Daily Papers

Controlling the motion of multiple objects in image-to-video (I2V) generation requires preserving object identities while enforcing adherence to distinct target trajectories. This becomes particularly challenging as the number of objects increases and their paths intersect or occlude one another. Existing approaches entangle multiple trajectories within a shared, dense conditioning signal, making object-level correspondence difficult to preserve in crowded scenes. We depart from this paradigm and enforce a strict, per object spatial constraint that isolates instances independently. Our method, TrajLoc, achieves this directly within the attention layers by substituting the cross-attention weights of each object token with a Gaussian heatmap centered on its target location at every frame. The same per object token interface carries trajectory and depth through a learned embedding and preserves identity by encoding first frame appearance in place of an object token. Evaluations across six datasets, featuring up to 20 simultaneously controlled objects and out of distribution real world scenes, demonstrate that our method consistently improves both visual fidelity and trajectory adherence. Applied to two architecturally distinct backbones (CogVideoX 5B and WaN 2.1 14B), our approach achieves average gains of +4.3 dB PSNR and a 51% reduction in trajectory end point error compared to the strongest baselines. Project page: https://sela-omer.github.io/traj-loc/

This work presents a novel online model-predictive trajectory planner for robotic manipulators called BoundMPC. This planner allows the collision-free following of Cartesian reference paths in the end-effector's position and orientation, including via-points, within desired asymmetric bounds of the orthogonal path error. The path parameter synchronizes the position and orientation reference paths. The decomposition of the path error into the tangential direction, describing the path progress, and the orthogonal direction, which represents the deviation from the path, is well known for the position from the path-following control in the literature. This paper extends this idea to the orientation by utilizing the Lie theory of rotations. Moreover, the orthogonal error plane is further decomposed into basis directions to define asymmetric Cartesian error bounds easily. Using piecewise linear position and orientation reference paths with via-points is computationally very efficient and allows replanning the pose trajectories during the robot's motion. This feature makes it possible to use this planner for dynamically changing environments and varying goals. The flexibility and performance of BoundMPC are experimentally demonstrated by two scenarios on a 7-DoF Kuka LBR iiwa 14 R820 robot. The first scenario shows the transfer of a larger object from a start to a goal pose through a confined space where the object must be tilted. The second scenario deals with grasping an object from a table where the grasping point changes during the robot's motion, and collisions with other obstacles in the scene must be avoided.

We present an experimental analysis on the use of a camera-based approach for high-altitude navigation by associating mapped landmarks from a satellite image database to camera images, and by leveraging inertial sensors between camera frames. We evaluate performance of both a sideways-tilted and downward-facing camera on data collected from a World View Enterprises high-altitude balloon with data beginning at an altitude of 33 km and descending to near ground level (4.5 km) with 1.5 hours of flight time. We demonstrate less than 290 meters of average position error over a trajectory of more than 150 kilometers. In addition to showing performance across a range of altitudes, we also demonstrate the robustness of the Terrain Relative Navigation (TRN) method to rapid rotations of the balloon, in some cases exceeding 20 degrees per second, and to camera obstructions caused by both cloud coverage and cords swaying underneath the balloon. Additionally, we evaluate performance on data collected by two cameras inside the capsule of Blue Origin's New Shepard rocket on payload flight NS-23, traveling at speeds up to 880 km/hr, and demonstrate less than 55 meters of average position error.

RTK-SLAM systems integrate simultaneous localization and mapping (SLAM) with real-time kinematic (RTK) GNSS positioning, promising both relative consistency and globally referenced coordinates for efficient georeferenced surveying. A critical and underappreciated issue is that the standard evaluation metric, Absolute Trajectory Error (ATE), first fits an optimal rigid-body transformation between the estimated trajectory and reference before computing errors. This so-called SE(3) alignment absorbs global drift and systematic errors, making trajectories appear more accurate than they are in practice, and is unsuitable for evaluating the global accuracy of RTK-SLAM. We present a geodetically referenced dataset and evaluation methodology that expose this gap. A key design principle is that the RTK receiver is used solely as a system input, while ground truth is established independently via a geodetic total station. This separation is absent from all existing datasets, where GNSS typically serves as (part of) the ground truth. The dataset is collected with a handheld RTK-SLAM device, comprising two scenes. We evaluate LiDAR-inertial, visual-inertial, and LiDAR-visual-inertial RTK-SLAM systems alongside standalone RTK, reporting direct global accuracy and SE(3)-aligned relative accuracy to make the gap explicit. Results show that SE(3) alignment can underestimate absolute positioning error by up to 76\%. RTK-SLAM achieves centimeter-level absolute accuracy in open-sky conditions and maintains decimeter-level global accuracy indoors, where standalone RTK degrades to tens of meters. The dataset, calibration files, and evaluation scripts are publicly available at https://rtk-slam-dataset.github.io/.

When a large language model under reinforcement learning commits a wrong reasoning step early in a trajectory, standard algorithms force it to keep generating until the maximum horizon, spending compute on tokens that never receive positive reward and polluting advantage estimates with post-failure noise. We propose ESPO (Early-Stopping Proximal Policy Optimization), which detects trajectory failure on-the-fly and terminates rollouts early. At each generation step, ESPO computes a surrogate regret using only the logits already computed during sampling, and terminates when the smoothed cumulative regret significantly exceeds its estimated values. Truncated trajectories are treated as absorbing failure states with a terminal reward, concentrating negative temporal-difference (TD) errors near the detected failure step without any additional reward model or human annotation. On DeepSeek-R1-Distill-Qwen-7B trained for mathematical reasoning, ESPO surpasses PPO on AIME~2024 (46.28% vs. 45.25%), AMC~2023 (85.83% vs. 82.94%), and MATH-500 (87.42% vs. 85.43%), while saving more than 20% rollout tokens cumulatively.

This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be formulated as the problem of stabilizing a path following error system that describes the dynamics of position and possibly orientation errors of a vehicle with respect to a path, with the errors defined in an appropriate reference frame. In spite of the large variety of path following methods described in the literature we show that, in principle, most of them can be categorized in two groups: stabilization of the path following error system expressed either in the vehicle's body frame or in a frame attached to a "reference point" moving along the path, such as a Frenet-Serret (F-S) frame or a Parallel Transport (P-T) frame. With this observation, we provide a unified formulation that is simple but general enough to cover many methods available in the literature. We then discuss the advantages and disadvantages of each method, comparing them from the design and implementation standpoint. We further show experimental results of the path following methods obtained from field trials testing with under-actuated and fully-actuated autonomous marine vehicles. In addition, we introduce open-source Matlab and Gazebo/ROS simulation toolboxes that are helpful in testing path following methods prior to their integration in the combined guidance, navigation, and control systems of autonomous vehicles.

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path, and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Furthermore, we discretize the set of velocity profiles along a given path into a selection of acceleration way-points along the path. Gradient-descent is then employed to minimize cost over feasible choices of the second derivative of curvature, and acceleration way-points, resulting in a method that repeatedly solves the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods.

We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To solve it, we propose a biconvex method that quickly produces an initial trajectory and iteratively refines it by solving two convex subproblems in alternation. This method is guaranteed to converge, returns a feasible trajectory even if stopped early, and does not require the selection of any line-search or trust-region parameter. Exhaustive experiments show that our method finds high-quality trajectories in a fraction of the time of state-of-the-art solvers for nonconvex optimization. In addition, it achieves runtimes comparable to industry-standard waypoint-based motion planners, while consistently designing lower-duration trajectories than existing optimization-based planners.

Best-of-N (BoN) Average Displacement Error (ADE)/ Final Displacement Error (FDE) is the most used metric for evaluating trajectory prediction models. Yet, the BoN does not quantify the whole generated samples, resulting in an incomplete view of the model's prediction quality and performance. We propose a new metric, Average Mahalanobis Distance (AMD) to tackle this issue. AMD is a metric that quantifies how close the whole generated samples are to the ground truth. We also introduce the Average Maximum Eigenvalue (AMV) metric that quantifies the overall spread of the predictions. Our metrics are validated empirically by showing that the ADE/FDE is not sensitive to distribution shifts, giving a biased sense of accuracy, unlike the AMD/AMV metrics. We introduce the usage of Implicit Maximum Likelihood Estimation (IMLE) as a replacement for traditional generative models to train our model, Social-Implicit. IMLE training mechanism aligns with AMD/AMV objective of predicting trajectories that are close to the ground truth with a tight spread. Social-Implicit is a memory efficient deep model with only 5.8K parameters that runs in real time of about 580Hz and achieves competitive results. Interactive demo of the problem can be seen at https://www.abduallahmohamed.com/social-implicit-amdamv-adefde-demo . Code is available at https://github.com/abduallahmohamed/Social-Implicit .

Model-based deep learning has achieved astounding successes due in part to the availability of large-scale real-world data. However, processing such massive amounts of data comes at a considerable cost in terms of computations, storage, training and the search for good neural architectures. Dataset distillation has thus recently come to the fore. This paradigm involves distilling information from large real-world datasets into tiny and compact synthetic datasets such that processing the latter ideally yields similar performances as the former. State-of-the-art methods primarily rely on learning the synthetic dataset by matching the gradients obtained during training between the real and synthetic data. However, these gradient-matching methods suffer from the so-called accumulated trajectory error caused by the discrepancy between the distillation and subsequent evaluation. To mitigate the adverse impact of this accumulated trajectory error, we propose a novel approach that encourages the optimization algorithm to seek a flat trajectory. We show that the weights trained on synthetic data are robust against the accumulated errors perturbations with the regularization towards the flat trajectory. Our method, called Flat Trajectory Distillation (FTD), is shown to boost the performance of gradient-matching methods by up to 4.7% on a subset of images of the ImageNet dataset with higher resolution images. We also validate the effectiveness and generalizability of our method with datasets of different resolutions and demonstrate its applicability to neural architecture search. Code is available at https://github.com/AngusDujw/FTD-distillation.

Accurate long-horizon vessel trajectory prediction remains challenging due to compounded uncertainty from complex navigation behaviors and environmental factors. Existing methods often struggle to maintain global directional consistency, leading to drifting or implausible trajectories when extrapolated over long time horizons. To address this issue, we propose a semantic-key-point-conditioned trajectory modeling framework, in which future trajectories are predicted by conditioning on a high-level Next Key Point (NKP) that captures navigational intent. This formulation decomposes long-horizon prediction into global semantic decision-making and local motion modeling, effectively restricting the support of future trajectories to semantically feasible subsets. To efficiently estimate the NKP prior from historical observations, we adopt a pretrain-finetune strategy. Extensive experiments on real-world AIS data demonstrate that the proposed method consistently outperforms state-of-the-art approaches, particularly for long travel durations, directional accuracy, and fine-grained trajectory prediction.

AI agents often fail in ways that are difficult to localize because executions are probabilistic, long-horizon, multi-agent, and mediated by noisy tool outputs. We address this gap by manually annotating failed agent runs and release a novel benchmark of 115 failed trajectories spanning structured API workflows, incident management, and open-ended web/file tasks. Each trajectory is annotated with a critical failure step and a category from a grounded-theory derived, cross-domain failure taxonomy. To mitigate the human cost of failure attribution, we present AGENTRX, an automated domain-agnostic diagnostic framework that pinpoints the critical failure step in a failed agent trajectory. It synthesizes constraints, evaluates them step-by-step, and produces an auditable validation log of constraint violations with associated evidence; an LLM-based judge uses this log to localize the critical step and category. Our framework improves step localization and failure attribution over existing baselines across three domains.

We propose GoalFlow, an end-to-end autonomous driving method for generating high-quality multimodal trajectories. In autonomous driving scenarios, there is rarely a single suitable trajectory. Recent methods have increasingly focused on modeling multimodal trajectory distributions. However, they suffer from trajectory selection complexity and reduced trajectory quality due to high trajectory divergence and inconsistencies between guidance and scene information. To address these issues, we introduce GoalFlow, a novel method that effectively constrains the generative process to produce high-quality, multimodal trajectories. To resolve the trajectory divergence problem inherent in diffusion-based methods, GoalFlow constrains the generated trajectories by introducing a goal point. GoalFlow establishes a novel scoring mechanism that selects the most appropriate goal point from the candidate points based on scene information. Furthermore, GoalFlow employs an efficient generative method, Flow Matching, to generate multimodal trajectories, and incorporates a refined scoring mechanism to select the optimal trajectory from the candidates. Our experimental results, validated on the NavsimDauner2024_navsim, demonstrate that GoalFlow achieves state-of-the-art performance, delivering robust multimodal trajectories for autonomous driving. GoalFlow achieved PDMS of 90.3, significantly surpassing other methods. Compared with other diffusion-policy-based methods, our approach requires only a single denoising step to obtain excellent performance. The code is available at https://github.com/YvanYin/GoalFlow.

We address the problem of runtime trajectory anomaly detection, a critical capability for enabling trustworthy LLM agents. Current safety measures predominantly focus on static input/output filtering. However, we argue that ensuring LLM agents reliability requires auditing the intermediate execution process. In this work, we formulate the task of Trajectory Anomaly Detection. The goal is not merely detection, but precise error localization. This capability is essential for enabling efficient rollback-and-retry. To achieve this, we construct TrajBench, a dataset synthesized via a perturb-and-complete strategy to cover diverse procedural anomalies. Using this benchmark, we investigate the capability of models in process supervision. We observe that general-purpose LLMs, even with zero-shot prompting, struggle to identify and localize these anomalies. This reveals that generalized capabilities do not automatically translate to process reliability. To address this, we propose TrajAD, a specialized verifier trained with fine-grained process supervision. Our approach outperforms baselines, demonstrating that specialized supervision is essential for building trustworthy agents.

End-to-end driving systems have recently made rapid progress, in particular on CARLA. Independent of their major contribution, they introduce changes to minor system components. Consequently, the source of improvements is unclear. We identify two biases that recur in nearly all state-of-the-art methods and are critical for the observed progress on CARLA: (1) lateral recovery via a strong inductive bias towards target point following, and (2) longitudinal averaging of multimodal waypoint predictions for slowing down. We investigate the drawbacks of these biases and identify principled alternatives. By incorporating our insights, we develop TF++, a simple end-to-end method that ranks first on the Longest6 and LAV benchmarks, gaining 14 driving score over the best prior work on Longest6.

Identifying travelers' transportation modes is important in transportation science and location-based services. It's appealing for researchers to leverage GPS trajectory data to infer transportation modes with the popularity of GPS-enabled devices, e.g., smart phones. Existing studies frame this problem as classification task. The dominant two-stage studies divide the trip into single-one mode segments first and then categorize these segments. The over segmentation strategy and inevitable error propagation bring difficulties to classification stage and make optimizing the whole system hard. The recent one-stage works throw out trajectory segmentation entirely to avoid these by directly conducting point-wise classification for the trip, whereas leaving predictions dis-continuous. To solve above-mentioned problems, inspired by YOLO and SSD in object detection, we propose to reframe change point detection and segment classification as a unified regression task instead of the existing classification task. We directly regress coordinates of change points and classify associated segments. In this way, our method divides the trip into segments under a supervised manner and leverage more contextual information, obtaining predictions with high accuracy and continuity. Two frameworks, TrajYOLO and TrajSSD, are proposed to solve the regression task and various feature extraction backbones are exploited. Exhaustive experiments on GeoLife dataset show that the proposed method has competitive overall identification accuracy of 0.853 when distinguishing five modes: walk, bike, bus, car, train. As for change point detection, our method increases precision at the cost of drop in recall. All codes are available at https://github.com/RadetzkyLi/TrajYOLO-SSD.

Reliable odometry for legged robots without cameras or LiDAR remains challenging due to IMU drift and noisy joint velocity sensing. This paper presents a purely proprioceptive state estimator that uses only IMU and motor measurements to jointly estimate body pose and velocity, with a unified formulation applicable to biped, quadruped, and wheel-legged robots. The key idea is to treat each contacting leg as a kinematic anchor: joint-torque--based foot wrench estimation selects reliable contacts, and the corresponding footfall positions provide intermittent world-frame constraints that suppress long-term drift. To prevent elevation drift during extended traversal, we introduce a lightweight height clustering and time-decay correction that snaps newly recorded footfall heights to previously observed support planes. To improve foot velocity observations under encoder quantization, we apply an inverse-kinematics cubature Kalman filter that directly filters foot-end velocities from joint angles and velocities. The implementation further mitigates yaw drift through multi-contact geometric consistency and degrades gracefully to a kinematics-derived heading reference when IMU yaw constraints are unavailable or unreliable. We evaluate the method on four quadruped platforms (three Astrall robots and a Unitree Go2 EDU) using closed-loop trajectories. On Astrall point-foot robot~A, a sim200\,m horizontal loop and a sim15\,m vertical loop return with 0.1638\,m and 0.219\,m error, respectively; on wheel-legged robot~B, the corresponding errors are 0.2264\,m and 0.199\,m. On wheel-legged robot~C, a sim700\,m horizontal loop yields 7.68\,m error and a sim20\,m vertical loop yields 0.540\,m error. Unitree Go2 EDU closes a sim120\,m horizontal loop with 2.2138\,m error and a sim8\,m vertical loop with less than 0.1\,m vertical error. github.com/ShineMinxing/Ros2Go2Estimator.git

End-to-end autonomous driving has emerged as a pivotal direction in the field of autonomous systems. Recent works have demonstrated impressive performance by incorporating high-level guidance signals to steer low-level trajectory planners. However, their potential is often constrained by inaccurate high-level guidance and the computational overhead of complex guidance modules. To address these limitations, we propose Mimir, a novel hierarchical dual-system framework capable of generating robust trajectories relying on goal points with uncertainty estimation: (1) Unlike previous approaches that deterministically model, we estimate goal point uncertainty with a Laplace distribution to enhance robustness; (2) To overcome the slow inference speed of the guidance system, we introduce a multi-rate guidance mechanism that predicts extended goal points in advance. Validated on challenging Navhard and Navtest benchmarks, Mimir surpasses previous state-of-the-art methods with a 20% improvement in the driving score EPDMS, while achieving 1.6 times improvement in high-level module inference speed without compromising accuracy. The code and models will be released soon to promote reproducibility and further development. The code is available at https://github.com/ZebinX/Mimir-Uncertainty-Driving

Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous differential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization problem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of Bézier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap rounding of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time.

In this work, we propose a novel Trajectory Score Matching (TSM) method that aims to solve the pseudo ground truth inconsistency problem caused by the accumulated error in Interval Score Matching (ISM) when using the Denoising Diffusion Implicit Models (DDIM) inversion process. Unlike ISM which adopts the inversion process of DDIM to calculate on a single path, our TSM method leverages the inversion process of DDIM to generate two paths from the same starting point for calculation. Since both paths start from the same starting point, TSM can reduce the accumulated error compared to ISM, thus alleviating the problem of pseudo ground truth inconsistency. TSM enhances the stability and consistency of the model's generated paths during the distillation process. We demonstrate this experimentally and further show that ISM is a special case of TSM. Furthermore, to optimize the current multi-stage optimization process from high-resolution text to 3D generation, we adopt Stable Diffusion XL for guidance. In response to the issues of abnormal replication and splitting caused by unstable gradients during the 3D Gaussian splatting process when using Stable Diffusion XL, we propose a pixel-by-pixel gradient clipping method. Extensive experiments show that our model significantly surpasses the state-of-the-art models in terms of visual quality and performance. Code: https://github.com/xingy038/Dreamer-XL.

Robust pedestrian trajectory forecasting is crucial to developing safe autonomous vehicles. Although previous works have studied adversarial robustness in the context of trajectory forecasting, some significant issues remain unaddressed. In this work, we try to tackle these crucial problems. Firstly, the previous definitions of robustness in trajectory prediction are ambiguous. We thus provide formal definitions for two kinds of robustness, namely label robustness and pure robustness. Secondly, as previous works fail to consider robustness about all points in a disturbance interval, we utilise a probably approximately correct (PAC) framework for robustness verification. Additionally, this framework can not only identify potential counterexamples, but also provides interpretable analyses of the original methods. Our approach is applied using a prototype tool named TrajPAC. With TrajPAC, we evaluate the robustness of four state-of-the-art trajectory prediction models -- Trajectron++, MemoNet, AgentFormer, and MID -- on trajectories from five scenes of the ETH/UCY dataset and scenes of the Stanford Drone Dataset. Using our framework, we also experimentally study various factors that could influence robustness performance.

Trajectory planning in unstructured environments is a fundamental and challenging capability for mobile robots. Traditional modular pipelines suffer from latency and cascading errors across perception, localization, mapping, and planning modules. Recent end-to-end learning methods map raw visual observations directly to control signals or trajectories, promising greater performance and efficiency in open-world settings. However, most prior end-to-end approaches still rely on separate localization modules that depend on accurate sensor extrinsic calibration for self-state estimation, thereby limiting generalization across embodiments and environments. We introduce LoGoPlanner, a localization-grounded, end-to-end navigation framework that addresses these limitations by: (1) finetuning a long-horizon visual-geometry backbone to ground predictions with absolute metric scale, thereby providing implicit state estimation for accurate localization; (2) reconstructing surrounding scene geometry from historical observations to supply dense, fine-grained environmental awareness for reliable obstacle avoidance; and (3) conditioning the policy on implicit geometry bootstrapped by the aforementioned auxiliary tasks, thereby reducing error propagation.We evaluate LoGoPlanner in both simulation and real-world settings, where its fully end-to-end design reduces cumulative error while metric-aware geometry memory enhances planning consistency and obstacle avoidance, leading to more than a 27.3\% improvement over oracle-localization baselines and strong generalization across embodiments and environments. The code and models have been made publicly available on the https://steinate.github.io/logoplanner.github.io/{project page}.

We present a fast algorithm for the design of smooth paths (or trajectories) that are constrained to lie in a collection of axis-aligned boxes. We consider the case where the number of these safe boxes is large, and basic preprocessing of them (such as finding their intersections) can be done offline. At runtime we quickly generate a smooth path between given initial and terminal positions. Our algorithm designs trajectories that are guaranteed to be safe at all times, and detects infeasibility whenever such a trajectory does not exist. Our algorithm is based on two subproblems that we can solve very efficiently: finding a shortest path in a weighted graph, and solving (multiple) convex optimal-control problems. We demonstrate the proposed path planner on large-scale numerical examples, and we provide an efficient open-source software implementation, fastpathplanning.

Topology reasoning, which unifies perception and structured reasoning, plays a vital role in understanding intersections for autonomous driving. However, its performance heavily relies on the accuracy of lane detection, particularly at connected lane endpoints. Existing methods often suffer from lane endpoints deviation, leading to incorrect topology construction. To address this issue, we propose TopoPoint, a novel framework that explicitly detects lane endpoints and jointly reasons over endpoints and lanes for robust topology reasoning. During training, we independently initialize point and lane query, and proposed Point-Lane Merge Self-Attention to enhance global context sharing through incorporating geometric distances between points and lanes as an attention mask . We further design Point-Lane Graph Convolutional Network to enable mutual feature aggregation between point and lane query. During inference, we introduce Point-Lane Geometry Matching algorithm that computes distances between detected points and lanes to refine lane endpoints, effectively mitigating endpoint deviation. Extensive experiments on the OpenLane-V2 benchmark demonstrate that TopoPoint achieves state-of-the-art performance in topology reasoning (48.8 on OLS). Additionally, we propose DET_p to evaluate endpoint detection, under which our method significantly outperforms existing approaches (52.6 v.s. 45.2 on DET_p). The code is released at https://github.com/Franpin/TopoPoint.

Trajectory prediction is fundamental in computer vision and autonomous driving, particularly for understanding pedestrian behavior and enabling proactive decision-making. Existing approaches in this field often assume precise and complete observational data, neglecting the challenges associated with out-of-view objects and the noise inherent in sensor data due to limited camera range, physical obstructions, and the absence of ground truth for denoised sensor data. Such oversights are critical safety concerns, as they can result in missing essential, non-visible objects. To bridge this gap, we present a novel method for out-of-sight trajectory prediction that leverages a vision-positioning technique. Our approach denoises noisy sensor observations in an unsupervised manner and precisely maps sensor-based trajectories of out-of-sight objects into visual trajectories. This method has demonstrated state-of-the-art performance in out-of-sight noisy sensor trajectory denoising and prediction on the Vi-Fi and JRDB datasets. By enhancing trajectory prediction accuracy and addressing the challenges of out-of-sight objects, our work significantly contributes to improving the safety and reliability of autonomous driving in complex environments. Our work represents the first initiative towards Out-Of-Sight Trajectory prediction (OOSTraj), setting a new benchmark for future research. The code is available at https://github.com/Hai-chao-Zhang/OOSTraj.

Generative sequence models are often trained to plan motion in physical domains, from robotics to mechanical simulations. When constructing a dataset to train such a model, engineers may curate demonstrations to specify how trajectories should be distributed over a physical quantity like travel distance or mechanical energy. For example, a roboticist building a maze navigation agent might choose demonstrations whose travel distances cover a fixed range uniformly, hoping to constrain the agent's expected power usage. We find that standard deep learning can violate this intent: each generated trajectory can seem plausible on its own, but the aggregate distribution over the physical quantity is wrong. We call this failure physical misgeneralization, and develop an account of its mechanism. Using controlled synthetic tasks, we show that physical misgeneralization arises when local errors typical of the model class propagate through the physical measurement to shift the recovered distribution. We estimate these errors with a data deviation kernel, and we use it to predict which physical quantities gain or lose mass in both our synthetic and more applied maze navigation and double-pendulum motion tasks. Finally, our mechanistic interpretation helps identify which mitigation strategies are structurally promising, and we use it to propose a kernel-informed intervention.

LLM agents are beginning to invoke industrial asset-management tools through the Model Context Protocol (MCP), yet whether they can act reliably on this substrate for safety-critical Prognostics and Health Management (PHM) is unanswered. Prior benchmarks conflate protocol fluency with reasoning, instrumentation failures with agent failures, and tool use with tool retrieval. We introduce PHMForge, an evaluation environment that closes each conflation. PHMForge ships 99 SME-authored scenarios across eight industrial asset classes spanning rotating equipment, aero-engines, and lithium-ion cells, on public datasets including NASA PCoE, served through 39 MCP-native tools wrapping published PHM algorithms (C-MAPSS, ISO~10816, Arrhenius capacity-fade models, time-series foundation models). Krippendorff's αin [0.74,,0.82] on a 30-scenario stratified rotating-equipment/aero-engine sample; the battery extension is single-rater. Across three agentic frameworks and six LLM backbones, the strongest configuration reaches 80.8\% pass@1, with the residual gap concentrated in orchestration and tool-sequencing errors. Crucially, an architectural ablation shows that replacing MCP execution with text-based Retrieval-Augmented Generation (RAG) over telemetry-equivalent evidence collapses Remaining Useful Life pass-all-3 from 100\% to 20\% (5/5 vs.\ 1/5) on the battery class, exposing the structural limits of static retrieval for prognostic computation. Trajectory decomposition shows orchestration errors dominate failures across backbones, while schema-invalid tool calls concentrate in smaller open-weight models. Frontier LLMs are stronger at calling tools than at planning when to call them. PHMForge is open-sourced with deterministic evaluators, a public leaderboard, and a datasheet.

We present a novel data-driven simulation environment for modeling traffic in metropolitan street intersections. Using real-world tracking data collected over an extended period of time, we train trajectory forecasting models to learn agent interactions and environmental constraints that are difficult to capture conventionally. Trajectories of new agents are first coarsely generated by sampling from the spatial and temporal generative distributions, then refined using state-of-the-art trajectory forecasting models. The simulation can run either autonomously, or under explicit human control conditioned on the generative distributions. We present the experiments for a variety of model configurations. Under an iterative prediction scheme, the way-point-supervised TrajNet++ model obtained 0.36 Final Displacement Error (FDE) in 20 FPS on an NVIDIA A100 GPU.

Tool-using LLM agents fail through trajectories rather than only final responses, as they may execute unsafe tool calls, follow injected instructions, comply with harmful requests, or over-refuse benign tasks despite producing a seemingly safe answer. Existing safety-alignment signals are largely response-level or off-policy, and often incur a safety-utility trade-off: improving agent safety comes at the cost of degraded task performance. Such sparse and single-objective rewards severely limit real-world usability. To bridge this gap, we propose FATE, an on-policy self-evolving framework that transforms verifier-scored failures into repair supervision without expert demonstrations. For each failure, the same policy proposes repair candidates, which are then re-scored by verifiers and filtered across security, utility, over-refusal control, and trajectory validity. This dense trajectory-level information is then used as a supervision signal for agent self-evolution. During this process, we further introduce Pareto-Front Policy Optimization (PFPO), combining supervised warmup with Pareto-aware policy optimization to preserve safety-utility trade-offs. Experiments on AgentDojo, AgentHarm, and ATBench show that FATE improves safety across different models and scales while preserving useful behavior. Compared with strong baselines, FATE reduces attack success rate by 33.5%, harmful compliance by 82.6%, and improves external trajectory-safety diagnosis by 6.5%. These results suggest that failed trajectories can provide structured repair supervision for safer self-evolving agents.

Accurate prediction of pedestrians' future motions is critical for intelligent driving systems. Developing models for this task requires rich datasets containing diverse sets of samples. However, the existing naturalistic trajectory prediction datasets are generally imbalanced in favor of simpler samples and lack challenging scenarios. Such a long-tail effect causes prediction models to underperform on the tail portion of the data distribution containing safety-critical scenarios. Previous methods tackle the long-tail problem using methods such as contrastive learning and class-conditioned hypernetworks. These approaches, however, are not modular and cannot be applied to many machine learning architectures. In this work, we propose a modular model-agnostic framework for trajectory prediction that leverages a specialized mixture of experts. In our approach, each expert is trained with a specialized skill with respect to a particular part of the data. To produce predictions, we utilise a router network that selects the best expert by generating relative confidence scores. We conduct experimentation on common pedestrian trajectory prediction datasets and show that besides achieving state-of-the-art performance, our method significantly performs better on long-tail scenarios. We further conduct ablation studies to highlight the contribution of different proposed components.

We introduce a new trajectory optimization method for robotic grasping based on a point-cloud representation of robots and task spaces. In our method, robots are represented by 3D points on their link surfaces. The task space of a robot is represented by a point cloud that can be obtained from depth sensors. Using the point-cloud representation, goal reaching in grasping can be formulated as point matching, while collision avoidance can be efficiently achieved by querying the signed distance values of the robot points in the signed distance field of the scene points. Consequently, a constrained nonlinear optimization problem is formulated to solve the joint motion and grasp planning problem. The advantage of our method is that the point-cloud representation is general to be used with any robot in any environment. We demonstrate the effectiveness of our method by performing experiments on a tabletop scene and a shelf scene for grasping with a Fetch mobile manipulator and a Franka Panda arm. The project page is available at https://irvlutd.github.io/GraspTrajOpt

LLM-based multi-agent systems are increasingly deployed on long-horizon tasks, but a single decisive error is often accepted by downstream agents and cascades into trajectory-level failure. Existing work frames this as post-hoc failure attribution, diagnosing the responsible agent and step after the trajectory has ended. However, this paradigm forfeits any opportunity to intervene while trajectory is still unfolding. In this work, we introduce AgentForesight, a framework that reframes this problem as online auditing: at each step of an unfolding trajectory, an auditor observes only the current prefix and must either continue the run or alarm at the earliest decisive error, without access to future steps. To this end, we curate AFTraj-2K, a corpus of agentic trajectories across Coding, Math, and Agentic domains, in which safe trajectories are retained under a strict curation pipeline and unsafe trajectories are annotated at the step of their decisive error via consensus among multiple LLM judges. Built on that, we develop AgentForesight-7B, a compact online auditor trained with a coarse-to-fine reinforcement learning recipe that first equips it with a risk-anticipation prior at the failure boundary on adjacent safe/unsafe prefix pairs, then sharpens this prior into precise step-level localization under a three-axis reward jointly targeting the what, where, and who of an audit verdict. Across AFTraj-2K and an external Who\&When benchmark, AgentForesight-7B outperforms leading proprietary models, including GPT-4.1 and DeepSeek-V4-Pro, achieving up to +19.9% performance gain and 3times lower step localization error, opening the loop from post-hoc failures detection to enabling deployment-time intervention. Project page: https://zbox1005.github.io/agent-foresight/

End-to-end multi-modal planning is a promising paradigm in autonomous driving, enabling decision-making with diverse trajectory candidates. A key component is a robust trajectory scorer capable of selecting the optimal trajectory from these candidates. While recent trajectory scorers focus on scoring either large sets of static trajectories or small sets of dynamically generated ones, both approaches face significant limitations in generalization. Static vocabularies provide effective coarse discretization but struggle to make fine-grained adaptation, while dynamic proposals offer detailed precision but fail to capture broader trajectory distributions. To overcome these challenges, we propose GTRS (Generalized Trajectory Scoring), a unified framework for end-to-end multi-modal planning that combines coarse and fine-grained trajectory evaluation. GTRS consists of three complementary innovations: (1) a diffusion-based trajectory generator that produces diverse fine-grained proposals; (2) a vocabulary generalization technique that trains a scorer on super-dense trajectory sets with dropout regularization, enabling its robust inference on smaller subsets; and (3) a sensor augmentation strategy that enhances out-of-domain generalization while incorporating refinement training for critical trajectory discrimination. As the winning solution of the Navsim v2 Challenge, GTRS demonstrates superior performance even with sub-optimal sensor inputs, approaching privileged methods that rely on ground-truth perception. Code will be available at https://github.com/NVlabs/GTRS.

Generative models have shown great potential in trajectory planning. Recent studies demonstrate that anchor-guided generative models are effective in modeling the uncertainty of driving behaviors and improving overall performance. However, these methods rely on discrete anchor vocabularies that must sufficiently cover the trajectory distribution during testing to ensure robustness, inducing an inherent trade-off between vocabulary size and model performance. To overcome this limitation, we propose MeanFuser, an end-to-end autonomous driving method that enhances both efficiency and robustness through three key designs. (1) We introduce Gaussian Mixture Noise (GMN) to guide generative sampling, enabling a continuous representation of the trajectory space and eliminating the dependency on discrete anchor vocabularies. (2) We adapt ``MeanFlow Identity" to end-to-end planning, which models the mean velocity field between GMN and trajectory distribution instead of the instantaneous velocity field used in vanilla flow matching methods, effectively eliminating numerical errors from ODE solvers and significantly accelerating inference. (3) We design a lightweight Adaptive Reconstruction Module (ARM) that enables the model to implicitly select from all sampled proposals or reconstruct a new trajectory when none is satisfactory via attention weights.Experiments on the NAVSIM closed-loop benchmark demonstrate that MeanFuser achieves outstanding performance without the supervision of the PDM Score and exceptional inference efficiency, offering a robust and efficient solution for end-to-end autonomous driving. Our code and model are available at https://github.com/wjl2244/MeanFuser.

As Multi-Agent Systems (MAS) become increasingly autonomous and complex, understanding their error modes is critical for ensuring their reliability and safety. However, research in this area has been severely hampered by the lack of large-scale, diverse datasets with precise, ground-truth error labels. To address this bottleneck, we introduce AEGIS, a novel framework for Automated Error Generation and Identification for Multi-Agent Systems. By systematically injecting controllable and traceable errors into initially successful trajectories, we create a rich dataset of realistic failures. This is achieved using a context-aware, LLM-based adaptive manipulator that performs sophisticated attacks like prompt injection and response corruption to induce specific, predefined error modes. We demonstrate the value of our dataset by exploring three distinct learning paradigms for the error identification task: Supervised Fine-Tuning, Reinforcement Learning, and Contrastive Learning. Our comprehensive experiments show that models trained on AEGIS data achieve substantial improvements across all three learning paradigms. Notably, several of our fine-tuned models demonstrate performance competitive with or superior to proprietary systems an order of magnitude larger, validating our automated data generation framework as a crucial resource for developing more robust and interpretable multi-agent systems. Our project website is available at https://kfq20.github.io/AEGIS-Website.

Urban mobility is naturally expressed both as trajectories in space and as natural-language descriptions of travel intent, constraints, and preferences. However, prior work rarely evaluates these two modalities together on the same real-world trajectories: trajectory modeling often stays geometry-centric, while language-centric mobility benchmarks frequently target route planning and tool use rather than fine-grained, verifiable alignment between text and the underlying route. We introduce TrajPrism, a multi-task benchmark for language-trajectory alignment that unifies (i) instruction-conditioned trajectory generation, (ii) language-driven semantic trajectory retrieval, and (iii) trajectory captioning, together with an evaluation protocol that measures trajectory fidelity, retrieval quality, and language groundedness. We construct TrajPrism by pairing real urban trajectories with judge-filtered language annotations generated under a four-dimensional travel-intent taxonomy. The benchmark contains 300K selected trajectories across Porto, San Francisco, and Beijing, yielding 2.1M task instances from three instruction variants, three retrieval queries, and one caption per trajectory. We further develop proof-of-concept models for each task: TrajAnchor for instruction-conditioned trajectory generation, TrajFuse for semantic trajectory retrieval, and TrajRap for trajectory captioning. These models instantiate the proposed tasks and show that geometry-only trajectory baselines leave a large gap on our protocol, especially where language is part of the input-output interface. We release TrajPrism with code and a reproducible annotation pipeline that is designed to be portable across cities, given compatible trajectory inputs and map resources.

Executing complex terminal tasks remains a significant challenge for open-weight LLMs, constrained by two fundamental limitations. First, high-fidelity, executable training environments are scarce: environments synthesized from real-world repositories are not diverse and scalable, while trajectories synthesized by LLMs suffer from hallucinations. Second, standard instruction tuning uses expert trajectories that rarely exhibit simple mistakes common to smaller models. This creates a distributional mismatch, leaving student models ill-equipped to recover from their own runtime failures. To bridge these gaps, we introduce TermiGen, an end-to-end pipeline for synthesizing verifiable environments and resilient expert trajectories. Termi-Gen first generates functionally valid tasks and Docker containers via an iterative multi-agent refinement loop. Subsequently, we employ a Generator-Critic protocol that actively injects errors during trajectory collection, synthesizing data rich in error-correction cycles. Fine-tuned on this TermiGen-generated dataset, our TermiGen-Qwen2.5-Coder-32B achieves a 31.3% pass rate on TerminalBench. This establishes a new open-weights state-of-the-art, outperforming existing baselines and notably surpassing capable proprietary models such as o4-mini. Dataset is avaiable at https://github.com/ucsb-mlsec/terminal-bench-env.

Path-velocity decomposition is an intuitive yet powerful approach to address the complexity of kinodynamic motion planning. The difficult trajectory planning problem is solved in two separate, simpler, steps: first, find a path in the configuration space that satisfies the geometric constraints (path planning), and second, find a time-parameterization of that path satisfying the kinodynamic constraints. A fundamental requirement is that the path found in the first step should be time-parameterizable. Most existing works fulfill this requirement by enforcing quasi-static constraints in the path planning step, resulting in an important loss in completeness. We propose a method that enables path-velocity decomposition to discover truly dynamic motions, i.e. motions that are not quasi-statically executable. At the heart of the proposed method is a new algorithm -- Admissible Velocity Propagation -- which, given a path and an interval of reachable velocities at the beginning of that path, computes exactly and efficiently the interval of all the velocities the system can reach after traversing the path while respecting the system kinodynamic constraints. Combining this algorithm with usual sampling-based planners then gives rise to a family of new trajectory planners that can appropriately handle kinodynamic constraints while retaining the advantages associated with path-velocity decomposition. We demonstrate the efficiency of the proposed method on some difficult kinodynamic planning problems, where, in particular, quasi-static methods are guaranteed to fail.

Safety and robustness are crucial factors in developing trustworthy autonomous vehicles. One essential aspect of addressing these factors is to equip vehicles with the capability to predict future trajectories for all moving objects in the surroundings and quantify prediction uncertainties. In this paper, we propose the Sequential Neural Variational Agent (SeNeVA), a generative model that describes the distribution of future trajectories for a single moving object. Our approach can distinguish Out-of-Distribution data while quantifying uncertainty and achieving competitive performance compared to state-of-the-art methods on the Argoverse 2 and INTERACTION datasets. Specifically, a 0.446 meters minimum Final Displacement Error, a 0.203 meters minimum Average Displacement Error, and a 5.35% Miss Rate are achieved on the INTERACTION test set. Extensive qualitative and quantitative analysis is also provided to evaluate the proposed model. Our open-source code is available at https://github.com/PurdueDigitalTwin/seneva.

Large language model (LLM)-based agents increasingly rely on tool use to complete real-world tasks. While existing works evaluate the LLMs' tool use capability, they largely focus on the final answers yet overlook the detailed tool usage trajectory, i.e., whether tools are selected, parameterized, and ordered correctly. We introduce TRAJECT-Bench, a trajectory-aware benchmark to comprehensively evaluate LLMs' tool use capability through diverse tasks with fine-grained evaluation metrics. TRAJECT-Bench pairs high-fidelity, executable tools across practical domains with tasks grounded in production-style APIs, and synthesizes trajectories that vary in breadth (parallel calls) and depth (interdependent chains). Besides final accuracy, TRAJECT-Bench also reports trajectory-level diagnostics, including tool selection and argument correctness, and dependency/order satisfaction. Analyses reveal failure modes such as similar tool confusion and parameter-blind selection, and scaling behavior with tool diversity and trajectory length where the bottleneck of transiting from short to mid-length trajectories is revealed, offering actionable guidance for LLMs' tool use.

Probabilistic completeness is an important property in motion planning. Although it has been established with clear assumptions for geometric planners, the panorama of completeness results for kinodynamic planners is still incomplete, as most existing proofs rely on strong assumptions that are difficult, if not impossible, to verify on practical systems. In this paper, we focus on an important class of kinodynamic planners, namely those that interpolate trajectories in the state space. We provide a proof of probabilistic completeness for these planners under assumptions that can be readily verified from the system's equations of motion and the user-defined interpolation function. Our proof relies crucially on a property of interpolated trajectories, termed second-order continuity (SOC), which we show is tightly related to the ability of a planner to benefit from denser sampling. We analyze the impact of this property in simulations on a low-torque pendulum. Our results show that a simple RRT using a second-order continuous interpolation swiftly finds solution, while it is impossible for the same planner using standard Bezier curves (which are not SOC) to find any solution.

Multi-modal trajectory forecasting methods commonly evaluate using single-agent metrics (marginal metrics), such as minimum Average Displacement Error (ADE) and Final Displacement Error (FDE), which fail to capture joint performance of multiple interacting agents. Only focusing on marginal metrics can lead to unnatural predictions, such as colliding trajectories or diverging trajectories for people who are clearly walking together as a group. Consequently, methods optimized for marginal metrics lead to overly-optimistic estimations of performance, which is detrimental to progress in trajectory forecasting research. In response to the limitations of marginal metrics, we present the first comprehensive evaluation of state-of-the-art (SOTA) trajectory forecasting methods with respect to multi-agent metrics (joint metrics): JADE, JFDE, and collision rate. We demonstrate the importance of joint metrics as opposed to marginal metrics with quantitative evidence and qualitative examples drawn from the ETH / UCY and Stanford Drone datasets. We introduce a new loss function incorporating joint metrics that, when applied to a SOTA trajectory forecasting method, achieves a 7% improvement in JADE / JFDE on the ETH / UCY datasets with respect to the previous SOTA. Our results also indicate that optimizing for joint metrics naturally leads to an improvement in interaction modeling, as evidenced by a 16% decrease in mean collision rate on the ETH / UCY datasets with respect to the previous SOTA.

Reasoning-trained language models often spend more tokens on harder problems, but longer chains of thought do not show whether a model is merely computing for more steps or following a different internal trajectory. We study this distinction through hidden-state trajectories during chain-of-thought generation across competitive programming, mathematics, and Boolean satisfiability. Raw trajectory geometry is strongly shaped by generation length: longer generations mechanically alter path statistics, so difficulty-dependent comparisons are misleading without adjustment. After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines. Corrected difficulty-geometry coupling is weaker, but still present, in mathematics and Boolean satisfiability. Prompt-stage linear probes do not mirror the code-domain separation, and behavioral annotations show that stronger corrected coupling co-occurs with strategy shifts and uncertainty monitoring. Together, these findings establish length correction as a prerequisite for generation-time trajectory analysis and show that reasoning training can be associated with distinct corrected trajectory geometry, with the strength of the effect depending on the domain.

As unmanned aerial systems (UASs) increasingly integrate into the US national airspace system, there is an increasing need to characterize how commercial and recreational UASs may encounter each other. To inform the development and evaluation of safety critical technologies, we demonstrate a methodology to analytically calculate all potential relative geometries between different UAS operations performing inspection missions. This method is based on a previously demonstrated technique that leverages open source geospatial information to generate representative unmanned aircraft trajectories. Using open source data and parallel processing techniques, we performed trillions of calculations to estimate the relative horizontal distance between geospatial points across sixteen locations.

The objective function used in trajectory optimization is often non-convex and can have an infinite set of local optima. In such cases, there are diverse solutions to perform a given task. Although there are a few methods to find multiple solutions for motion planning, they are limited to generating a finite set of solutions. To address this issue, we presents an optimization method that learns an infinite set of solutions in trajectory optimization. In our framework, diverse solutions are obtained by learning latent representations of solutions. Our approach can be interpreted as training a deep generative model of collision-free trajectories for motion planning. The experimental results indicate that the trained model represents an infinite set of homotopic solutions for motion planning problems.

The field of trajectory forecasting has grown significantly in recent years, partially owing to the release of numerous large-scale, real-world human trajectory datasets for autonomous vehicles (AVs) and pedestrian motion tracking. While such datasets have been a boon for the community, they each use custom and unique data formats and APIs, making it cumbersome for researchers to train and evaluate methods across multiple datasets. To remedy this, we present trajdata: a unified interface to multiple human trajectory datasets. At its core, trajdata provides a simple, uniform, and efficient representation and API for trajectory and map data. As a demonstration of its capabilities, in this work we conduct a comprehensive empirical evaluation of existing trajectory datasets, providing users with a rich understanding of the data underpinning much of current pedestrian and AV motion forecasting research, and proposing suggestions for future datasets from these insights. trajdata is permissively licensed (Apache 2.0) and can be accessed online at https://github.com/NVlabs/trajdata

In Reinforcement Learning (RL), an agent acts in an unknown environment to maximize the expected cumulative discounted sum of an external reward signal, i.e., the expected return. In practice, in many tasks of interest, such as policy optimization, the agent usually spends its interaction budget by collecting episodes of fixed length within a simulator (i.e., Monte Carlo simulation). However, given the discounted nature of the RL objective, this data collection strategy might not be the best option. Indeed, the rewards taken in early simulation steps weigh exponentially more than future rewards. Taking a cue from this intuition, in this paper, we design an a-priori budget allocation strategy that leads to the collection of trajectories of different lengths, i.e., truncated. The proposed approach provably minimizes the width of the confidence intervals around the empirical estimates of the expected return of a policy. After discussing the theoretical properties of our method, we make use of our trajectory truncation mechanism to extend Policy Optimization via Importance Sampling (POIS, Metelli et al., 2018) algorithm. Finally, we conduct a numerical comparison between our algorithm and POIS: the results are consistent with our theory and show that an appropriate truncation of the trajectories can succeed in improving performance.

Trajectory prediction plays an important role in various applications, including autonomous driving, robotics, and scene understanding. Existing approaches mainly focus on developing compact neural networks to increase prediction precision on public datasets, typically employing a standardized input duration. However, a notable issue arises when these models are evaluated with varying observation lengths, leading to a significant performance drop, a phenomenon we term the Observation Length Shift. To address this issue, we introduce a general and effective framework, the FlexiLength Network (FLN), to enhance the robustness of existing trajectory prediction techniques against varying observation periods. Specifically, FLN integrates trajectory data with diverse observation lengths, incorporates FlexiLength Calibration (FLC) to acquire temporal invariant representations, and employs FlexiLength Adaptation (FLA) to further refine these representations for more accurate future trajectory predictions. Comprehensive experiments on multiple datasets, ie, ETH/UCY, nuScenes, and Argoverse 1, demonstrate the effectiveness and flexibility of our proposed FLN framework.

LiDAR relocalization has attracted increasing attention as it can deliver accurate 6-DoF pose estimation in complex 3D environments. Recent learning-based regression methods offer efficient solutions by directly predicting global poses without the need for explicit map storage. However, these methods often struggle in challenging scenes due to their equal treatment of all predicted points, which is vulnerable to noise and outliers. In this paper, we propose LEADER, a robust LiDAR-based relocalization framework enhanced by a simple, yet effective geometric encoder. Specifically, a Robust Projection-based Geometric Encoder architecture which captures multi-scale geometric features is first presented to enhance descriptiveness in geometric representation. A Truncated Relative Reliability loss is then formulated to model point-wise ambiguity and mitigate the influence of unreliable predictions. Extensive experiments on the Oxford RobotCar and NCLT datasets demonstrate that LEADER outperforms state-of-the-art methods, achieving 24.1% and 73.9% relative reductions in position error over existing techniques, respectively. The source code is released on https://github.com/JiansW/LEADER.

Multi-agent systems (MAS) are increasingly capable of tackling complex real-world tasks, yet their reliance on inter-agent coordination, tool use, and long-horizon reasoning makes error recognition particularly challenging. Minor errors can propagate across agents, escalating into task failures while producing long, intertwined execution trajectories that impose significant costs for both human developers and automated systems to debug and analyze. Our key insight is that, despite surface differences in failure trajectories (e.g., logs), MAS errors often recur with similar structural patterns. This paper presents CORRECT, the first lightweight, training-free framework that leverages an online cache of distilled error schemata to recognize and transfer knowledge of failure structures across new requests. This cache-based reuse allows LLMs to perform targeted error localization at inference time, avoiding the need for expensive retraining while adapting to dynamic MAS deployments in subseconds. To support rigorous study in this domain, we also introduce CORRECT-Error, a large-scale dataset of over 2,000 annotated trajectories collected through a novel error-injection pipeline guided by real-world distributions, and further validated through human evaluation to ensure alignment with natural failure patterns. Experiments across seven diverse MAS applications show that CORRECT improves step-level error localization up to 19.8% over existing advances while at near-zero overhead, substantially narrowing the gap between automated and human-level error recognition.

Robotic manipulation is often specified through language instructions or task identifiers, yet cluttered environments with similar objects are better handled by spatially indicating what to move and where to place it. Addressing the vision-centric challenge of object and goal specification, we present, to the best of our knowledge, the first formalization of Spatially Prompted Visual Trajectory Prediction (SP-VTP). This novel setting utilizes initial spatial prompts (like bounding boxes or points) to define task objectives, tasking the model with forecasting future end-effector trajectories from egocentric streams. To study this problem, we collect and annotate EgoSPT, a dataset of egocentric spatially prompted manipulation trajectories with first-frame object and target grounding annotations and recovered 3D end-effector motion. SP-VTP is challenging because the task specification is static, while the scene configuration evolves over time. To solve this problem, we propose SPOT(Spatially Prompted Object-Target Policy), which combines a task encoder for first-frame visual and coordinate spatial prompts, an observation encoder for current visual and history context, and a trajectory generator for future end-effector motion. Experiments under strict scene-level splits show that SPOT improves cross-scene trajectory prediction over non-prompted or single-source prompted baselines. Together, EgoSPT and SPOT establish a new spatial prompting problem SP-VTP, as a simple and scalable task condition for egocentric manipulation.

Geometric methods for solving open-world off-road navigation tasks, by learning occupancy and metric maps, provide good generalization but can be brittle in outdoor environments that violate their assumptions (e.g., tall grass). Learning-based methods can directly learn collision-free behavior from raw observations, but are difficult to integrate with standard geometry-based pipelines. This creates an unfortunate conflict -- either use learning and lose out on well-understood geometric navigational components, or do not use it, in favor of extensively hand-tuned geometry-based cost maps. In this work, we reject this dichotomy by designing the learning and non-learning-based components in a way such that they can be effectively combined in a self-supervised manner. Both components contribute to a planning criterion: the learned component contributes predicted traversability as rewards, while the geometric component contributes obstacle cost information. We instantiate and comparatively evaluate our system in both in-distribution and out-of-distribution environments, showing that this approach inherits complementary gains from the learned and geometric components and significantly outperforms either of them. Videos of our results are hosted at https://sites.google.com/view/hybrid-imitative-planning

Large language models (LLMs) can call tools effectively, yet they remain brittle in multi-turn execution: following a tool call error, smaller models often degenerate into repetitive invalid re-invocations, failing to interpret error feedback and self-correct. This brittleness hinders reliable real-world deployment, where the execution errors are inherently inevitable during tool interaction procedures. We identify a key limitation of current approaches: standard reinforcement learning (RL) treats errors as sparse negative rewards, providing no guidance on how to recover, while pre-collected synthetic error-correction datasets suffer from distribution mismatch with the model's on-policy error modes. To bridge this gap, we propose Fission-GRPO, a framework that converts execution errors into corrective supervision within the RL training loop. Our core mechanism fissions each failed trajectory into a new training instance by augmenting it with diagnostic feedback from a finetuned Error Simulator, then resampling recovery rollouts on-policy. This enables the model to learn from the precise errors it makes during exploration, rather than from static, pre-collected error cases. On the BFCL v4 Multi-Turn, Fission-GRPO improves the error recovery rate of Qwen3-8B by 5.7% absolute, crucially, yielding a 4% overall accuracy gain (42.75% to 46.75%) over GRPO and outperforming specialized tool-use agents.

Trajectory generation has garnered significant attention from researchers in the field of spatio-temporal analysis, as it can generate substantial synthesized human mobility trajectories that enhance user privacy and alleviate data scarcity. However, existing trajectory generation methods often focus on improving trajectory generation quality from a singular perspective, lacking a comprehensive semantic understanding across various scales. Consequently, we are inspired to develop a HOlistic SEmantic Representation (HOSER) framework for navigational trajectory generation. Given an origin-and-destination (OD) pair and the starting time point of a latent trajectory, we first propose a Road Network Encoder to expand the receptive field of road- and zone-level semantics. Second, we design a Multi-Granularity Trajectory Encoder to integrate the spatio-temporal semantics of the generated trajectory at both the point and trajectory levels. Finally, we employ a Destination-Oriented Navigator to seamlessly integrate destination-oriented guidance. Extensive experiments on three real-world datasets demonstrate that HOSER outperforms state-of-the-art baselines by a significant margin. Moreover, the model's performance in few-shot learning and zero-shot learning scenarios further verifies the effectiveness of our holistic semantic representation.

This work introduces BEV-LIO(LC), a novel LiDAR-Inertial Odometry (LIO) framework that combines Bird's Eye View (BEV) image representations of LiDAR data with geometry-based point cloud registration and incorporates loop closure (LC) through BEV image features. By normalizing point density, we project LiDAR point clouds into BEV images, thereby enabling efficient feature extraction and matching. A lightweight convolutional neural network (CNN) based feature extractor is employed to extract distinctive local and global descriptors from the BEV images. Local descriptors are used to match BEV images with FAST keypoints for reprojection error construction, while global descriptors facilitate loop closure detection. Reprojection error minimization is then integrated with point-to-plane registration within an iterated Extended Kalman Filter (iEKF). In the back-end, global descriptors are used to create a KD-tree-indexed keyframe database for accurate loop closure detection. When a loop closure is detected, Random Sample Consensus (RANSAC) computes a coarse transform from BEV image matching, which serves as the initial estimate for Iterative Closest Point (ICP). The refined transform is subsequently incorporated into a factor graph along with odometry factors, improving the global consistency of localization. Extensive experiments conducted in various scenarios with different LiDAR types demonstrate that BEV-LIO(LC) outperforms state-of-the-art methods, achieving competitive localization accuracy. Our code, video and supplementary materials can be found at https://github.com/HxCa1/BEV-LIO-LC.

Established sampling protocols for 3D point cloud learning, such as Farthest Point Sampling (FPS) and Fixed Sample Size (FSS), have long been relied upon. However, real-world data often suffer from corruptions, such as sensor noise, which violates the benign data assumption in current protocols. As a result, these protocols are highly vulnerable to noise, posing significant safety risks in critical applications like autonomous driving. To address these issues, we propose an enhanced point cloud sampling protocol, PointSP, designed to improve robustness against point cloud corruptions. PointSP incorporates key point reweighting to mitigate outlier sensitivity and ensure the selection of representative points. It also introduces a local-global balanced downsampling strategy, which allows for scalable and adaptive sampling while maintaining geometric consistency. Additionally, a lightweight tangent plane interpolation method is used to preserve local geometry while enhancing the density of the point cloud. Unlike learning-based approaches that require additional model training, PointSP is architecture-agnostic, requiring no extra learning or modification to the network. This enables seamless integration into existing pipelines. Extensive experiments on synthetic and real-world corrupted datasets show that PointSP significantly improves the robustness and accuracy of point cloud classification, outperforming state-of-the-art methods across multiple benchmarks.

End-to-end planning has emerged as a dominant paradigm for autonomous driving, where recent models often adopt a scoring-selection framework to choose trajectories from a large set of candidates, with diffusion-based decoding showing strong promise. However, directly selecting from the entire candidate space remains difficult to optimize, and Gaussian perturbations used in diffusion often introduce unrealistic trajectories that complicate the denoising process. In addition, for training these models, reinforcement learning (RL) has shown promise, but existing end-to-end RL approaches typically rely on a single coupled reward without structured signals, limiting optimization effectiveness. To address these challenges, we propose HAD, an end-to-end planning framework with a Hierarchical Diffusion Policy that decomposes planning into a coarse-to-fine process. To improve trajectory generation, we introduce Structure-Preserved Trajectory Expansion, which produces realistic candidates while maintaining kinematic structure. For policy learning, we develop Metric-Decoupled Policy Optimization (MDPO) to enable structured RL optimization across multiple driving objectives. Extensive experiments show that HAD achieves new state-of-the-art performance on both NAVSIM and HUGSIM, outperforming prior arts by a huge margin: +2.3 EPDMS on NAVSIM and +4.9 Route Completion on HUGSIM.

Realistic scene reconstruction in driving scenarios poses significant challenges due to fast-moving objects. Most existing methods rely on labor-intensive manual labeling of object poses to reconstruct dynamic objects in canonical space and move them based on these poses during rendering. While some approaches attempt to use 3D object trackers to replace manual annotations, the limited generalization of 3D trackers -- caused by the scarcity of large-scale 3D datasets -- results in inferior reconstructions in real-world settings. In contrast, 2D foundation models demonstrate strong generalization capabilities. To eliminate the reliance on 3D trackers and enhance robustness across diverse environments, we propose a stable object tracking module by leveraging associations from 2D deep trackers within a 3D object fusion strategy. We address inevitable tracking errors by further introducing a motion learning strategy in an implicit feature space that autonomously corrects trajectory errors and recovers missed detections. Experimental results on Waymo-NOTR and KITTI show that our method outperforms existing approaches. Our code will be released on https://lolrudy.github.io/No3DTrackSG/.

Next point-of-interest (POI) recommendation predicts a user's next destination from historical movements. Traditional models require intensive training, while LLMs offer flexible and generalizable zero-shot solutions but often generate generic or geographically irrelevant results due to missing trajectory and spatial context. To address these issues, we propose RALLM-POI, a framework that couples LLMs with retrieval-augmented generation and self-rectification. We first propose a Historical Trajectory Retriever (HTR) that retrieves relevant past trajectories to serve as contextual references, which are then reranked by a Geographical Distance Reranker (GDR) for prioritizing spatially relevant trajectories. Lastly, an Agentic LLM Rectifier (ALR) is designed to refine outputs through self-reflection. Without additional training, RALLM-POI achieves substantial accuracy gains across three real-world Foursquare datasets, outperforming both conventional and LLM-based baselines. Code is released at https://github.com/LKRcrocodile/RALLM-POI.

In the era of mega-constellations, the need for accurate and publicly available information has become fundamental for satellite operators to guarantee the safety of spacecrafts and the Low Earth Orbit (LEO) space environment. This study critically evaluates the accuracy and reliability of publicly available ephemeris data for a LEO mega-constellation - Starlink. The goal of this work is twofold: (i) compare and analyze the quality of the data against high-precision numerical propagation. (ii) Leverage Physics-Informed Machine Learning to extract relevant satellite quantities, such as non-conservative forces, during the decay process. By analyzing two months of real orbital data for approximately 1500 Starlink satellites, we identify discrepancies between high precision numerical algorithms and the published ephemerides, recognizing the use of simplified dynamics at fixed thresholds, planned maneuvers, and limitations in uncertainty propagations. Furthermore, we compare data obtained from multiple sources to track and analyze deorbiting satellites over the same period. Empirically, we extract the acceleration profile of satellites during deorbiting and provide insights relating to the effects of non-conservative forces during reentry. For non-deorbiting satellites, the position Root Mean Square Error (RMSE) was approximately 300 m, while for deorbiting satellites it increased to about 600 m. Through this in-depth analysis, we highlight potential limitations in publicly available data for accurate and robust Space Situational Awareness (SSA), and importantly, we propose a data-driven model of satellite decay in mega-constellations.

Training deep research agents requires long-horizon trajectories that interleave search, evidence aggregation, and multi-step reasoning. However, existing data collection pipelines typically rely on proprietary web APIs, making large-scale trajectory synthesis costly, unstable, and difficult to reproduce. We present OpenResearcher, a reproducible pipeline that decouples one-time corpus bootstrapping from multi-turn trajectory synthesis and executes the search-and-browse loop entirely offline using three explicit browser primitives: search, open, and find, over a 15M-document corpus. Using GPT-OSS-120B as the teacher model, we synthesize over 97K trajectories, including a substantial long-horizon tail with 100+ tool calls. Supervised fine-tuning a 30B-A3B backbone on these trajectories achieves 54.8\% accuracy on BrowseComp-Plus, a +34.0 point improvement over the base model, while remaining competitive on BrowseComp, GAIA, and xbench-DeepSearch. Because the environment is offline and fully instrumented, it also enables controlled analysis, where our study reveals practical insights into deep research pipeline design, including data filtering strategies, agent configuration choices, and how retrieval success relates to final answer accuracy. We release the pipeline, synthesized trajectories, model checkpoints, and the offline search environment at https://github.com/TIGER-AI-Lab/OpenResearcher.

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

Outcome-reward reinforcement learning (RL) has proven effective at improving the reasoning capabilities of large language models (LLMs). However, standard RL assigns credit only at the level of the final answer, penalizing entire reasoning traces when the outcome is incorrect and uniformly reinforcing all steps when it is correct. As a result, correct intermediate steps may be discouraged in failed traces, while spurious steps may be reinforced in successful ones. We refer to this failure mode as the problem of credit assignment. While a natural remedy is to train a process reward model, accurately optimizing such models to identify corrective reasoning steps remains challenging. We introduce Intervention Training (InT), a training paradigm in which the model performs fine-grained credit assignment on its own reasoning traces by proposing short, targeted corrections that steer trajectories toward higher reward. Using reference solutions commonly available in mathematical reasoning datasets and exploiting the fact that verifying a model-generated solution is easier than generating a correct one from scratch, the model identifies the first error in its reasoning and proposes a single-step intervention to redirect the trajectory toward the correct solution. We then apply supervised fine-tuning (SFT) to the on-policy rollout up to the point of error concatenated with the intervention, localizing error to the specific step that caused failure. We show that the resulting model serves as a far better initialization for RL training. After running InT and subsequent fine-tuning with RL, we improve accuracy by nearly 14% over a 4B-parameter base model on IMO-AnswerBench, outperforming larger open-source models such as gpt-oss-20b.

End-to-end driving systems have made rapid progress, but have so far not been applied to the challenging new CARLA Leaderboard 2.0. Further, while there is a large body of literature on end-to-end architectures and training strategies, the impact of the training dataset is often overlooked. In this work, we make a first attempt at end-to-end driving for Leaderboard 2.0. Instead of investigating architectures, we systematically analyze the training dataset, leading to new insights: (1) Expert style significantly affects downstream policy performance. (2) In complex data sets, the frames should not be weighted on the basis of simplistic criteria such as class frequencies. (3) Instead, estimating whether a frame changes the target labels compared to previous frames can reduce the size of the dataset without removing important information. By incorporating these findings, our model ranks first and second respectively on the map and sensors tracks of the 2024 CARLA Challenge, and sets a new state-of-the-art on the Bench2Drive test routes. Finally, we uncover a design flaw in the current evaluation metrics and propose a modification for future challenges. Our dataset, code, and pre-trained models are publicly available at https://github.com/autonomousvision/carla_garage.

As hyperparameter tuning becomes increasingly costly at scale, efficient tuning methods are essential. Yet principles for guiding hyperparameter tuning remain limited. In this work, we seek to establish such principles by considering a broad range of hyperparameters, including batch size, learning rate, and weight decay. We identify a phenomenon we call trajectory invariance, where pre-training loss curves, gradient noise, and gradient norm exhibit invariance--closely overlapping--with respect to a quantity that combines learning rate and weight decay. This phenomenon effectively reduces the original two-dimensional hyperparameter space to one dimension, yielding an efficient tuning rule: follow the salient direction revealed by trajectory invariance. Furthermore, we refine previous scaling laws and challenge several existing viewpoints. Overall, our work proposes new principles for efficient tuning and inspires future research on scaling laws.

We present MiniVLA-Nav v1, a simulation dataset for Language-Conditioned Object Approach (LCOA) navigation: given a short natural-language instruction, an NVIDIA Nova Carter differential-drive robot must navigate to the named object and stop within 1 m across four photorealistic Isaac Sim environments (Office, Hospital, Full Warehouse, and Warehouse with Multiple Shelves). Each of the 1,174 episodes pairs an instruction with synchronized 640x640 RGB images, metric depth maps (float32, metres), and instance segmentation masks, together with continuous (v,omega) and 7x7 tokenized expert action labels recorded at 60 Hz from a vision-based proportional controller. Trajectory diversity is ensured through three spawn-distance tiers (near: 1.5-3.5 m, mid: 3.5-7.0 m, far: global curated points; Pearson r=0.94 between spawn distance and trajectory length), 12 object categories, 18 training templates, and 12 paraphrase-OOD templates. Five evaluation splits support in-distribution accuracy, template-paraphrase robustness, and OOD object-category benchmarking. The dataset is publicly available at https://huggingface.co/datasets/alibustami/miniVLA-Nav

Existing agent-safety evaluation has focused mainly on externally induced risks. Yet agents may still enter unsafe trajectories under benign conditions. We study this complementary but underexplored setting through the lens of intrinsic risk, where intrinsic failures remain latent, propagate across long-horizon execution, and eventually lead to high-consequence outcomes. To evaluate this setting, we introduce non-attack intrinsic risk auditing and present HINTBench, a benchmark of 629 agent trajectories (523 risky, 106 safe; 33 steps on average) supporting three tasks: risk detection, risk-step localization, and intrinsic failure-type identification. Its annotations are organized under a unified five-constraint taxonomy. Experiments reveal a substantial capability gap: strong LLMs perform well on trajectory-level risk detection, but their performance drops to below 35 Strict-F1 on risk-step localization, while fine-grained failure diagnosis proves even harder. Existing guard models transfer poorly to this setting. These findings establish intrinsic risk auditing as an open challenge for agent safety.

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sampled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on completeness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show experimentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.

Capturing high-dimensional social interactions and feasible futures is essential for predicting trajectories. To address this complex nature, several attempts have been devoted to reducing the dimensionality of the output variables via parametric curve fitting such as the B\'ezier curve and B-spline function. However, these functions, which originate in computer graphics fields, are not suitable to account for socially acceptable human dynamics. In this paper, we present EigenTrajectory (ET), a trajectory prediction approach that uses a novel trajectory descriptor to form a compact space, known here as ET space, in place of Euclidean space, for representing pedestrian movements. We first reduce the complexity of the trajectory descriptor via a low-rank approximation. We transform the pedestrians' history paths into our ET space represented by spatio-temporal principle components, and feed them into off-the-shelf trajectory forecasting models. The inputs and outputs of the models as well as social interactions are all gathered and aggregated in the corresponding ET space. Lastly, we propose a trajectory anchor-based refinement method to cover all possible futures in the proposed ET space. Extensive experiments demonstrate that our EigenTrajectory predictor can significantly improve both the prediction accuracy and reliability of existing trajectory forecasting models on public benchmarks, indicating that the proposed descriptor is suited to represent pedestrian behaviors. Code is publicly available at https://github.com/inhwanbae/EigenTrajectory .

While GUI agents have advanced rapidly, they often lack the robustness to recover from their own errors, hindering real-world deployment. To bridge this gap at both the evaluation and data levels, we introduce GUI-RobustEval and propose Robustness-driven Trajectory Synthesis. GUI-RobustEval contains 1,216 executable test cases that systematically measure error recovery capabilities across a broad and realistic spectrum of error modes. At the data level, RoTS is a scalable synthesis framework that creates 800k high-quality data via a tree-based pipeline that proactively discovers diverse error modes and synthesizes corresponding recovery steps. Our two models, RoTS-7B and RoTS-32B, fine-tuned on our dataset, both demonstrate significant gains on GUI-RobustEval and traditional GUI benchmarks. Notably, RoTS-32B achieves state-of-the-art performance on OSWorld, with a 47.4% success rate and a 33.8% All-Pass@4 score, suggesting that improved long-horizon error recovery ability contributes to both robustness and overall performance. Our code is available at https://github.com/AlibabaResearch/RoTS.

LiDAR point clouds often contain motion-induced distortions, degrading the accuracy of object appearances in the captured data. In this paper, we first characterize the underlying reasons for the point cloud distortion and show that this is present in public datasets. We find that this distortion is more pronounced in high-speed environments such as highways, as well as in multi-LiDAR configurations, a common setup for heavy vehicles. Previous work has dealt with point cloud distortion from the ego-motion but fails to consider distortion from the motion of other objects. We therefore introduce a novel undistortion pipeline, HiMo, that leverages scene flow estimation for object motion compensation, correcting the depiction of dynamic objects. We further propose an extension of a state-of-the-art self-supervised scene flow method. Due to the lack of well-established motion distortion metrics in the literature, we also propose two metrics for compensation performance evaluation: compensation accuracy at a point level and shape similarity on objects. To demonstrate the efficacy of our method, we conduct extensive experiments on the Argoverse 2 dataset and a new real-world dataset. Our new dataset is collected from heavy vehicles equipped with multi-LiDARs and on highways as opposed to mostly urban settings in the existing datasets. The source code, including all methods and the evaluation data, will be provided upon publication. See https://kin-zhang.github.io/HiMo for more details.

Designing rewards for Reinforcement Learning (RL) is challenging because it needs to convey the desired task, be efficient to optimize, and be easy to compute. The latter is particularly problematic when applying RL to robotics, where detecting whether the desired configuration is reached might require considerable supervision and instrumentation. Furthermore, we are often interested in being able to reach a wide range of configurations, hence setting up a different reward every time might be unpractical. Methods like Hindsight Experience Replay (HER) have recently shown promise to learn policies able to reach many goals, without the need of a reward. Unfortunately, without tricks like resetting to points along the trajectory, HER might require many samples to discover how to reach certain areas of the state-space. In this work we investigate different approaches to incorporate demonstrations to drastically speed up the convergence to a policy able to reach any goal, also surpassing the performance of an agent trained with other Imitation Learning algorithms. Furthermore, we show our method can also be used when the available expert trajectories do not contain the actions, which can leverage kinesthetic or third person demonstration. The code is available at https://sites.google.com/view/goalconditioned-il/.

Off-policy learning from multistep returns is crucial for sample-efficient reinforcement learning, but counteracting off-policy bias without exacerbating variance is challenging. Classically, off-policy bias is corrected in a per-decision manner: past temporal-difference errors are re-weighted by the instantaneous Importance Sampling (IS) ratio after each action via eligibility traces. Many off-policy algorithms rely on this mechanism, along with differing protocols for cutting the IS ratios to combat the variance of the IS estimator. Unfortunately, once a trace has been fully cut, the effect cannot be reversed. This has led to the development of credit-assignment strategies that account for multiple past experiences at a time. These trajectory-aware methods have not been extensively analyzed, and their theoretical justification remains uncertain. In this paper, we propose a multistep operator that can express both per-decision and trajectory-aware methods. We prove convergence conditions for our operator in the tabular setting, establishing the first guarantees for several existing methods as well as many new ones. Finally, we introduce Recency-Bounded Importance Sampling (RBIS), which leverages trajectory awareness to perform robustly across lambda-values in an off-policy control task.

3D LiDAR sensors are essential for autonomous navigation, environmental monitoring, and precision mapping in remote sensing applications. To efficiently process the massive point clouds generated by these sensors, LiDAR data is often projected into 2D range images that organize points by their angular positions and distances. While these range image representations enable efficient processing, conventional projection methods suffer from fundamental geometric inconsistencies that cause irreversible information loss, compromising high-fidelity applications. We present ALICE-LRI (Automatic LiDAR Intrinsic Calibration Estimation for Lossless Range Images), the first general, sensor-agnostic method that achieves lossless range image generation from spinning LiDAR point clouds without requiring manufacturer metadata or calibration files. Our algorithm automatically reverse-engineers the intrinsic geometry of any spinning LiDAR sensor by inferring critical parameters including laser beam configuration, angular distributions, and per-beam calibration corrections, enabling lossless projection and complete point cloud reconstruction with zero point loss. Comprehensive evaluation across the complete KITTI and DurLAR datasets demonstrates that ALICE-LRI achieves perfect point preservation, with zero points lost across all point clouds. Geometric accuracy is maintained well within sensor precision limits, establishing geometric losslessness with real-time performance. We also present a compression case study that validates substantial downstream benefits, demonstrating significant quality improvements in practical applications. This paradigm shift from approximate to lossless LiDAR projections opens new possibilities for high-precision remote sensing applications requiring complete geometric preservation.

In this paper, we propose a third-order, i.e., white-noise-on-jerk, Gaussian Process (GP) Trajectory Representation (TR) framework for continuous-time (CT) motion estimation (ME) tasks. Our framework features a unified trajectory representation that encapsulates the kinematic models of both SO(3)timesR^3 and SE(3) pose representations. This encapsulation strategy allows users to use the same implementation of measurement-based factors for either choice of pose representation, which facilitates experimentation and comparison to achieve the best model for the ME task. In addition, unique to our framework, we derive the kinematic models with the closed-form temporal derivatives of the local variable of SO(3) and SE(3), which so far has only been approximated based on the Taylor expansion in the literature. Our experiments show that these kinematic models can improve the estimation accuracy in high-speed scenarios. All analytical Jacobians of the interpolated states with respect to the support states of the trajectory representation, as well as the motion prior factors, are also provided for accelerated Gauss-Newton (GN) optimization. Our experiments demonstrate the efficacy and efficiency of the framework in various motion estimation tasks such as localization, calibration, and odometry, facilitating fast prototyping for ME researchers. We release the source code for the benefit of the community. Our project is available at https://github.com/brytsknguyen/gptr.

Kalman filter (KF) based methods for multi-object tracking (MOT) make an assumption that objects move linearly. While this assumption is acceptable for very short periods of occlusion, linear estimates of motion for prolonged time can be highly inaccurate. Moreover, when there is no measurement available to update Kalman filter parameters, the standard convention is to trust the priori state estimations for posteriori update. This leads to the accumulation of errors during a period of occlusion. The error causes significant motion direction variance in practice. In this work, we show that a basic Kalman filter can still obtain state-of-the-art tracking performance if proper care is taken to fix the noise accumulated during occlusion. Instead of relying only on the linear state estimate (i.e., estimation-centric approach), we use object observations (i.e., the measurements by object detector) to compute a virtual trajectory over the occlusion period to fix the error accumulation of filter parameters during the occlusion period. This allows more time steps to correct errors accumulated during occlusion. We name our method Observation-Centric SORT (OC-SORT). It remains Simple, Online, and Real-Time but improves robustness during occlusion and non-linear motion. Given off-the-shelf detections as input, OC-SORT runs at 700+ FPS on a single CPU. It achieves state-of-the-art on multiple datasets, including MOT17, MOT20, KITTI, head tracking, and especially DanceTrack where the object motion is highly non-linear. The code and models are available at https://github.com/noahcao/OC_SORT.

We present Generative Anchored Fields (GAF), a generative model that learns independent endpoint predictors, J (noise) and K (data), from any point on a linear bridge. Unlike existing approaches that use a single trajectory or score predictor, GAF is trained to recover the bridge endpoints directly via coordinate learning. The velocity field v=K-J emerges from their time-conditioned disagreement. This factorization enables Transport Algebra: algebraic operations on multiple J/K heads for compositional control. With class-specific K_n heads, GAF defines directed transport maps between a shared base noise distribution and multiple data domains, allowing controllable interpolation, multi-class composition, and semantic editing. This is achieved either directly on the predicted data coordinates (K) using Iterative Endpoint Refinement (IER), a novel sampler that achieves high-quality generation in 5-8 steps, or on the emergent velocity field (v). We achieve strong sample quality (FID 7.51 on ImageNet 256times256 and 7.27 on CelebA-HQ 256times 256, without classifier-free guidance) while treating compositional generation as an architectural primitive. Code available at https://github.com/IDLabMedia/GAF.

In recent years there have been excellent results in Visual-Inertial Odometry techniques, which aim to compute the incremental motion of the sensor with high accuracy and robustness. However these approaches lack the capability to close loops, and trajectory estimation accumulates drift even if the sensor is continually revisiting the same place. In this work we present a novel tightly-coupled Visual-Inertial Simultaneous Localization and Mapping system that is able to close loops and reuse its map to achieve zero-drift localization in already mapped areas. While our approach can be applied to any camera configuration, we address here the most general problem of a monocular camera, with its well-known scale ambiguity. We also propose a novel IMU initialization method, which computes the scale, the gravity direction, the velocity, and gyroscope and accelerometer biases, in a few seconds with high accuracy. We test our system in the 11 sequences of a recent micro-aerial vehicle public dataset achieving a typical scale factor error of 1% and centimeter precision. We compare to the state-of-the-art in visual-inertial odometry in sequences with revisiting, proving the better accuracy of our method due to map reuse and no drift accumulation.

When an LLM agent reads a confidential file, then writes a summary, then emails it externally, no single step is unsafe, but the sequence is a data leak. We call this safety drift: individually safe actions compounding into violations. Prior work has measured this problem; we predict it. SafetyDrift models agent safety trajectories as absorbing Markov chains, computing the probability that a trajectory will reach a violation within a given number of steps via closed form absorption analysis. A consequence of the monotonic state design is that every agent will eventually violate safety if left unsupervised (absorption probability 1.0 from all states), making the practical question not if but when, and motivating our focus on finite horizon prediction. Across 357 traces spanning 40 realistic tasks in four categories, we discover that "points of no return" are sharply task dependent: in communication tasks, agents that reach even a mild risk state have an 85% chance of violating safety within five steps, while in technical tasks the probability stays below 5% from any state. A lightweight monitor built on these models detects 94.7% of violations with 3.7 steps of advance warning at negligible computational cost, outperforming both keyword matching (44.7% detection, 55.9% false positive rate) and per step LLM judges (52.6% detection, 38.2% false positive rate) while running over 60,000x faster.

We consider the problem of learning good trajectories for manipulation tasks. This is challenging because the criterion defining a good trajectory varies with users, tasks and environments. In this paper, we propose a co-active online learning framework for teaching robots the preferences of its users for object manipulation tasks. The key novelty of our approach lies in the type of feedback expected from the user: the human user does not need to demonstrate optimal trajectories as training data, but merely needs to iteratively provide trajectories that slightly improve over the trajectory currently proposed by the system. We argue that this co-active preference feedback can be more easily elicited from the user than demonstrations of optimal trajectories, which are often challenging and non-intuitive to provide on high degrees of freedom manipulators. Nevertheless, theoretical regret bounds of our algorithm match the asymptotic rates of optimal trajectory algorithms. We demonstrate the generalizability of our algorithm on a variety of grocery checkout tasks, for whom, the preferences were not only influenced by the object being manipulated but also by the surrounding environment.For more details and a demonstration video, visit: \url{http://pr.cs.cornell.edu/coactive}

End-to-end autonomous driving research currently faces a critical challenge in bridging the gap between open-loop training and closed-loop deployment. Current approaches are trained to predict trajectories in an open-loop environment, which struggle with quick reactions to other agents in closed-loop environments and risk generating kinematically infeasible plans due to the gap between open-loop training and closed-loop driving. In this paper, we introduce Hydra-NeXt, a novel multi-branch planning framework that unifies trajectory prediction, control prediction, and a trajectory refinement network in one model. Unlike current open-loop trajectory prediction models that only handle general-case planning, Hydra-NeXt further utilizes a control decoder to focus on short-term actions, which enables faster responses to dynamic situations and reactive agents. Moreover, we propose the Trajectory Refinement module to augment and refine the planning decisions by effectively adhering to kinematic constraints in closed-loop environments. This unified approach bridges the gap between open-loop training and closed-loop driving, demonstrating superior performance of 65.89 Driving Score (DS) and 48.20% Success Rate (SR) on the Bench2Drive dataset without relying on external experts for data collection. Hydra-NeXt surpasses the previous state-of-the-art by 22.98 DS and 17.49 SR, marking a significant advancement in autonomous driving. Code will be available at https://github.com/woxihuanjiangguo/Hydra-NeXt.

End-to-end (E2E) autonomous driving presents a promising approach for translating perceptual inputs directly into driving actions. However, prohibitive annotation costs and temporal data quality degradation hinder long-term real-world deployment. While combining imitation learning (IL) and reinforcement learning (RL) is a common strategy for policy improvement, conventional RL training relies on delayed, event-based rewards-policies learn only from catastrophic outcomes such as collisions, leading to premature convergence to suboptimal behaviors. To address these limitations, we introduce GSDrive, a framework that exploits 3D Gaussian Splatting (3DGS) for differentiable, physics-based reward shaping in E2E driving policy improvement. Our method incorporates a flow matching-based trajectory predictor within the 3DGS simulator, enabling multi-mode trajectory probing where candidate trajectories are rolled out to assess prospective rewards. This establishes a bidirectional knowledge exchange between IL and RL by grounding reward functions in physically simulated interaction signals, offering immediate dense feedback instead of sparse catastrophic events. Evaluated on the reconstructed nuScenes dataset, our method surpasses existing simulation-based RL driving approaches in closed-loop experiments. Code is available at https://github.com/ZionGo6/GSDrive.

Efficient and accurate motion prediction is crucial for ensuring safety and informed decision-making in autonomous driving, particularly under dynamic real-world conditions that necessitate multi-modal forecasts. We introduce TrajFlow, a novel flow matching-based motion prediction framework that addresses the scalability and efficiency challenges of existing generative trajectory prediction methods. Unlike conventional generative approaches that employ i.i.d. sampling and require multiple inference passes to capture diverse outcomes, TrajFlow predicts multiple plausible future trajectories in a single pass, significantly reducing computational overhead while maintaining coherence across predictions. Moreover, we propose a ranking loss based on the Plackett-Luce distribution to improve uncertainty estimation of predicted trajectories. Additionally, we design a self-conditioning training technique that reuses the model's own predictions to construct noisy inputs during a second forward pass, thereby improving generalization and accelerating inference. Extensive experiments on the large-scale Waymo Open Motion Dataset (WOMD) demonstrate that TrajFlow achieves state-of-the-art performance across various key metrics, underscoring its effectiveness for safety-critical autonomous driving applications. The code and other details are available on the project website https://traj-flow.github.io/.

This paper reports on the second "Throughput" phase of the Tracking Machine Learning (TrackML) challenge on the Codalab platform. As in the first "Accuracy" phase, the participants had to solve a difficult experimental problem linked to tracking accurately the trajectory of particles as e.g. created at the Large Hadron Collider (LHC): given O(10^5) points, the participants had to connect them into O(10^4) individual groups that represent the particle trajectories which are approximated helical. While in the first phase only the accuracy mattered, the goal of this second phase was a compromise between the accuracy and the speed of inference. Both were measured on the Codalab platform where the participants had to upload their software. The best three participants had solutions with good accuracy and speed an order of magnitude faster than the state of the art when the challenge was designed. Although the core algorithms were less diverse than in the first phase, a diversity of techniques have been used and are described in this paper. The performance of the algorithms are analysed in depth and lessons derived.

Large language model-driven multi-agent systems (LLM-MAS) excel at complex tasks, yet unreliable agents remain a key bottleneck to system-level reliability. Automatic failure attribution is therefore critical, but existing approaches, such as direct prediction of agent-error pairs and agent-first failure attribution, rely on local logs of agents and miss global failures that only manifest over full interaction trajectories, such as cross-step inconsistencies and inter-agent coordination errors. Moreover, directly predicting failures induces a large combinatorial search space, hindering fine-grained attribution. To address these challenges, we propose VerifyMAS, a hypothesis verification framework for agent failure attribution. Instead of directly predicting faulty agents and error types, VerifyMAS formulates and verifies failure hypotheses against full trajectories. This verification-based approach decomposes attribution into trajectory-level error validation and fine-grained agent localization, providing an error-first attribution approach that captures global failure patterns while substantially reducing the search space. We further introduce a hypothesis-based data construction strategy grounded in a structured error taxonomy and fine-tune a specialized LLM verifier model for trajectory-level failure verification and agent attribution. Experiments on Aegis-Bench and Who&When show that VerifyMAS consistently improves diverse backbone models, including open-source Qwen and API-based GPT models, outperforming prior methods without sacrificing inference efficiency for long multi-agent trajectories.

We introduce a novel system for human-to-robot trajectory transfer that enables robots to manipulate objects by learning from human demonstration videos. The system consists of four modules. The first module is a data collection module that is designed to collect human demonstration videos from the point of view of a robot using an AR headset. The second module is a video understanding module that detects objects and extracts 3D human-hand trajectories from demonstration videos. The third module transfers a human-hand trajectory into a reference trajectory of a robot end-effector in 3D space. The last module utilizes a trajectory optimization algorithm to solve a trajectory in the robot configuration space that can follow the end-effector trajectory transferred from the human demonstration. Consequently, these modules enable a robot to watch a human demonstration video once and then repeat the same mobile manipulation task in different environments, even when objects are placed differently from the demonstrations. Experiments of different manipulation tasks are conducted on a mobile manipulator to verify the effectiveness of our system

Rapidly-exploring Random Trees (RRT) and its variations have emerged as a robust and efficient tool for finding collision-free paths in robotic systems. However, adding dynamic constraints makes the motion planning problem significantly harder, as it requires solving two-value boundary problems (computationally expensive) or propagating random control inputs (uninformative). Alternatively, Iterative Discontinuity Bounded A* (iDb-A*), introduced in our previous study, combines search and optimization iteratively. The search step connects short trajectories (motion primitives) while allowing a bounded discontinuity between the motion primitives, which is later repaired in the trajectory optimization step. Building upon these foundations, in this paper, we present iDb-RRT, a sampling-based kinodynamic motion planning algorithm that combines motion primitives and trajectory optimization within the RRT framework. iDb-RRT is probabilistically complete and can be implemented in forward or bidirectional mode. We have tested our algorithm across a benchmark suite comprising 30 problems, spanning 8 different systems, and shown that iDb-RRT can find solutions up to 10x faster than previous methods, especially in complex scenarios that require long trajectories or involve navigating through narrow passages.

Recovering dense and long-range pixel motion in videos is a challenging problem. Part of the difficulty arises from the 3D-to-2D projection process, leading to occlusions and discontinuities in the 2D motion domain. While 2D motion can be intricate, we posit that the underlying 3D motion can often be simple and low-dimensional. In this work, we propose to estimate point trajectories in 3D space to mitigate the issues caused by image projection. Our method, named SpatialTracker, lifts 2D pixels to 3D using monocular depth estimators, represents the 3D content of each frame efficiently using a triplane representation, and performs iterative updates using a transformer to estimate 3D trajectories. Tracking in 3D allows us to leverage as-rigid-as-possible (ARAP) constraints while simultaneously learning a rigidity embedding that clusters pixels into different rigid parts. Extensive evaluation shows that our approach achieves state-of-the-art tracking performance both qualitatively and quantitatively, particularly in challenging scenarios such as out-of-plane rotation.

Next Point of Interest (POI) recommendation is essential for modern mobility and location-based services. To provide a smooth user experience, models must understand several components of a journey holistically: "when to depart", "how to travel", "where to go", and "what needs arise via the route". However, current research is limited by fragmented datasets that focus merely on next POI recommendation ("where to go"), neglecting the departure time, travel mode, and situational requirements along the journey. Furthermore, the limited scale of these datasets impedes accurate evaluation of performance. To bridge this gap, we introduce IntTravel, the first large-scale public dataset for integrated travel recommendation, including 4.1 billion interactions from 163 million users with 7.3 million POIs. Built upon this dataset, we introduce an end-to-end, decoder-only generative framework for multi-task recommendation. It incorporates information preservation, selection, and factorization to balance task collaboration with specialized differentiation, yielding substantial performance gains. The framework's generalizability is highlighted by its state-of-the-art performance across both IntTravel dataset and an additional non-travel benchmark. IntTravel has been successfully deployed on Amap serving hundreds of millions of users, leading to a 1.09% increase in CTR. IntTravel is available at https://github.com/AMAP-ML/IntTravel.

End-to-end paradigm has emerged as a promising approach to autonomous driving. However, existing single-agent end-to-end pipelines are often constrained by occlusion and limited perception range, resulting in hazardous driving. Furthermore, their black-box nature prevents the interpretability of the driving behavior, leading to an untrustworthiness system. To address these limitations, we introduce Risk Map as Middleware (RiskMM) and propose an interpretable cooperative end-to-end driving framework. The risk map learns directly from the driving data and provides an interpretable spatiotemporal representation of the scenario from the upstream perception and the interactions between the ego vehicle and the surrounding environment for downstream planning. RiskMM first constructs a multi-agent spatiotemporal representation with unified Transformer-based architecture, then derives risk-aware representations by modeling interactions among surrounding environments with attention. These representations are subsequently fed into a learning-based Model Predictive Control (MPC) module. The MPC planner inherently accommodates physical constraints and different vehicle types and can provide interpretation by aligning learned parameters with explicit MPC elements. Evaluations conducted on the real-world V2XPnP-Seq dataset confirm that RiskMM achieves superior and robust performance in risk-aware trajectory planning, significantly enhancing the interpretability of the cooperative end-to-end driving framework. The codebase will be released to facilitate future research in this field.

Micro Aerial Vehicles (MAVs) that operate in unstructured, unexplored environments require fast and flexible local planning, which can replan when new parts of the map are explored. Trajectory optimization methods fulfill these needs, but require obstacle distance information, which can be given by Euclidean Signed Distance Fields (ESDFs). We propose a method to incrementally build ESDFs from Truncated Signed Distance Fields (TSDFs), a common implicit surface representation used in computer graphics and vision. TSDFs are fast to build and smooth out sensor noise over many observations, and are designed to produce surface meshes. Meshes allow human operators to get a better assessment of the robot's environment, and set high-level mission goals. We show that we can build TSDFs faster than Octomaps, and that it is more accurate to build ESDFs out of TSDFs than occupancy maps. Our complete system, called voxblox, will be available as open source and runs in real-time on a single CPU core. We validate our approach on-board an MAV, by using our system with a trajectory optimization local planner, entirely on-board and in real-time.

Object goal navigation aims to navigate an agent to locations of a given object category in unseen environments. Classical methods explicitly build maps of environments and require extensive engineering while lacking semantic information for object-oriented exploration. On the other hand, end-to-end learning methods alleviate manual map design and predict actions using implicit representations. Such methods, however, lack an explicit notion of geometry and may have limited ability to encode navigation history. In this work, we propose an implicit spatial map for object goal navigation. Our implicit map is recursively updated with new observations at each step using a transformer. To encourage spatial reasoning, we introduce auxiliary tasks and train our model to reconstruct explicit maps as well as to predict visual features, semantic labels and actions. Our method significantly outperforms the state of the art on the challenging MP3D dataset and generalizes well to the HM3D dataset. We successfully deploy our model on a real robot and achieve encouraging object goal navigation results in real scenes using only a few real-world demonstrations. Code, trained models and videos are available at https://www.di.ens.fr/willow/research/onav_rim/.

We introduce a learning-guided motion planning framework that generates seed trajectories using a diffusion model for trajectory optimization. Given a workspace, our method approximates the configuration space (C-space) obstacles through an environment representation consisting of a sparse set of task-related key configurations, which is then used as a conditioning input to the diffusion model. The diffusion model integrates regularization terms that encourage smooth, collision-free trajectories during training, and trajectory optimization refines the generated seed trajectories to correct any colliding segments. Our experimental results demonstrate that high-quality trajectory priors, learned through our C-space-grounded diffusion model, enable the efficient generation of collision-free trajectories in narrow-passage environments, outperforming previous learning- and planning-based baselines. Videos and additional materials can be found on the project page: https://kiwi-sherbet.github.io/PRESTO.

End-to-end autonomous driving aims to produce planning trajectories from raw sensors directly. Currently, most approaches integrate perception, prediction, and planning modules into a fully differentiable network, promising great scalability. However, these methods typically rely on deterministic modeling of online maps in the perception module for guiding or constraining vehicle planning, which may incorporate erroneous perception information and further compromise planning safety. To address this issue, we delve into the importance of online map uncertainty for enhancing autonomous driving safety and propose a novel paradigm named UncAD. Specifically, UncAD first estimates the uncertainty of the online map in the perception module. It then leverages the uncertainty to guide motion prediction and planning modules to produce multi-modal trajectories. Finally, to achieve safer autonomous driving, UncAD proposes an uncertainty-collision-aware planning selection strategy according to the online map uncertainty to evaluate and select the best trajectory. In this study, we incorporate UncAD into various state-of-the-art (SOTA) end-to-end methods. Experiments on the nuScenes dataset show that integrating UncAD, with only a 1.9% increase in parameters, can reduce collision rates by up to 26% and drivable area conflict rate by up to 42%. Codes, pre-trained models, and demo videos can be accessed at https://github.com/pengxuanyang/UncAD.

In the Lagrange-Newton method, where Newton's method is applied to a Lagrangian function that includes equality constraints, all stationary points are saddle points. It is therefore not possible to use a line-search method based on the value of the objective function; instead, the line search can operate on merit functions. In this report, we explore an alternative line-search method which is applicable to this case; it particulary addresses the damping of the step length in tight valleys. We propose a line-search criterion based on the divergence of the field of Newton step vectors. The visualization of the criterion for two-dimensional test functions reveals a network of ravines with flat bottom at the zero points of the criterion. The ravines are typically connected to stationary points. To traverse this ravine network in order to approach a stationary point, a zigzag strategy is devised. Numerical experiments demonstrate that the novel line-search strategy succeeds from most starting points in all test functions, but only exhibits the desired damping of the step length in some situations. At the present stage it is therefore difficult to appraise the utility of this contribution.

The autonomous driving community has witnessed a rapid growth in approaches that embrace an end-to-end algorithm framework, utilizing raw sensor input to generate vehicle motion plans, instead of concentrating on individual tasks such as detection and motion prediction. End-to-end systems, in comparison to modular pipelines, benefit from joint feature optimization for perception and planning. This field has flourished due to the availability of large-scale datasets, closed-loop evaluation, and the increasing need for autonomous driving algorithms to perform effectively in challenging scenarios. In this survey, we provide a comprehensive analysis of more than 250 papers, covering the motivation, roadmap, methodology, challenges, and future trends in end-to-end autonomous driving. We delve into several critical challenges, including multi-modality, interpretability, causal confusion, robustness, and world models, amongst others. Additionally, we discuss current advancements in foundation models and visual pre-training, as well as how to incorporate these techniques within the end-to-end driving framework. To facilitate future research, we maintain an active repository that contains up-to-date links to relevant literature and open-source projects at https://github.com/OpenDriveLab/End-to-end-Autonomous-Driving.

Human trajectory prediction is a practical task of predicting the future positions of pedestrians on the road, which typically covers all temporal ranges from short-term to long-term within a trajectory. However, existing works attempt to address the entire trajectory prediction with a singular, uniform training paradigm, neglecting the distinction between short-term and long-term dynamics in human trajectories. To overcome this limitation, we introduce a novel Progressive Pretext Task learning (PPT) framework, which progressively enhances the model's capacity of capturing short-term dynamics and long-term dependencies for the final entire trajectory prediction. Specifically, we elaborately design three stages of training tasks in the PPT framework. In the first stage, the model learns to comprehend the short-term dynamics through a stepwise next-position prediction task. In the second stage, the model is further enhanced to understand long-term dependencies through a destination prediction task. In the final stage, the model aims to address the entire future trajectory task by taking full advantage of the knowledge from previous stages. To alleviate the knowledge forgetting, we further apply a cross-task knowledge distillation. Additionally, we design a Transformer-based trajectory predictor, which is able to achieve highly efficient two-step reasoning by integrating a destination-driven prediction strategy and a group of learnable prompt embeddings. Extensive experiments on popular benchmarks have demonstrated that our proposed approach achieves state-of-the-art performance with high efficiency. Code is available at https://github.com/iSEE-Laboratory/PPT.

Code agents can autonomously resolve GitHub issues, yet when they fail, current evaluation provides no visibility into where or why. Metrics such as Pass@1 collapse an entire execution into a single binary outcome, making it difficult to identify where and why the agent went wrong. To address this limitation, we introduce TRAJEVAL, a diagnostic framework that decomposes agent trajectories into three interpretable stages: search (file localization), read (function comprehension), and edit (modification targeting). For each stage, we compute precision and recall by comparing against reference patches. Analyzing 16,758 trajectories across three agent architectures and seven models, we find universal inefficiencies (all agents examine approximately 22x more functions than necessary) yet distinct failure modes: GPT-5 locates relevant code but targets edits incorrectly, while Qwen-32B fails at file discovery entirely. We validate that these diagnostics are predictive, achieving model-level Pass@1 prediction within 0.87-2.1% MAE, and actionable: real-time feedback based on trajectory signals improves two state-of-the-art models by 2.2-4.6 percentage points while reducing costs by 20-31%. These results demonstrate that our framework not only provides a more fine-grained analysis of agent behavior, but also translates diagnostic signals into tangible performance gains. More broadly, TRAJEVAL transforms agent evaluation beyond outcome-based benchmarking toward mechanism-driven diagnosis of agent success and failure.

Unmanned vehicle navigation concerns estimating attitude, position, and linear velocity of the vehicle the six degrees of freedom (6 DoF). It has been known that the true navigation dynamics are highly nonlinear modeled on the Lie Group of SE_{2}(3). In this paper, a nonlinear filter for inertial navigation is proposed. The filter ensures systematic convergence of the error components starting from almost any initial condition. Also, the errors converge asymptotically to the origin. Experimental results validates the robustness of the proposed filter.

Recent advances in end-to-end autonomous driving leverage multi-view images to construct BEV representations for motion planning. In motion planning, autonomous vehicles need considering both hard constraints imposed by geometrically occupied obstacles (e.g., vehicles, pedestrians) and soft, rule-based semantics with no explicit geometry (e.g., lane boundaries, traffic priors). However, existing end-to-end frameworks typically rely on BEV features learned in an implicit manner, lacking explicit modeling of risk and guidance priors for safe and interpretable planning. To address this, we propose FlowDrive, a novel framework that introduces physically interpretable energy-based flow fields-including risk potential and lane attraction fields-to encode semantic priors and safety cues into the BEV space. These flow-aware features enable adaptive refinement of anchor trajectories and serve as interpretable guidance for trajectory generation. Moreover, FlowDrive decouples motion intent prediction from trajectory denoising via a conditional diffusion planner with feature-level gating, alleviating task interference and enhancing multimodal diversity. Experiments on the NAVSIM v2 benchmark demonstrate that FlowDrive achieves state-of-the-art performance with an EPDMS of 86.3, surpassing prior baselines in both safety and planning quality. The project is available at https://astrixdrive.github.io/FlowDrive.github.io/.

Dataset Distillation is used to create a concise, yet informative, synthetic dataset that can replace the original dataset for training purposes. Some leading methods in this domain prioritize long-range matching, involving the unrolling of training trajectories with a fixed number of steps (NS) on the synthetic dataset to align with various expert training trajectories. However, traditional long-range matching methods possess an overfitting-like problem, the fixed step size NS forces synthetic dataset to distortedly conform seen expert training trajectories, resulting in a loss of generality-especially to those from unencountered architecture. We refer to this as the Accumulated Mismatching Problem (AMP), and propose a new approach, Automatic Training Trajectories (ATT), which dynamically and adaptively adjusts trajectory length NS to address the AMP. Our method outperforms existing methods particularly in tests involving cross-architectures. Moreover, owing to its adaptive nature, it exhibits enhanced stability in the face of parameter variations.

LLM-based agents increasingly solve complex tasks through long trajectories involving reasoning steps, tool calls, and inter-agent communication. However, when these agents fail, it is often unclear which agent caused the failure and which step introduced the decisive error. This attribution problem is challenging because mistakes can propagate across the trajectory: later actions may appear incorrect, but only because they depend on an earlier corrupted state. Therefore, failure attribution cannot be treated as independent step-level classification. We propose FALAT, a diagnostic framework for failure attribution in LLM agent trajectories. FALAT frames attribution as a dependency-guided search problem. It first constructs an expectation of how the task should be solved and uses this expectation to identify suspicious regions in the trajectory. It then traces dependencies among decisions, tool outputs, and agent messages to distinguish error-introducing steps from steps that merely inherit or propagate prior mistakes. Finally, FALAT evaluates whether correcting a candidate step would be sufficient to recover the expected outcome, allowing it to identify both the responsible agent and the decisive failure step. We evaluate FALAT on the Who&When benchmark, which includes both algorithm-generated and hand-crafted multi-agent failure trajectories. The results show that FALAT consistently improves responsible-agent and decisive-step attribution. Its best configurations achieve 46.0% step-level accuracy on algorithm-generated trajectories and 29.1% on the more challenging hand-crafted trajectories, outperforming specialized attribution baselines and direct prompting with standalone LLMs. These findings suggest that dependency-aware reasoning is essential for reliable failure diagnosis in LLM agent systems.

Large language model agents now act on codebases, browsers, operating systems, calendars, files, and tool ecosystems, but the benchmarks used to evaluate them are fragmented: each emphasizes a different unit of measurement (final task success, tool-call validity, repeated-pass consistency, trajectory safety, or attack robustness). A line of 2024-2025 work has converged on the diagnosis that a single accuracy column is no longer the right unit of comparison for deployable agents. AgentAtlas extends this line of work with four components: (i) a six-state control-decision taxonomy (Act / Ask / Refuse / Stop / Confirm / Recover); (ii) a nine-category trajectory-failure taxonomy with two orthogonal hierarchical labels (primary_error_source, impact); (iii) a taxonomy-aware vs. taxonomy-blind methodology that measures how much of a model's apparent capability comes from the supervision in the prompt; and (iv) a benchmark-coverage audit mapping fifteen agent benchmarks against six behavioral axes. To demonstrate the methodology we run a small fixed eight-model set (1,342 generated items, four frontier closed and four open-weight) under both prompt modes. Removing the explicit label menu drops every model's trajectory accuracy by 14-40 pp to a tight 0.54-0.62 floor regardless of family, and no single model wins on all three of control accuracy, trajectory diagnosis, and tool-context utility retention. We treat the synthetic run as a measurement-protocol demonstration, not a benchmark release.

We present a versatile NeRF-based simulator for testing autonomous driving (AD) software systems, designed with a focus on sensor-realistic closed-loop evaluation and the creation of safety-critical scenarios. The simulator learns from sequences of real-world driving sensor data and enables reconfigurations and renderings of new, unseen scenarios. In this work, we use our simulator to test the responses of AD models to safety-critical scenarios inspired by the European New Car Assessment Programme (Euro NCAP). Our evaluation reveals that, while state-of-the-art end-to-end planners excel in nominal driving scenarios in an open-loop setting, they exhibit critical flaws when navigating our safety-critical scenarios in a closed-loop setting. This highlights the need for advancements in the safety and real-world usability of end-to-end planners. By publicly releasing our simulator and scenarios as an easy-to-run evaluation suite, we invite the research community to explore, refine, and validate their AD models in controlled, yet highly configurable and challenging sensor-realistic environments. Code and instructions can be found at https://github.com/atonderski/neuro-ncap

While long-horizon agentic tasks require language agents to perform dozens of sequential decisions, training such agents with reinforcement learning remains challenging. We identify two root causes: credit misattribution, where correct early actions are penalized due to terminal failures, and sample inefficiency, where scarce successful trajectories result in near-total loss of learning signal. We introduce a milestone-guided policy learning framework, BEACON, that leverages the compositional structure of long-horizon tasks to ensure precise credit assignment. BEACON partitions trajectories at milestone boundaries, applies temporal reward shaping within segments to credit partial progress, and estimates advantages at dual scales to prevent distant failures from corrupting the evaluation of local actions. On ALFWorld, WebShop, and ScienceWorld, BEACON consistently outperforms GRPO and GiGPO. Notably, on long-horizon ALFWorld tasks, BEACON achieves 92.9% success rate, nearly doubling GRPO's 53.5%, while improving effective sample utilization from 23.7% to 82.0%. These results establish milestone-anchored credit assignment as an effective paradigm for training long-horizon language agents. Code is available at https://github.com/ZJU-REAL/BEACON.

Multivariate time series anomalies often manifest as shifts in cross-channel dependencies rather than simple amplitude excursions. In autonomous driving, for instance, a steering command might be internally consistent but decouple from the resulting lateral acceleration. Residual-based detectors can miss such anomalies when flexible sequence models still reconstruct signals plausibly despite altered coordination. We introduce AxonAD, an unsupervised detector that treats multi-head attention query evolution as a short horizon predictable process. A gradient-updated reconstruction pathway is coupled with a history-only predictor that forecasts future query vectors from past context. This is trained via a masked predictor-target objective against an exponential moving average (EMA) target encoder. At inference, reconstruction error is combined with a tail-aggregated query mismatch score, which measures cosine deviation between predicted and target queries on recent timesteps. This dual approach provides sensitivity to structural dependency shifts while retaining amplitude-level detection. On proprietary in-vehicle telemetry with interval annotations and on the TSB-AD multi-variate suite (17 datasets, 180 series) with threshold-free and range-aware metrics, AxonAD improves ranking quality and temporal localization over strong baselines. Ablations confirm that query prediction and combined scoring are the primary drivers of the observed gains. Code is available at the URL https://github.com/iis-esslingen/AxonAD.

Autonomous driving has seen significant progress, driven by extensive real-world data. However, in long-tail scenarios, accurately predicting the safety of the ego vehicle's future motion remains a major challenge due to uncertainties in dynamic environments and limitations in data coverage. In this work, we aim to explore whether it is possible to enhance the motion risk prediction capabilities of Vision-Language Models (VLM) by synthesizing high-risk motion data. Specifically, we introduce a Bird's-Eye View (BEV) based motion simulation method to model risks from three aspects: the ego-vehicle, other vehicles, and the environment. This allows us to synthesize plug-and-play, high-risk motion data suitable for VLM training, which we call DriveMRP-10K. Furthermore, we design a VLM-agnostic motion risk estimation framework, named DriveMRP-Agent. This framework incorporates a novel information injection strategy for global context, ego-vehicle perspective, and trajectory projection, enabling VLMs to effectively reason about the spatial relationships between motion waypoints and the environment. Extensive experiments demonstrate that by fine-tuning with DriveMRP-10K, our DriveMRP-Agent framework can significantly improve the motion risk prediction performance of multiple VLM baselines, with the accident recognition accuracy soaring from 27.13% to 88.03%. Moreover, when tested via zero-shot evaluation on an in-house real-world high-risk motion dataset, DriveMRP-Agent achieves a significant performance leap, boosting the accuracy from base_model's 29.42% to 68.50%, which showcases the strong generalization capabilities of our method in real-world scenarios.

Motion planning problems have been studied by both the robotics and the controls research communities for a long time, and many algorithms have been developed for their solution. Among them, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs), and the Probabilistic Road Maps (PRMs) have become very popular recently, owing to their implementation simplicity and their advantages in handling high-dimensional problems. Although these algorithms work very well in practice, the quality of the computed solution is often not good, i.e., the solution can be far from the optimal one. A recent variation of RRT, namely the RRT* algorithm, bypasses this drawback of the traditional RRT algorithm, by ensuring asymptotic optimality as the number of samples tends to infinity. Nonetheless, the convergence rate to the optimal solution may still be slow. This paper presents a new incremental sampling-based motion planning algorithm based on Rapidly-exploring Random Graphs (RRG), denoted RRT# (RRT "sharp") which also guarantees asymptotic optimality but, in addition, it also ensures that the constructed spanning tree of the geometric graph is consistent after each iteration. In consistent trees, the vertices which have the potential to be part of the optimal solution have the minimum cost-come-value. This implies that the best possible solution is readily computed if there are some vertices in the current graph that are already in the goal region. Numerical results compare with the RRT* algorithm.

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths have been designed principally under the assumption of Euclidean geometry, resulting in straight interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals. In this paper, we propose Metric Flow Matching (MFM), a novel simulation-free framework for conditional flow matching where interpolants are approximate geodesics learned by minimizing the kinetic energy of a data-induced Riemannian metric. This way, the generative model matches vector fields on the data manifold, which corresponds to lower uncertainty and more meaningful interpolations. We prescribe general metrics to instantiate MFM, independent of the task, and test it on a suite of challenging problems including LiDAR navigation, unpaired image translation, and modeling cellular dynamics. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction.

Inference-time steering enables pretrained diffusion/flow models to be adapted to new tasks without retraining. A widely used approach is the ratio-of-densities method, which defines a time-indexed target path by reweighting probability-density trajectories from multiple models with positive, or in some cases, negative exponents. This construction, however, harbors a critical and previously unformalized failure mode: Marginal Path Collapse, where intermediate densities become non-normalizable even though endpoints remain valid. Collapse arises systematically when composing heterogeneous models trained on different noise schedules or datasets, including a common setting in molecular design where de-novo, conformer, and pocket-conditioned models must be combined for tasks such as flexible-pose scaffold decoration. We provide a novel and complete solution for the problem. First, we derive a simple path existence criterion that predicts exactly when collapse occurs from noise schedules and exponents alone. Second, we introduce Adaptive path Correction with Exponents (ACE), which extends Feynman-Kac steering to time-varying exponents and guarantees a valid probability path. On a synthetic 2D benchmark and on flexible-pose scaffold decoration, ACE eliminates collapse and enables high-guidance compositional generation, improving distributional and docking metrics over constant-exponent baselines and even specialized task-specific scaffold decoration models. Our work turns ratio-of-densities steering with heterogeneous experts from an unstable heuristic into a reliable tool for controllable generation.

Ensuring vertical separation is a key means of maintaining safe separation between aircraft in congested airspace. Aircraft trajectories are modelled in the presence of significant epistemic uncertainty, leading to discrepancies between observed trajectories and the predictions of deterministic models, hampering the task of planning to ensure safe separation. In this paper a probabilistic model is presented, for the purpose of emulating the trajectories of aircraft in climb and bounding the uncertainty of the predicted trajectory. A monotonic, functional representation exploits the spatio-temporal correlations in the radar observations. Through the use of Gaussian Process Emulators, features that parameterise the climb are mapped directly to functional outputs, providing a fast approximation, while ensuring that the resulting trajectory is monotonic. The model was applied as a probabilistic digital twin for aircraft in climb and baselined against BADA, a deterministic model widely used in industry. When applied to an unseen test dataset, the probabilistic model was found to provide a mean prediction that was 21% more accurate, with a 34% sharper forecast.

LiDAR-based 3D sensors provide point clouds, a canonical 3D representation used in various scene understanding tasks. Modern LiDARs face key challenges in several real-world scenarios, such as long-distance or low-albedo objects, producing sparse or erroneous point clouds. These errors, which are rooted in the noisy raw LiDAR measurements, get propagated to downstream perception models, resulting in potentially severe loss of accuracy. This is because conventional 3D processing pipelines do not retain any uncertainty information from the raw measurements when constructing point clouds. We propose Probabilistic Point Clouds (PPC), a novel 3D scene representation where each point is augmented with a probability attribute that encapsulates the measurement uncertainty (or confidence) in the raw data. We further introduce inference approaches that leverage PPC for robust 3D object detection; these methods are versatile and can be used as computationally lightweight drop-in modules in 3D inference pipelines. We demonstrate, via both simulations and real captures, that PPC-based 3D inference methods outperform several baselines using LiDAR as well as camera-LiDAR fusion models, across challenging indoor and outdoor scenarios involving small, distant, and low-albedo objects, as well as strong ambient light. Our project webpage is at https://bhavyagoyal.github.io/ppc .

Generating accurate 3D reconstructions from endoscopic video is a promising avenue for longitudinal radiation-free analysis of sinus anatomy and surgical outcomes. Several methods for monocular reconstruction have been proposed, yielding visually pleasant 3D anatomical structures by retrieving relative camera poses with structure-from-motion-type algorithms and fusion of monocular depth estimates. However, due to the complex properties of the underlying algorithms and endoscopic scenes, the reconstruction pipeline may perform poorly or fail unexpectedly. Further, acquiring medical data conveys additional challenges, presenting difficulties in quantitatively benchmarking these models, understanding failure cases, and identifying critical components that contribute to their precision. In this work, we perform a quantitative analysis of a self-supervised approach for sinus reconstruction using endoscopic sequences paired with optical tracking and high-resolution computed tomography acquired from nine ex-vivo specimens. Our results show that the generated reconstructions are in high agreement with the anatomy, yielding an average point-to-mesh error of 0.91 mm between reconstructions and CT segmentations. However, in a point-to-point matching scenario, relevant for endoscope tracking and navigation, we found average target registration errors of 6.58 mm. We identified that pose and depth estimation inaccuracies contribute equally to this error and that locally consistent sequences with shorter trajectories generate more accurate reconstructions. These results suggest that achieving global consistency between relative camera poses and estimated depths with the anatomy is essential. In doing so, we can ensure proper synergy between all components of the pipeline for improved reconstructions that will facilitate clinical application of this innovative technology.

Unmodeled aerodynamic disturbances pose a key challenge for multirotor flight when multiple vehicles are in close proximity to each other. However, certain missions require two multirotors to approach each other within 1-2 body-lengths of each other and hold formation -- we consider one such practical instance: vertically docking two multirotors in the air. In this leader-follower setting, the follower experiences significant downwash interference from the leader in its final docking stages. To compensate for this, we employ a learnt downwash model online within an optimal feedback controller to accurately track a docking maneuver and then hold formation. Through real-world flights with different maneuvers, we demonstrate that this compensation is crucial for reducing the large vertical separation otherwise required by conventional/naive approaches. Our evaluations show a tracking error of less than 0.06m for the follower (a 3-4x reduction) when approaching vertically within two body-lengths of the leader. Finally, we deploy the complete system to effect a successful physical docking between two airborne multirotors in a single smooth planned trajectory.

We propose a data augmentation method for offline reinforcement learning, motivated by active positioning problems. Particularly, our approach enables the training of off-policy models from a limited number of suboptimal trajectories. We introduce a trajectory-based augmentation technique that exploits task structure and the geometric relationship between rewards, value functions, and mathematical properties of logging policies. During data collection, our augmentation supports suboptimal logging policies, leading to higher data quality and improved offline reinforcement learning performance. We provide theoretical justification for these strategies and validate them empirically across positioning tasks of varying dimensionality and under partial observability.

End-to-end autonomous driving models increasingly benefit from large vision--language models for semantic understanding, yet ensuring safe and accurate operation under long-tail conditions remains challenging. These challenges are particularly prominent in long-tail mixed-traffic scenarios, where autonomous vehicles must interact with heterogeneous road users, including human-driven vehicles and vulnerable road users, under complex and uncertain conditions. This paper proposes HERMES, a holistic risk-aware end-to-end multimodal driving framework designed to inject explicit long-tail risk cues into trajectory planning. HERMES employs a foundation-model-assisted annotation pipeline to produce structured Long-Tail Scene Context and Long-Tail Planning Context, capturing hazard-centric cues together with maneuver intent and safety preference, and uses these signals to guide end-to-end planning. HERMES further introduces a Tri-Modal Driving Module that fuses multi-view perception, historical motion cues, and semantic guidance, ensuring risk-aware accurate trajectory planning under long-tail scenarios. Experiments on the real-world long-tail dataset demonstrate that HERMES consistently outperforms representative end-to-end and VLM-driven baselines under long-tail mixed-traffic scenarios. Ablation studies verify the complementary contributions of key components.

Predicting future motion is crucial in video understanding and controllable video generation. Dense point trajectories are a compact, expressive motion representation, but modeling their future evolution from observed video remains challenging. We propose a framework that predicts future trajectories and visibility from past trajectories and video context. Our method has three components: (1) Grid-Anchor Offset Encoding, which reduces location-dependent bias by representing each point as an offset from its pixel-center anchor; (2) TrajLoom-VAE, which learns a compact spatiotemporal latent space for dense trajectories with masked reconstruction and a spatiotemporal consistency regularizer; and (3) TrajLoom-Flow, which generates future trajectories in latent space via flow matching, with boundary cues and on-policy K-step fine-tuning for stable sampling. We also introduce TrajLoomBench, a unified benchmark spanning real and synthetic videos with a standardized setup aligned with video-generation benchmarks. Compared with state-of-the-art methods, our approach extends the prediction horizon from 24 to 81 frames while improving motion realism and stability across datasets. The predicted trajectories directly support downstream video generation and editing. Code, model checkpoints, and datasets are available at https://trajloom.github.io/.

3D multi-object tracking (MOT) is vital for many applications including autonomous driving vehicles and service robots. With the commonly used tracking-by-detection paradigm, 3D MOT has made important progress in recent years. However, these methods only use the detection boxes of the current frame to obtain trajectory-box association results, which makes it impossible for the tracker to recover objects missed by the detector. In this paper, we present TrajectoryFormer, a novel point-cloud-based 3D MOT framework. To recover the missed object by detector, we generates multiple trajectory hypotheses with hybrid candidate boxes, including temporally predicted boxes and current-frame detection boxes, for trajectory-box association. The predicted boxes can propagate object's history trajectory information to the current frame and thus the network can tolerate short-term miss detection of the tracked objects. We combine long-term object motion feature and short-term object appearance feature to create per-hypothesis feature embedding, which reduces the computational overhead for spatial-temporal encoding. Additionally, we introduce a Global-Local Interaction Module to conduct information interaction among all hypotheses and models their spatial relations, leading to accurate estimation of hypotheses. Our TrajectoryFormer achieves state-of-the-art performance on the Waymo 3D MOT benchmarks. Code is available at https://github.com/poodarchu/EFG .

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

There are five types of trajectory prediction tasks: deterministic, stochastic, domain adaptation, momentary observation, and few-shot. These associated tasks are defined by various factors, such as the length of input paths, data split and pre-processing methods. Interestingly, even though they commonly take sequential coordinates of observations as input and infer future paths in the same coordinates as output, designing specialized architectures for each task is still necessary. For the other task, generality issues can lead to sub-optimal performances. In this paper, we propose SingularTrajectory, a diffusion-based universal trajectory prediction framework to reduce the performance gap across the five tasks. The core of SingularTrajectory is to unify a variety of human dynamics representations on the associated tasks. To do this, we first build a Singular space to project all types of motion patterns from each task into one embedding space. We next propose an adaptive anchor working in the Singular space. Unlike traditional fixed anchor methods that sometimes yield unacceptable paths, our adaptive anchor enables correct anchors, which are put into a wrong location, based on a traversability map. Finally, we adopt a diffusion-based predictor to further enhance the prototype paths using a cascaded denoising process. Our unified framework ensures the generality across various benchmark settings such as input modality, and trajectory lengths. Extensive experiments on five public benchmarks demonstrate that SingularTrajectory substantially outperforms existing models, highlighting its effectiveness in estimating general dynamics of human movements. Code is publicly available at https://github.com/inhwanbae/SingularTrajectory .