-query budget, against 0.2031 for an uncalibrated twin. In partially observable Waterworld, five controllers produce different observed error profiles across three hidden parameters, and an estimator trained on a five-controller mixture reaches online normalized errors of roughly 4-5%. These exploratory case studies are not controlled ablations, but they motivate treating trajectory design and query allocation as explicit design variables in data-scarce calibration.

Visual tool use has emerged as a fundamental capability for multimodal agents to actively acquire evidence beyond a fixed image encoding. The prevailing recipe learns this capability from teacher-generated trajectories filtered for answer correctness, implicitly assuming that every successful demonstration provides effective supervision. We argue this assumption is flawed: a strong teacher often reaches the correct answer without needing its tool calls, and imitating such trajectories teaches a student that tool calls accompany correct answers, not that tool observations ground them. We present OpenVisTool, an open framework for constructing instructive visual tool-use trajectories that provide effective supervision for tool learning. The key insight is that a trajectory should be retained only if its answer is correct (outcome validity) and its tool observations causally contribute to that answer (causal utility). The framework operates in three stages: difficulty screening to select queries that are not reliably answerable without tools, domain-specific trajectory synthesis to elicit coherent tool-use trajectories, and supervision verification to jointly test both conditions. Rather than encouraging models to imitate tool calls, the resulting supervision teaches when and how visual evidence should be acquired. Using this framework, we construct OpenVisTool-42K, a dataset spanning five visual reasoning domains, together with OpenVisTool-Bench, a benchmark covering the same domains. Across four backbones (4B-27B), fine-tuning on OpenVisTool-42K consistently improves visual tool-use performance and yields gains on two out-of-distribution benchmarks; the larger models approach leading closed-source systems. The evidence suggests that effective visual tool use is learned from causally grounded supervision rather than tool-calling patterns.

Agentic skills improve large language model (LLM) agents by encoding reusable procedures for complex tasks. However, manually authored skills often adapt poorly to long-horizon tasks and changing environments. To address the limitation, self-evolving skill systems have been developed to automatically construct and update skills from execution trajectories, shifting skill acquisition from external marketplaces to a trusted evolution pipeline. By replacing external skill acquisition with trusted internal construction, self-evolving skill systems reduce exposure to skill injection attacks that rely on direct skill manipulation. However, this skill evolution pipeline may introduce a new attack surface in which an attacker can indirectly steer skill evolution by inducing compromised trajectories through agent interactions. To demonstrate the threat, we propose Trajectory Backdoor Attack (TBA), a query-only attack that steers a trusted skill-evolution pipeline toward producing a backdoored skill. Specifically, we craft attacker-submitted queries to lead the agent to perform the target action and explicitly state the corresponding activation condition in the trajectory. We repeat the same condition-action pattern across diverse triggered tasks, while leaving clean queries unchanged, encouraging the evolver to consolidate the pattern as a reusable trigger-dependent rule into the evolved skill. Experiments on three benchmarks across two skill-evolution systems using four open- and closed-source backbone models demonstrate that TBA reliably implants conditional backdoors while preserving clean-task utility, matching or even surpassing direct skill injection. The results reveal a critical vulnerability in trajectory-driven skill evolution.