Trajectory Prediction

Accurate 4D trajectory prediction and closed-loop tracking are essential for Unmanned Aerial Vehicle (UAV) swarms to achieve safe and efficient operations in complex low-altitude environments such as urban airspaces, industrial sites, and indoor facilities. However, this task remains challenging due to intrinsic nonlinearity of UAV swarm dynamics and strict real-time constraints of swarm formation control. To address these challenges, we propose a unified framework that couples coarse-to-fine trajectory forecasting with uncertainty-aware Distributed Nonlinear Model Predictive Control (DNMPC). Our approach features two key innovations: 1) a dimension-decoupled trajectory prediction module that reduces computational complexity by forecasting axis-wise motion, and 2) a diffusion-based residual dynamics refinement module that captures temporally correlated dynamic uncertainties. These refined predictions are then integrated into a DNMPC loop to ensure formation stability. We also introduce a synchronized multi-scenario 4D UAV swarm dataset spanning six representative airspace scenarios. The dataset contains over \textbf{7,900} frames of synchronized three-UAV trajectories with frame-level annotations of speed intention and target sector. Extensive experiments demonstrate that our approach outperforms state-of-the-art baselines, reducing trajectory tracking error by up to \textbf{10-15%} and achieving sub-\textbf{0.07,m} average tracking error in complex urban and industrial environments, while maintaining real-time inference speeds of 34 FPS (sub-30 ms latency) suitable for agile flight.

Large-scale datasets and fast simulators have enabled improvements in driving policies that appear safe and robust, yet strong performance in nominal scenarios can still mask flawed reasoning and unsafe heuristics. Summary scores from closed-loop simulators do not give significant insight into the policy, making it difficult to determine whether they truly predict the motion of surrounding vehicles, how the ego vehicle generates future plans, or whether they merely rely on brittle heuristics that happen to succeed in nominal scenarios. To better understand the limits and weaknesses of driving policies, we focus on probing for forms of prediction, i.e., where surrounding vehicles will move next, and planning, i.e., understanding how to generate safe trajectories. We focus on these two capabilities because they reflect behaviors expected of effective driving policies, and use their presence or absence to assess policy quality across data-driven behavior cloning and simulation-driven reinforcement learning policies. To evaluate the presence of these capabilities, we investigate them as a function of scale, asking whether the closed-loop gains from larger datasets and longer simulation training reflect stronger prediction and planning or merely better behavioral heuristics. We use linear probing and targeted perturbations in both imitation learning and reinforcement learning models to track when these internal signals emerge, plateau, or fail. Despite good closed-loop performance, policies often fail to form timely surrounding-vehicle predictions during near-collision events, revealing a limitation in the predictive signals available for ego planning. Finally, causal intervention shows that correcting mistaken predictions improves ego planning toward safer trajectories.

The growing availability of trajectory datasets has fueled major advances in data-driven motion prediction. Yet, models trained on one dataset often fail to generalize beyond their training domain as a result of differences in scene layouts, agent behaviors, and sensing conditions. A framework that learns latent representations of datasets and quantifies their similarity using distributional metrics is presented. This large-scale study covers 24 major datasets, including the most widely used motion-prediction benchmarks, and shows that the resulting transferability scores strongly correlate with cross-dataset model performance. The results provide practical guidance for dataset selection, pretraining, and large-scale foundation models for motion prediction, paving the way toward more generalizable and robust predictive systems.

Autonomous driving systems are steadily moving toward end-to-end paradigms to mitigate the limited adaptability of rule-based pipelines in complex traffic environments. However, most existing learning-based methods still make decisions from static representations of the current scene, without explicit future rollouts or modeling of the temporal causal dynamics in traffic interactions. This limitation often results in unstable or overly conservative planning under high-uncertainty conditions, such as occlusions and unexpected events. To overcome these challenges, we introduce OWMDrive, a generative end-to-end driving framework built upon an Occupancy World Model for multi-step 3D occupancy forecasting, which serves as a conditional prior to guide diffusion-based planning. Conditioned on both current observations and predicted future states, the planner iteratively refines trajectory candidates to generate a reinforced driving trajectory. By explicitly modeling scene evolution over future horizons, OWMDrive captures key spatiotemporal causal dependencies, which leads to more foresighted and robust trajectory generation. Extensive experiments demonstrate that OWMDrive significantly improves planning reliability and safety, especially in challenging and partially observable driving scenarios.

Interactive video generation systems for camera-controlled world exploration roll out growing sequences of latent video frames, entangling state transition with high-frequency observation synthesis. We propose Walking in the Implicit, a scene-centric paradigm that changes the rollout variable from frame latents to a fixed-length, renderable implicit state, termed Neural Implicit Scene (NIS). This factorizes interactive generation into stochastic transition of a compact scene state and deterministic pose-conditioned rendering given the sampled state. We instantiate this paradigm as NeuWorld: a transformer VAE learns locally anchored NIS from sparse posed frames, and a diffusion transformer evolves NIS conditioned on future camera trajectories and geometry-aware retrieved history. By reusing the VAE encoder as a unified conditioner, NeuWorld maps camera, reference-image, and history cues into the same NIS modality, avoiding external heterogeneous encoders. Trained from scratch on public posed-view data without pretrained video backbones or auxiliary 3D reconstructors, NeuWorld achieves strong long-horizon consistency with favorable inference efficiency.

Vision-Language Models (VLMs) provide powerful semantic understanding and commonsense reasoning for End-to-End Autonomous Driving (E2E-AD) planning. However, trajectories directly generated by VLMs often encode only coarse driving intentions and remain insufficient for geometrically accurate, future-aware, and multi-view-grounded planning. To address these limitations, we develop the Layer-Wise World-Model-Guided Driving framework (LWDrive). LWDrive is a VLM planning framework that refines coarse trajectories through layer-wise world-model guidance. Instead of treating the VLM output as the final trajectory, LWDrive uses it as an intent-aware coarse plan, expands a diverse candidate space around it, and progressively refines the candidates through a Foresight Cascade Planner (FCP). Specifically, we introduce future-frame generation supervision to encourage the VLM to learn forward-looking scene representations, thereby injecting planning-relevant predictive dynamics into its internal hidden states. Built upon these world-model-supervised representations, FCP exploits VLM features across multiple layers and integrates historical temporal states, Action-Query representations, and current-frame multi-view Bird's-Eye-View (BEV) features to refine candidate trajectories in a coarse-to-fine manner. This design enables progressive correction of spatial positions and motion trends while grounding trajectory refinement with multi-view scene cues and preserving the high-level driving intention produced by the large model. Finally, a score head evaluates the refined candidates and selects the best trajectory as the final planning output. Experiments show that LWDrive achieves a score of 92.0 on the NAVSIM benchmark and 89.6 on NAVSIM-v2. Code and models will be made publicly available.

Predicting a patient's physiological trajectory under a planned treatment sequence is a prospective interventional problem, not standard time-series extrapolation. We study this problem in glucose management, where insulin and carbohydrate records are policy-dependent: future drivers are coupled to patient state, behavior, and clinical decision rules, so observational forecasting accuracy alone does not guarantee correct responses to planned interventions. We introduce Interventional Flow Matching (IFM), a continuous-time generative framework for physiologically constrained prospective forecasting. IFM conditions a flow-matching velocity field on patient history and planned future drivers in a bounded latent glucose space. Rather than embedding strict mechanistic glucose--insulin ODE equations or enforcing causality through rollout-based simulations, IFM uses a solver-free regularization: it penalizes the Jacobian of the instantaneous velocity field with respect to smoothed treatment drivers. This imposes signed, dose-bounded local sensitivities directly on the learned dynamics: insulin lowers glucose, carbohydrates raise it, and both responses remain within plausible ranges. On a simulated UVA/Padova type 1 diabetes cohort, IFM achieves the strongest balance between observed-driver RMSE and interventional response metrics. Across experiments, it consistently produces physiologically correct responses to both insulin and carbohydrate drivers while maintaining high directional, and ranking consistency.

The robustness of trajectory prediction models is crucial for developing safe autonomous driving systems. Adversarial attacks on trajectory prediction can significantly impair the accuracy of predicted trajectories, leading to hazardous driving behaviors. While heuristic defense strategies have been implemented to enhance the robustness of trajectory prediction models, these measures often fail against more sophisticated, targeted adversarial attacks. Hence, there is a pressing need to establish verifiable safety assurances for trajectory prediction models. In this paper, we extend the traditional Randomized Smoothing framework to "TrajRS", which provides a certified robust radius for smoothed trajectory predictors. We clarify and expand the formal definitions of robustness in trajectory prediction and tailor the practical TrajRS scheme specifically to "robustness for the optimal prediction" and "robustness for all possible predictions". An extensive set of experiments demonstrates that TrajRS effectively achieves robustness certification for all smoothed pedestrian trajectory predictors in this work.

The adoption of powerful diffusion models is hindered by their significant inference latency. Recent ``cache-then-forecast'' schemes alleviate this issue by accelerating DiTs using derivative-based polynomials, but they suffer from severe quality degradation at high acceleration ratios. Our analysis reveals its root cause: the discrete extrapolation performed on representations that are misaligned with the continuous diffusion trajectory and are numerically unstable. Thus, accelerated DiTs suffer from accumulated spatial errors, noisy derivative amplification, and high-order instability. We therefore reformulate accelerated inference as stable macro-trajectory extrapolation in ordinary differential equation (ODE) space. Instead of predicting intermediate features, we align forecasting with the model's Global Drift (GD), i.e., the end-to-end state evolution, thereby eliminating feature inconsistency and memory overhead. However, even this smooth macro-trajectory remains vulnerable to the derivative fallacy: its higher-order temporal derivatives are intrinsically noisy. Thus, we introduce a derivative-free barycentric Lagrange extrapolator to effectively bypass derivative instability and approximation error. We further propose a bounded Phase Mapping that regularizes the extrapolation domain, suppressing oscillatory error growth. These elements collectively constitute ResilPhase, a noise-resilient acceleration framework. Experiments on FLUX.1-dev and HunyuanVideo demonstrate state-of-the-art fidelity under aggressive acceleration ratios.

Motion forecasting is essential for autonomous driving systems to enable safe decision-making and planning in complex driving scenarios. While existing predictors excel at minimizing standard displacement errors, they often overlook the adherence to lane topology of multimodal predictions, particularly for lower-probability modes. Consequently, predicted trajectories may violate physical and logical constraints, making the prediction set unreliable for safety-critical planning. In this paper, we propose LAMP (Lane-Aligned Motion Primitives), a topology-aware forecasting framework that anchors multimodal prediction to structured motion primitives aligned with lane topology. Specifically, we use a VQ-VAE to learn shape-aware motion primitives as discrete intention queries, capturing spatiotemporal patterns beyond endpoint-based intentions. We further introduce a feasibility-aware intention selector trained with a lane-topology prior for filtering unreachable intention queries, guiding the decoder to prioritize topology-consistent intentions while preserving behavioral diversity. Extensive experiments on the Argoverse 2 dataset demonstrate that LAMP achieves prediction accuracy comparable to state-of-the-art baselines while outperforming them in feasibility and diversity metrics.

Trajectory forecasting for autonomous driving has advanced rapidly, yet representative models often produce uninformative posteriors over forecast modes, causing problems for mode pruning. We trace this to a modeling-training mismatch: forecasters are typically modeled as conditional Gaussian mixture models (GMMs) but trained with a winner-take-all (WTA) loss that assigns each sample to its nearest mode. We argue that this K-means-like hard assignment (one-hot), while preventing mode collapse, is the source of uninformative mode probabilities: it over-segments the trajectory space, ignores relatedness among nearby modes, and yields assignment instability under small perturbations. Guided by this lens, we introduce two post-hoc treatments: (1) test-time posterior-weighted merging that aggregates nearby candidate trajectories; and (2) a one-step expectation-maximization (EM) update that replaces hard labels with soft responsibilities, sharing probability mass across neighboring modes. Across several WTA-trained architectures, these lightweight steps produce more informative, faithfully ranked mode posteriors and strengthen final forecasts on popular displacement metrics -- without retraining. Our analysis unifies recent design choices through a GMM-vs-K-means perspective and offers principled, practical corrections that better align training objectives with inference.

Diffusion models have shown strong potential for multi-modal planning in end-to-end autonomous driving. However, most existing methods confine diffusion to the planning module, conditioning on fixed outputs from separate discriminative perception networks. This decoupled design propagates perception errors to the planner, increasing optimization difficulty and reducing robustness. To overcome these limitations, we propose UniTeD, a Unified Temporal Diffusion framework that jointly models perception and planning through iterative denoising in a shared generative space. By enabling bidirectional information exchange, the framework facilitates mutual refinement between tasks and improves robustness via noise-conditioned multi-task training. We further extend this unified diffusion paradigm to a streaming setting by incorporating temporal context. A Temporal Transition Module (TTM) is introduced to resolve the noise-level mismatch between historical and current frames. In addition, we propose an Anchor Refresh Strategy (ARS) to alleviate the training-inference distribution shift commonly observed in sparse diffusion-based end-to-end driving frameworks. Without bells and whistles, UniTeD achieves state-of-the-art performance across multiple benchmarks, surpassing both recent discriminative end-to-end methods and diffusion-based planning approaches.

High-level humanoid planners often output sparse task-space, low-rate trajectories, whereas whole-body controllers run at high frequency. This creates temporal asynchrony between the planning and execution, and structural incompleteness for full-body control. We propose an asynchronous upper body task-space tracking framework for humanoids. A student policy is initialized by teacher-student distillation, conditioned on the full cached future trajectory and an execution-time index, and trained with a sliding-window global reward to reduce frame drift without explicit frame estimation. For task-specific post-training, an MPC module completes sparse references into floating-base and upper-body guidance, while action- and FK level self-guidance constrain policy drift. Simulation and Unitree G1 hardware experiments show improved tracking under low update rates, stronger performance than synchronous and decoupled baselines, and safer adaptation to out-of-distribution motions.

Longitudinal modelling of Alzheimer's disease progression is clinically useful only if it can describe not just the most likely next diagnosis, but how a patient may evolve over time and how reliable that forecast is. Most deep learning approaches reduce this problem to single-step classification, treating cognitively normal, mild cognitive impairment, and dementia as flat categories while providing limited insight into how uncertainty accumulates across future visits. We propose a probabilistic framework that combines ordinal diagnosis prediction, multi-horizon trajectory generation, and decomposed uncertainty estimation. A Temporal Fusion Transformer encoder is adapted with a CORAL ordinal output layer, asymmetric loss weighting, and converter oversampling to respect disease-stage ordering and improve sensitivity to MCI-to-dementia transitions. Conditioned on the learned patient-context representation, an autoregressive Mixture Density Network generates five-year probabilistic trajectories for diagnosis state, CDR Sum of Boxes, MMSE orientation, and hippocampal volume. On ADNI, the model outperforms linear, recurrent, and transformer baselines for next-visit diagnosis prediction, with the strongest gains on MCI-versus-dementia discrimination. Generated trajectories achieve near-nominal 90% credible interval coverage, widening uncertainty across the forecast horizon, and biomarker dynamics consistent with expected Alzheimer's disease progression. We further separate aleatoric from epistemic uncertainty using analytic mixture variance and a five-member bootstrap ensemble, which provides the strongest encoder diversity and output-level epistemic signal. Epistemic uncertainty is higher for rare progression archetypes, MCI and dementia patients, and under external evaluation on OASIS-3, where it increases alongside prediction error.

Conventional visual navigation policies often struggle with myopic decision-making and mode collapse in complex environments. While world models offer a promising alternative, existing paradigms typically isolate perception, generation, and control, failing to capture their shared spatio-temporal dynamics. In this paper, we propose NavWM, a unified navigation world model that seamlessly integrates latent world reasoning, multimodal action prediction, and controllable visual generation. At its core, NavWM leverages latent world tokens to distill geometric and semantic priors, endowing the agent with robust structural understanding. To overcome the limitations of deterministic policies, we introduce an anchor-based multimodal trajectory forecasting framework that generates a diverse action space. This inherent diversity explicitly empowers the generative world model to act as a robust closed-loop planner, utilizing visual foresight to evaluate and select the optimal path. Extensive experiments across diverse robotics datasets demonstrate that NavWM significantly advances the state-of-the-art, delivering remarkable improvements in both high-fidelity future state generation and zero-shot navigation success.

Traffic microsimulators rely on hand-crafted behavior models that reproduce aggregate flow but miss the heterogeneous interactions between vehicles at signalized intersections. Learned trajectory predictors capture richer interactions but are short-horizon and tend to be unstable when run in closed loop. We present Enactor, an actor-centric generative model for closed-loop intersection microsimulation. The model focuses on vehicles; pedestrians are included as context that can influence vehicle decisions but not predicted. Dynamic actors and lane polylines are encoded in polar coordinates referenced to the intersection center. A transformer with separate spatial and temporal attention blocks predicts a distribution over each actor's next-step motion ($s$, $α$). Training uses a closed-loop curriculum so the model is exposed to its own predictions. We evaluate Enactor in two regimes. In a 4000-second simulation-in-the-loop test at two intersection geometries, Enactor controls every dynamic vehicle against a continuously refreshing actor set rather than the fixed cohort that learned trajectory predictors are usually evaluated against. It recovers the SUMO data generator's speed and travel-time distributions with KL divergence over an order of magnitude lower than a recent transformer baseline on travel time, and substantially lower on speed (roughly $5\times$ lower at Site 1), and reduces red-light violations relative to the same baseline by more than an order of magnitude. An ablation isolates the leader rear-bumper feature as the change with the largest effect on intersection-aware safety metrics. We also evaluate on real-world field data and apply the same architecture to naturalistic vehicle trajectories from a fish-eye camera at a signalized intersection and evaluate it on multi-horizon predictive tasks. Enactor outperforms a constant-velocity baseline at every horizon evaluated.

Accurate dynamics models are critical for informed decision-making in robotic systems, particularly for agile aerial vehicles operating under uncertainty. Neural network dynamics models are attractive for capturing complex nonlinear effects, but existing predictive approaches struggle with long-horizon forecasting because their autoregressive rollout mechanism amplifies errors over time. Joint Embedding Predictive Architectures (JEPAs) offer a compelling alternative by modeling dynamics in latent space, yet prior JEPA-style methods for robot navigation have been studied primarily for kinematic-level planning, with limited investigation in high-frequency control. In this work, we introduce the JEPA-style model for real-time quadrotor control. The proposed approach combines a latent dynamics model with a novel physics-inspired prober that maps frozen latents to interpretable state, enabling physically grounded long-horizon prediction. Additionally, we combine the learned model with a sampling-based optimal control solution to take advantage of its predictive capabilities for real-time control on embedded hardware. Finally, to reduce the dependence on expensive and unsafe real-world data collection, we develop a structured pipeline for automated dataset generation. Extensive open-loop and outdoor closed-loop experiments demonstrate accurate prediction, robust zero-shot sim-to-real transfer, and strong generalization across diverse operating conditions.

Instruction-conditioned trajectory prediction is an emerging problem in autonomous driving, where a model predicts the future ego trajectory not only from visual scene context and historical motion, but also from a natural-language maneuver instruction. This paper presents our submission to the doScenes Instructed Driving Challenge, built upon OmniDrive, a vision-language-action driving agent with 3D perception, reasoning, and planning capabilities. We adapt OmniDrive to the doScenes setting by training it on instruction-annotated nuScenes scenes and generating a 6-second ego trajectory represented by 12 future waypoints. To improve multi-view visual grounding, we further introduce a DVPE-style divided-view perception module into the OmniDrive perception head. Instead of attending globally to all camera features, the proposed module groups query features and image tokens into divided local view spaces and performs visibility-aware cross-attention within each view. This design reduces irrelevant cross-view interference and helps the model better align language instructions with local driving-relevant visual evidence. The code is publicly available at: https://github.com/feel12348/doscenes-omnidrive.

Trajectory prediction allows autonomous vehicles to anticipate the future behavior of surrounding objects (or agents) and, accordingly, maximize the safety and efficiency of their driving. State-of-the-art Transformed-based interaction-aware trajectory prediction models, which rely on attention mechanisms to capture multi-agent interactions and maximize prediction accuracy, are commonly trained and evaluated on long-range high-quality datasets. These datasets are typically obtained by aggregating data from multiple vehicles or drones and removing any object detection or tracking noise offline. Yet, information about a surrounding object's state (its position, speed, heading) is far from being noiseless in real-world deployments. Object state estimation is affected by perception uncertainties and localization errors that can be particularly large for objects received via Vehicle-to-Everything (V2X) communications. In this paper, we analyze the impact of noisy object state information on the trajectory prediction accuracy of a state-of-the-art Transformer-based interaction-aware trajectory prediction model. Our study demonstrates that trajectory prediction accuracy can rapidly deteriorate as the noise intensity increases. Numerical results show that the prediction accuracy can reduce by a 1.3x factor under small noise levels and by as much as a 3.9x factor under the highest (yet realistic) noise conditions. These findings reveal the strong sensitivity of trajectory prediction models to noisy data, underscoring the need for more realistic training and evaluation datasets as well as noise mitigation strategies.

Long-horizon spacecraft trajectory forecasting suffers from error accumulation due to the absence of corrective observations in the forecast regime, making reliable uncertainty estimation crucial for safety-critical decision-making such as space domain awareness and conjunction assessment. While high-fidelity physics-based orbit propagators provide accurate deterministic forecasts, they typically lack calibrated uncertainty estimates over long horizons. We introduce a Predictor--Corrector framework in which a physics-based continuous-time $\textit{deterministic}$ forecaster is augmented with a learned continuous-time $\textit{probabilistic}$ Corrector that models forecast errors. The proposed Corrector can be wrapped around an existing deterministic propagator to improve forecast accuracy while producing sharp and calibrated full-covariance uncertainty estimates. The Corrector is based on Latent Neural Controlled Differential Equations (Latent NCDEs) and models the probabilistic temporal evolution of forecast errors in continuous time, naturally supporting irregular sampling and missing features. We further introduce a loss function that promotes calibration and sharpness in long-horizon uncertainty propagation. We evaluate the proposed framework on long-horizon spacecraft trajectory forecasting using real-world data from NASA's Crustal Dynamics Data Information System (CDDIS), wrapping the Corrector around NASA's General Mission Analysis Tool (GMAT). Across forecast horizons of 2--4 days without observations and six rolling test windows, the proposed approach consistently improves accuracy and uncertainty calibration compared to deterministic baselines and Latent ODE-based correctors, demonstrating the effectiveness of the continuous-time probabilistic Corrector for trajectory forecasting.

Camera-first autonomous-driving models predict future ego waypoints from images, ego-state features, and route commands, but waypoint supervision alone does not explicitly supervise actor-level representations of nearby road users. We study this as supervised representation learning for open-loop waypoint prediction. The deployable model uses multi-view RGB, ego state, and route command at inference. During training, simulator-derived sidecar labels supervise actor grounding, privileged hindsight actor relevance relative to the logged ego trajectory, and selected-actor short-horizon motion; these labels are never inference inputs. We evaluate route-disjoint splits with matched architecture, optimizer, validation criterion, checkpoint selection, and three seeds. A plain waypoint-only RGB baseline obtains 1.815$\pm$0.02 m final displacement error (FDE), and the matched no-teacher non-sidecar RGB control obtains 1.716$\pm$0.02 m. Road-user sidecar supervision (RU-sidecar) reduces FDE to 1.223$\pm$0.01 m, a 32.6% reduction over the plain baseline and 28.7% over the matched no-teacher non-sidecar RGB control. It improves over the plain baseline on 1445/1494 routes and over the matched no-teacher non-sidecar RGB control on 1417/1494 routes. Actor-conditioned slices show gains in all nonempty subsets, including 29.1% reduction for samples with at least four valid sidecar actors and 30.0% when a vulnerable road user is present. Optional simulator-state teacher alignment reaches 1.186$\pm$0.15 m FDE, but higher seed variability makes it secondary. Non-deployable simulator-state diagnostics remain stronger, indicating a privileged-to-camera gap. The evidence is limited to open-loop simulation diagnostics.

Autonomous vehicles must plan trajectories that satisfy a multitude of requirements on safety, passenger comfort, and compliance with traffic rules. However, in safety-critical scenarios, it is not always possible to satisfy all requirements simultaneously, necessitating their prioritization based on importance. At the same time, in these safety-critical scenarios, the uncertainty in trajectory predictions of the surrounding traffic, such as other vehicles and pedestrians, should be explicitly accounted for. In this work, we propose an uncertainty-aware trajectory planning framework that incorporates a predefined lexicographic ordering over Signal Temporal Logic (STL) specifications that stays valid under uncertainty. We implement this formulation with Model Predictive Path Integral (MPPI) control and we demonstrate the effectiveness of our method on simulation scenarios, showing that our framework efficiently handles conflicting objectives under realistic multi-modal uncertainty.

This paper proposes a constant time-delay trajectory tracking method for vehicle convoys operating without inter-vehicle communication, a common coordinate system, or global positioning. The method integrates a probabilistic sequence-to-sequence (Seq2Seq) neural network with an invariant extended Kalman filter (IEKF) to warm-start the prediction process, allowing accurate estimation of a leader vehicle's relative trajectory on the SE(2) manifold. A geometric model predictive controller is further incorporated to fully exploit the manifold-based trajectory predictions for improved control performance. The system can handle arbitrary nonlinear trajectories with varying speeds and motion profiles while reducing the need for expert-based domain knowledge for the design of trajectory following systems, even under long trajectory delays. The effectiveness of the method is validated through comparisons with a pure IEKF baseline, learning-based methods, and the ground-truth trajectory in kinematic simulations, as well as in experiments using real robotic vehicles.

Pedestrian trajectory prediction from an ego-centric camera is challenging since it depends on complex interactions with vehicles and scene context, as well as the intention of the pedestrian. By modelling correlation and intent from the historical and future trajectories of the pedestrian, it will usually result in a multimodal (i.e. multiple modes) distribution. Existing stochastic predictors often sample multiple futures from a single unimodal distribution, which can yield sub-optimal 'mixed-mode' trajectories that lie between distinct motion patterns and become implausible in real scenes. In this paper, we propose MMPM, a mode-aware framework that separately models future trajectory distributions into semantically meaningful modes based on the pedestrian's crossing behavior. MMPM consists of two modules: behavior-aware Pedestrian Interaction Module (PIM) that jointly captures pedestrian-vehicle and pedestrian-environment interactions by introducing gaze, head and hand gesture, and a CVAE-based Mode-aware Trajectory Predictor (MTP) module to model the future trajectory distributions on two modes, crossing and non-crossing the road, separately. A query-based decoder further enforces mode consistency during decoding. Experiments on PIE and JAAD datasets show that our method surpasses state-of-the-art baselines. Our proposed MTP is model-agnostic, which can be integrated into existing frameworks such as BiTrap-NP and SGNet-ED to further improve future trajectory prediction performance. We additionally introduce a data-driven validation protocol that matches predictions to spatio-temporally consistent ground-truth trajectories, demonstrating improved frame-wise displacement errors over previous work.

Motion forecasting is central to visual intelligence: agents must anticipate how objects will move in order to plan actions, reason about physical interactions, and synthesize realistic futures. We argue that 3D points in world coordinates provide a general representation that is class-agnostic, view-stable, compact, and directly useful for downstream tasks. We formalize the task of goal-conditioned 3D point motion forecasting: given a short visual history, a set of 3D query points on an object of interest, and a language description of the intended goal, the model predicts the future 3D trajectory of each point. We introduce a full stack to study this task at scale: (1) MolmoMotion-1M is a large corpus of action-described, object-grounded 3D point trajectories annotated from 1.16M unconstrained videos; (2) PointMotionBench is a human-verified benchmark spanning 111 object categories and 61 motion types; and (3) MolmoMotion is a general motion forecasting model that supports both autoregressive coordinate prediction and flow-matching-based trajectory generation. MolmoMotion accurately predicts diverse motion patterns with different language instructions, and significantly outperforms existing motion prediction baselines on PointMotionBench. Finally, we show that the learned 3D motion prior transfers well to downstream applications: it improves training efficiency and generalization for robot manipulation, and its predicted trajectories provide effective motion guidance for generative models to synthesize videos with more realistic object motion.

Adaptive torque prediction in dynamic exoskeleton scenarios requires expensive motion capture systems, which are infeasible in complex outdoor environments. Trajectory prediction has emerged as one of the effective approaches to address such an issue. However, the core challenges of exoskeleton trajectory prediction are twofold: establishing the mapping from multi-modal features to trajectory information; constructing the mapping from trajectory to torque. For the former, most existing methods perform only single-step prediction and neglect inter-subject trajectory variability, thereby limiting the trajectory optimization space and prediction generalization. To address this, this paper proposes a fast flow matching method that enables accurate trajectory prediction and better generalization for real-time performance, where trajectory generation errors and encoded observations are used to guide the training direction. For the second challenge, due to the high dynamics of the human-robot system and the strong coupling between perception and control, simple control methods struggle to achieve efficient assistance based on the predicted trajectory. This paper utilizes model predictive control and designs a novel optimization objective to optimize torque, ensuring the exoskeleton achieves comfortable and robust assistance. By integrating the above two components, the unified policy, denoted as ExoTraj, is developed to enable adaptive assistance in complex outdoor scenarios without high data acquisition cost. Experimental results show that compared to traditional methods, ExoTraj reduces cross-subject prediction error by 14.0% during the online phase and maintains robustness against external noise. Relative to the zero torque condition, ExoTraj decreases metabolic rate by 11.5-24.4%, heart rate by 1.7-19.5%, and peak muscle activation levels by 10.9-41.3%, respectively.

End-to-end autonomous driving has made significant progress by unifying perception, prediction, and planning within a single learning framework, achieving strong performance in short-horizon decision making. However, most existing E2E-AD methods remain confined to short-horizon planning and lack the ability to model long-term temporal dependencies, which severely limits their generalization and security in complex and highly interactive driving scenarios. In this work, we propose GraphWorld, an E2E-AD framework that explicitly enhances long-horizon planning through latent world modeling. We introduce an Ego-Centric Interaction Graph, which adaptively models critical neighboring agents based on spatial proximity, and propagates relational context to planning queries via cross-node cross-attention. We present a World-State-Conditioned Planning that learns ego-centric latent world representations by modeling interactions between an ego vehicle and surrounding agents. This latent world state captures key interaction dynamics and safety-relevant semantics, and serves as a conditioning signal to guide long-horizon, safety-aware trajectory planning. Extensive experiments on Bench2Drive, NAVSIMv1/2, and nuScenes demonstrate that GraphWorld significantly reduces collision rates and improves long-horizon planning performance, validating its effectiveness in complex driving environments.

Vessel trajectory prediction is important for intelligent shipping, maritime surveillance, and navigation safety. However, existing public maritime AIS resources are often limited by inconsistent forecasting protocols, uneven data quality, and the lack of benchmark-ready contextual annotations, which hinder fair comparison and context-aware modeling. To address this gap, we present EnvShip-Bench, a unified benchmark for short-term vessel trajectory prediction built from large-scale raw AIS data from the Danish Maritime Authority (DMA) and NOAA through a common processing pipeline. EnvShip-Bench adopts a standardized forecasting protocol with 10 minutes of observation, 10 minutes of prediction, and 20-second sampling in vessel-centric local metric coordinates. Beyond the large-scale core benchmark, it provides a quality-first compact subset for efficient and reproducible experimentation, together with synchronized environmental and nearby-vessel context extensions. As a result, EnvShip-Bench supports trajectory-only, environment-aware, and interaction-aware forecasting under a unified evaluation framework. Extensive benchmark statistics and analysis demonstrate that EnvShip-Bench offers a standardized, extensible, and context-aware foundation for maritime trajectory forecasting research.

Autonomous driving systems rely on precise trajectory prediction to plan safe and efficient movement. Graph Neural Networks (GNNs) have become a promising approach for modelling spatiotemporal interactions among road agents. However, designing GNN architectures for trajectory prediction remains non-standardized, with little guidance on which graph layers effectively capture spatial interactions and temporal dynamics. This paper offers a detailed comparative study of 19 graph layer types, focusing on their spatial and temporal processing capabilities to discover the most effective architectures for trajectory prediction. Within the explored hyperparameter setting, we highlight five standout layer combinations, with ARMA, Chebyshev, and topology-aware layers consistently performing better than others. Beyond performance metrics, our findings yield practical design principles: sum-based aggregation is more effective than mean-based methods, multi-head attention mechanisms enable richer interactions, and assigning different weights to different hop distances significantly improves prediction accuracy. These findings offer useful guidance for designing more interpretable and effective trajectory prediction models.

Accurate and computationally efficient vehicle models are essential for motion planning of autonomous vehicles, where positional accuracy directly affects trajectory feasibility and safety. However, the positional accuracy has not been systematically evaluated against real measurements. Therefore, this paper compares the short-horizon positional accuracy of three single-track vehicle models against vehicle measurements across various driving maneuvers. Model parameters are identified through dedicated experiments with the instrumented test vehicle. Rather than identifying a single best model, this work aims to provide insight into the trade-offs between model complexity, parameterization quality, and positional accuracy for informed model selection in Model Predictive Control applications.

End-to-end autonomous parking has emerged as a critical task within the realm of autonomous driving. However, existing methods suffer from black-box characteristics, lacking high-level semantic understanding and interpretability, which impedes the realization of seamless long-distance autonomous parking from the road to the target spot. To address these limitations, we propose ParkingTransformer, a novel framework that leverages multi-view perception and the scene understanding capability of Large Language Models (LLMs). By combining trajectory queries with LLMs implicit state features, our method interacts directly with historical information and raw sensor data to output planning trajectories, eliminating the need for dense Bird's-View (BEV) representations. To compensate for the inadequate spatial reasoning ability of LLMs, we introduce 3D positional encoding to explicitly inject spatial geometric awareness. Furthermore, a fixed-window streaming mechanism is designed for historical information processing, significantly improving long-term temporal processing efficiency and inference speed. Additionally, a coarse-to-fine decoding strategy is employed to progressively enhance trajectory precision. Extensive closed-loop experiments are conducted on the CARLA simulator and real-world vehicle platforms. The results demonstrate that our method achieves a driving score of 61.32 in CARLA simulator and an average success rate of 88.70% in real-world experiments, validating the feasibility and effectiveness of the proposed algorithms.

We introduce First-Order Trajectory Matching (FTM), a surrogate-modeling method that learns the first-order local transport of probability mass from trajectories of stochastic systems. By matching the symmetric first-order motion of trajectories, FTM learns the probability current velocity, whose flow preserves time marginals to match ensemble averages, while also capturing current-like trajectory quantities such as fluxes, circulations, and barrier-crossing currents. FTM learns the current velocity directly from trajectories, avoiding drift, diffusion, and score estimation. Our stability analysis separates discretization error from sampling variance and shows that the one-step simulation-free FTM loss is stable when temporal resolution and sample size are properly balanced. Across stochastic dynamical systems and PDE examples, we empirically demonstrate that FTM provides trajectory-aware ensemble predictions at low, deterministic-rollout cost.

Learning-based motion planners, despite recent progress, often suffer from temporal inconsistency. Small perturbations across frames can accumulate into unstable trajectories, degrading comfort and safety in closed-loop driving. Several methods attempt to inject history as a static conditioning signal to stabilize outputs, only to induce the planner to copy historical patterns instead of adapting to environment contexts. To address this limitation, we propose Diffusion Forcing Planner (DFP), a diffusion-based planning framework driven by history-guided control. Specifically, DFP decomposes the full trajectory into history, current and future segments, and assign independent noise levels to each segment. The model jointly denoises the historical and the future segments, enforcing a heterogeneous joint diffusion process. At inference, classifier-free guidance (CFG) is applied to steer future sampling using annealed history in a controllable manner. Closed-loop evaluation and comprehensive ablations on nuPlan show that DFP achieves competitive performance while producing continuous, stable, and controllable motion plans in complex driving scenarios.

Autonomous race cars, such as in Formula Student Driverless, operate close to their physical handling limits. The resulting highly nonlinear vehicle behavior increases the path tracking complexity, especially on narrow tracks. Model Predictive Control (MPC) is commonly used to address this issue, a method whose performance is closely tied to the accuracy of the underlying prediction model. This paper presents a novel, real-time capable prediction model for autonomous race cars that adjusts to changing conditions by combining information from past runs and the current driving situation. Our model is divided into three consecutive submodels: a nominal Kinematic Bicycle Model, an offline Bayesian Linear Regression (BLR) model, and an online Sparse Gaussian Process Regression (SGPR) model. The proposed approach enables efficient integration of all available data without significantly increasing computational cost, ensuring high prediction accuracy and a quantitative uncertainty assessment right from the start of the run. Compared to existing approaches, an improvement in prediction accuracy of up to 57% was achieved. Further, we successfully demonstrated the practical applicability of the model within an MPC-based path tracking controller on a real Formula Student race car.

We present NOVA, an autonomous symbolic regression framework that identifies interpretable car-following and lane-change structures from raw trajectory data with minimal behavioral priors. Applied to 4,765,788 active driving observations from the NGSIM I-80 and US-101 datasets, NOVA's deterministic Rust-powered search engine evaluates over 10,000 candidate algebraic structures and identifies a compact two-term acceleration model under a forward-shifted rolling-mean prediction target. Evaluated under two complementary preprocessing pipelines, NOVA achieves $RMSE = 1.376 m/s^2$ ($R^2 = 15.57\%$) on the intent-forecasting benchmark, outperforming the best recalibrated symbolic-regression baseline (SR-LLM, PNAS~2025) by 0.135 m/s$^2$ in RMSE under an identical evaluation protocol. Across eight independent experiments, a single dominant nonlinear term emerges as a robust backbone of human car-following; a residual-guided extension further links the selected structure to an established psychophysical theory of collision avoidance. The discovered feature operators transfer zero-shot between freeway sites with under 3 pp $R^2$ loss. Extended to lane-change modelling within a multinomial logit framework, NOVA achieves 67.4% balanced accuracy under strict vehicle-ID holdout on 502 unseen drivers, surpassing existing lane-changing baselines by +29.8 percentage points on a three-class problem.

Long-horizon maritime trajectory prediction is important for shipping management, logistics planning, and maritime risk analysis, yet month-level forecasting remains insufficiently studied. Existing deep learning methods mainly focus on short- and mid-term coordinate extrapolation and often struggle to preserve route feasibility and destination correctness over extended horizons. This paper investigates joint long-horizon vessel trajectory and destination forecasting with reasoning-capable large language models, and develops a Maritime LLM post-training framework based on Reinforcement Learning with Verifiable Reward (RLVR). An AIS-based benchmark is constructed with 60-day historical trajectories and 30-day forecasting horizons, where trajectories are converted into semantic textual representations for RL prompt construction. RLVR aligns LLMs with maritime forecasting objectives by enforcing physical validity, providing early-weighted trajectory supervision, and evaluating destination correctness through hierarchical matching and curriculum learning. Experimental results show that RLVR-trained LLMs substantially improve over zero-shot LLMs and representative deep learning baselines, especially on destination-related metrics. Among the evaluated RLVR-trained variants, 4B LLMs achieve the best overall performance, suggesting that reward-compatible optimization and task-specific capacity matching are more important than simply using larger 8B or 14B LLMs. The results also show that LSTM remains a strong deep learning baseline under limited fine-tuning data, while Transformer-style spatio-temporal models typically require larger datasets and richer structured inputs. Overall, this work advances semantic, verifier-aligned maritime forecasting for operational decision support.

Alzheimer's disease is a progressive neurodegenerative disorder, and its progression varies substantially across patients. Existing work aims to forecast patients' future cognitive state, with minimal focus on reconstructing the state from past visits. Furthermore, in current research, quantifying predictive uncertainty remains underexplored and relies on costly modalities such as MRI, PET, and CSF, limiting their deployment in resource-limited settings. In this research, our primary objectives are: First, bidirectional prediction of cognitive scores from irregular visits to present the complete disease trajectory. Second, to enable interpolation and extrapolation capabilities to assist clinicians in informed prognostic decision making, and third, to provide a well-calibrated uncertainty estimate for all predictions, and finally, to achieve the objectives using the modalities available during routine visits. We propose a unified framework, GNOVA: A GRU-Neural ODE Variational Autoencoder. The architecture combines a Gated Recurrent Unit encoder and a Neural ODE decoder within a variational autoencoder framework. In our work, we forecast the CDR-SB and MMSE Scores. The GRU encoder allows for any number of inputs at any time point. The Neural-ODE decoder performs continuous estimation, allowing interpolation and extrapolation at any desired time point. The Variational autoencoder allows for uncertainty estimation in predictions. We worked with 1,727 patients from the ADNI dataset over 10 years; the model achieved mean absolute errors of 1.35 and 2.28 for CDR-SB and MMSE scores, respectively, without requiring any neuroimaging or biomarker data. Feature-ablation studies revealed that age, BMI, and APOE4 status were strong predictors. The proposed framework enables the reconstruction of incomplete patient histories and the anticipation of future cognitive states.

Detecting transient chaos from scalar observations without governing equations represents a fundamental challenge in nonlinear dynamics. We propose a geometry-guided machine learning framework that unifies predictive trajectory divergence with macroscopic attractor morphology to track abrupt regime shifts. The methodology extracts a local instability scale via out-of-sample k-nearest neighbor forecast errors to establish the ML-FTLE estimator, subsequently mapping this temporal divergence onto a structural closeness matrix derived from a minimal dictionary of Poincare occupancy grids. By employing partial least squares regression, we extract a latent geometric component calibrated directly to the empirical finite-time Lyapunov spectrum, yielding the Poincare-based geometric-guided FTLE. Validation against analytical QR-FTLE baselines confirms that fusing topological state spaces with predictive divergence systematically improves continuous transition tracking. The Structural Similarity Index optimally resolves gradual damping, while Hausdorff Distance exhibits extreme resilience during abrupt phase-space collapses. Furthermore, macroscopic spatial discretization acts as a robust topological regularizer against additive Gaussian noise, preserving deterministic signatures even at moderate signal thresholds. This equation-free framework provides a highly accurate, noise-resilient diagnostic for monitoring structural transitions in complex non-stationary systems.

Vessel trajectory prediction from Automatic Identification System (AIS) data is essential for maritime situational awareness, yet it remains challenging due to irregular sampling, missing reports, and complex dynamics. Beyond accurate point forecasts, maritime applications also demand well-calibrated uncertainty estimates for reliable decision-making. Bayesian Neural Ordinary Differential Equations (ODEs) offer a principled framework for continuous-time trajectory modeling with uncertainty quantification by placing a prior over the neural vector field parameters. However, the commonly used isotropic Gaussian weight prior fails to encode informative structural properties of vessel dynamics, such as smoothness and locality. Existing function-space Bayesian neural network methods address this limitation for static mappings, but do not transfer directly to Neural ODEs, where the primary quantity of interest is the trajectory rather than the vector field itself. In principle, one could place a Gaussian process (GP) prior directly over ODE solutions, but this requires propagating distributions through a nonlinear ODE solver, which is analytically intractable. To address this challenge, we adopt a practical approach that imposes a GP-kernel-based prior directly on the vector field evaluated at a finite set of measurement points. Specifically, we augment the standard weight-space variational objective with a kernel-based regularizer that penalizes deviations of the vector field from the structure implied by a GP prior. To handle long and irregular AIS trajectories, we further combine this function-space regularization with probabilistic multiple shooting, which decouples inference across temporal segments while maintaining global consistency.

Accurate vessel trajectory prediction is essential for safe and efficient maritime operations, enabling collision avoidance and supporting route optimization. Although memory-augmented neural networks have recently shown strong performance in pedestrian and road-vehicle trajectory prediction by selectively retrieving relevant information from an external memory, their potential for vessel trajectory prediction remains underexplored. This paper presents an empirical investigation of memory-based trajectory prediction using Automatic Identification System (AIS) data. Experiments on data from the Gulf of Mexico and the New York Bight demonstrate consistent and substantial performance gains over a range of deep learning baselines that do not incorporate an external memory.

Complex, dynamic, and interactive driving environments pose significant challenges for autonomous driving, primarily due to the pervasive uncertainty of surrounding traffic. A fundamental bottleneck in current systems is the disconnect between highly expressive uncertainty modeling and interpretable, safe motion planning. In this paper, we propose a novel sample-conditioned differentiable planning framework that bridges this gap by explicitly incorporating diffusion-generated future trajectories into the optimization process. Rather than compressing predictions into a single deterministic future or relying on black-box end-to-end architectures, our approach leverages a conditional diffusion model to generate a diverse set of plausible future scenarios. Crucially, these samples are directly fed into a differentiable planner, which explicitly mitigates predictive uncertainty via an empirical Conditional Value-at-Risk (CVaR) tail-risk constraint. This allows the planner to optimize a physically interpretable trajectory that is robust to rare yet safety-critical interactions. Furthermore, we introduce a directed graph representation for scene context that yields substantial improvements in both predictive effectiveness and computational efficiency. Validated through extensive open-loop and closed-loop evaluations on the Waymo Open Motion and Argoverse 2 datasets, our framework significantly outperforms state-of-the-art baselines in safety, efficiency, and ride comfort.

Accurate and reliable vehicle trajectory prediction is essential for safe autonomous driving. Recent studies have incorporated safety risk into trajectory prediction to quantify dangers posed by surrounding agents. However, most risk-aware approaches use past risk information as a secondary signal to help guide decisions, overlooking its future evolution and uncertainty. In this paper, we propose a risk horizon profiling (RHP) module that incorporates a continuous, learnable potential field model for risk-aware trajectory prediction. The RHP module calculates the spatial-temporal proximity of surrounding objects to profile risk distributions across future horizons, which supports better trajectory prediction by adaptively identifying what human drivers perceive as critical moments. We evaluate our method on two datasets from different driving settings, highD for highway corridors and SHRP2 for urban streets, which cover diverse risk scenarios including safe, near-crash, and crash events. Compared to the baseline methods, our framework achieves a 25.0% reduction in 5s RMSE on the highD dataset and a 29.1% reduction in 5s minFDE on SHRP2. These results indicate strong performance for both short and long horizon prediction and robust generalization across highway and urban scenarios. The proposed method enables more realistic AV path planning and strategic selection, thereby supporting safer autonomous driving and more advanced driver-assistance systems. The source code for this work is available at: https://github.com/bilab-nyu/RHP

End-to-end autonomous driving has emerged as a compelling paradigm for learning planning directly from sensor observations, while recent world-model-based approaches further enrich this paradigm by enabling explicit reasoning about how the scene may evolve in the future. Yet future prediction alone does not guarantee better planning unless the predicted evolution can be converted into planning-relevant trajectory updates. Many current methods still forecast future scene states without explicitly decoding the motion implications hidden in state transitions. As a result, future reasoning often remains descriptively useful but only weakly coupled to executable motion generation. To address this limitation, we propose \mathbf{IDOL}, an inverse-dynamics-guided future prediction framework for world-model-based end-to-end planning in latent BEV space, where inverse dynamics serves as the key bridge between future prediction and trajectory optimization. IDOL first predicts multiple future latent scene states with a BEV world model, then applies an inverse dynamics model to adjacent latent futures to decode transition-aware trajectory features and recover planning-relevant motion deltas that explain how the latent world evolves over time. These inverse-dynamics-derived signals are used to optimize the planned trajectory, turning future forecasting from passive scene anticipation into actionable planning guidance. A lightweight closed-loop refinement module further improves long-horizon consistency by reusing the optimized trajectory for another round of future-aware reasoning. By introducing inverse dynamics into latent future reasoning, IDOL tightens the coupling between world modeling and planning. Extensive experiments on the NAVSIM v1 and NAVSIM v2 benchmarks show that IDOL achieves state-of-the-art performance among comparable methods.

Embodied intelligence is often studied through specialized models for individual tasks such as manipulation or navigation, resulting in fragmented capabilities and limited generalization across tasks, environments, and robot embodiments. In this work, we study whether heterogeneous embodied decision-making problems can be unified within a single vision-language-action model. We present Qwen-VLA, a unified embodied foundation model that extends Qwen's vision-language modeling stack from perception, understanding, and reasoning to continuous action and trajectory generation through a DiT-based action decoder. Qwen-VLA is trained with a large-scale joint pretraining recipe over diverse data sources, including robotics manipulation trajectories, human egocentric demonstrations, synthetic simulation data, vision-and-language navigation data, trajectory-centric supervision, and auxiliary vision-language data. To support multiple robot platforms, we introduce embodiment-aware prompt conditioning, where robot-specific textual descriptions specify the current embodiment and control convention. We further cast manipulation, navigation, and trajectory prediction into a unified action-and-trajectory prediction framework, enabling transferable visual grounding, spatial reasoning, and continuous action generation across robot morphologies, task families, and environments. Experiments on manipulation, navigation, and trajectory-centric benchmarks show consistent multi-task performance and out-of-distribution generalization under variations in scene layout, background, lighting, object configuration, and robot embodiment. Qwen-VLA-Instruct achieves 97.9% on LIBERO, 73.7% on Simpler-WidowX, 86.1%/87.2% on RoboTwin-Easy/Hard, 69.0% OSR on R2R, 59.6% SR on RxR, 76.9% average OOD success in real-world ALOHA experiments, and 26.6% zero-shot success on DOMINO dynamic manipulation.

Trajectory prediction is a fundamental task for autonomous systems, requiring complex reasoning about multi-agent interactions and intents. Large language models (LLMs) have recently been adopted for this task, as they provide strong contextual reasoning and interpretable, language-based trajectory representations. However, these LLM-based predictors are extremely memory- and compute-intensive, making them difficult to deploy on resource-constrained edge devices such as on-board computers in autonomous robots. To bridge this gap, we propose BitTP, which converts an LLM-based trajectory predictor into a lightweight bitlinear architecture. We demonstrate that weight-only quantization to 1.58-bit (BitTP-Weight) is optimal. Crucially, activations must remain in full precision, as quantizing them leads to severe degradation and instability in spatio-temporal reasoning. Empirically, BitTP-Weight not only preserves but improves prediction quality over the full-precision (BF16) LLM baseline, reducing ADE by 14.29% and FDE by 20.97% on average, while simultaneously reducing memory usage and inference latency relative to other quantization methods. These results demonstrate that carefully designed quantization acts as an effective regularizer, enabling the practical deployment of sophisticated LLM-based reasoning on edge devices. Code is available at: https://github.com/MintCat98/BitTP.

Early battery degradation trajectory forecasting (BDTF), which predicts the full-life state-of-health trajectory from early operational data, is critical for battery optimization, manufacturing, and deployment. Battery degradation data exhibit two key characteristics. First, degradation data present a multi-level structure, including regularities shared within aging conditions and trajectory patterns shared across batteries. Second, degradation-related variations in voltage-current profiles are often localized to specific state of charge (SOC) intervals. Existing approaches often fail to explicitly model these characteristics. To bridge this gap, we propose BatteryMFormer, a multi-level Transformer for early BDTF. BatteryMFormer integrates (1) an aging-condition-aware decoder that injects aging-condition priors via aging-condition-informed queries and aging-condition-aware attention, (2) a meta degradation pattern memory that learns and retrieves trajectory prototypes to guide long-horizon forecasting, and (3) a dual-view encoder that jointly captures temporal dynamics and SOC-localized variations from voltage and current time series. Extensive experiments on four battery domains show that BatteryMFormer consistently outperforms state-of-the-art baselines, marking a significant step toward reliable BDTF. Our code is available at https://github.com/Ruifeng-Tan/BatteryMFormer.

Vision-Language Models (VLMs) provide a promising foundation for autonomous driving planning, yet bridging semantic reasoning and precise 3D spatial forecasting remains a critical challenge. Existing representation strategies generally follow two paths: text-aligned methods flatten continuous spatial states into symbols, which compromises geometric structure and induces "spatial hallucinations"; dense visual methods preserve spatial topology but overwhelm standard tokenizers with redundant background textures, leading to "representation interference". To address these limitations, we introduce TPS-Drive, a novel framework centered on Task-Guided Representation Purification that empowers VLMs to Think in Purified Space. At its core, an Agent-Centric Tokenizer utilizes a task-guided vector quantization mechanism supervised by a frozen 3D detection head, which explicitly reallocates limited codebook capacity from pervasive static backgrounds to critical dynamic agents and effectively isolates spatial redundancy. Leveraging this purified spatial vocabulary, TPS-Drive employs a decoupled reasoning pipeline that sequentially performs scene understanding, future forecasting, and action generation. The framework is optimized via a progressive three-stage training paradigm, culminating in reward-driven refinement that surpasses pure imitation learning. Extensive experiments validate our approach: TPS-Drive achieves accurate agent spatial state forecasting and reduces collision rates in open-loop nuScenes evaluations, while establishing new safety records on the rigorous closed-loop NAVSIMv1 and NAVSIMv2 benchmarks.

Maritime intelligent transportation systems (MITS) are essential for ensuring navigation safety and efficiency in busy waterways. However, accurate vessel trajectory prediction remains challenging due to the limitations of single-source data. Automatic identification system (AIS) data is often sparse or unavailable for small vessels, while closed-circuit television (CCTV) data alone cannot fully capture dynamic vessel behavior. To mitigate these challenges, we propose a cross-modal interaction-based vessel trajectory prediction (named CmIVTP) framework to model the intricate interactions between vessel dynamics and environmental constraints. Specifically, we introduce a target-aware scene encoder to extract scene semantic features, effectively capturing vessel-environment interactions and enhancing trajectory prediction accuracy. In addition, we propose a cross-modal interaction transformer, which integrates AIS-derived motion features, CCTV-based environmental features, and scene representations. It leverages cross-modal attention mechanisms to simultaneously capture intra-modal semantics and inter-modal interactions, ensuring dynamically consistent and environmentally feasible predictions. Furthermore, we construct a vessel group trajectory bank by clustering historical AIS trajectories into representative motion patterns, providing an efficient and scalable approach for candidate trajectory generation. Additionally, we introduce the maritime multimodal dataset plus (named Maritime-MmD$^+$), a large-scale dataset that synchronizes AIS data and CCTV video data, providing robust support for multimodal trajectory prediction research. Extensive experiments demonstrate that CmIVTP achieves better performance on multimodal-driven vessel trajectory prediction benchmarks. The code resources for this work can be available at https://github.com/LouisYxLu/CmIVTP.

Predicting the interaction between pedestrian and vehicle is essential for autonomous driving safety in unstructured and semi-structured scenarios; however, this task is severely hindered by the scarcity of public datasets that feature dense pedestrian-vehicle interactions. Most current studies rely on structured road data, leaving the complex, heterogeneous interactions found in unstructured environments insufficiently represented and researched. In this paper, we propose a dataset annotation framework based on video data from uncalibrated surveillance cameras and present PINNS (Pedestrian-vehicle Interaction dataset from uNcalibrated cameras in uNstructured Scenes). The dataset covers multiple countries and regions, includes diverse typical traffic scenarios, and considers variations in seasons, lighting conditions, and weather. It focuses on complex scenes with dense pedestrian-vehicle interactions and is designed to be easily extensible. The dataset is constructed and annotated according to the standard issued by the Chinese Association of Automation, providing both trajectory data and corresponding scene-level information. Furthermore, this paper analyzes current challenges and research directions in heterogeneous agent trajectory prediction, shows the necessity and usefulness of the proposed dataset. We hope our framework and dataset will facilitate research on trajectory prediction and autonomous driving in complex mixed traffic scenarios. PINNS is publicly available at https://github.com/Songan-Lab.

Recent vision-language-action (VLA) models and world action models (WAMs) advance robotic manipulation by enriching intermediate representations with auxiliary spatial features or future visual-state prediction. However, these representations largely remain within the observation space and do not share the rigid-body geometry of the action space, forcing the action decoder to implicitly recover this geometry. We propose OASIS, a visuomotor policy that aligns the intermediate representation with the action space via $SE(3)$ end-effector trajectory prediction. OASIS couples a 3D-aware feature encoder that fuses vision-language and metric-depth features with an $SE(3)$ trajectory predictor that produces a camera-frame end-effector trajectory. Conditioned on the predictor's pose-supervised hidden states, the action decoder generates action chunks consistent with rigid-body motion. Across simulation and real-world experiments, OASIS outperforms VLA and WAM baselines in success rate and out-of-distribution generalization. Our project page is available at https://npuhandsome.github.io/OASIS_web.

Trajectory prediction methods have demonstrated remarkable capabilities in capturing complex motion patterns. However, existing methods rely on global state assumptions, suffer from insufficient belief inference under partial observability, and lack cognitive behavioral constraints in prediction. These limitations severely compromise both deployment feasibility and physical plausibility in real-world settings. In this work, we propose FEP-Diff, an agent-centric trajectory prediction framework grounded in the Free Energy Principle, aimed at achieving cognitively plausible predictions under realistic constraints. Specifically, a dual-branch spatiotemporal encoder extracts ego-motion dynamics and social interaction cues from local observations. Building upon this, a goal-conditioned belief learner infers multimodal latent belief distributions optimized via a free-energy objective, with a social consistency constraint on the local neighborhood graph to promote cognitive alignment among neighboring agents. Finally, a residual diffusion trajectory generator is conditioned on the learned belief representations with token-level proxy conditioning, producing precise and diverse future predictions. Extensive experiments on five public benchmarks demonstrate that FEP-Diff consistently outperforms state-of-the-art methods under restricted observability. Code: https://anonymous.4open.science/r/FEP-Diff-8876.

We propose Drift-Resistant Navigation World Model, a generative model that mitigates both perceptual drift and geometric drift in conventional rollout-based navigation world models. Existing methods recursively feed generated content into subsequent steps, causing noise accumulation and degraded predictions, i.e., perceptual drift. Meanwhile, their predictions often deviate from the agent's motion, resulting in geometry drift. We address both types of drift by redesigning world-model prediction as an anchor-guided rollout. Instead of rolling out every frame sequentially, we first predict sparse future anchors that serve as stable long-range targets, and then generate intermediate frames within each chunk conditioned on both past context and future anchors. Importantly, these sparse anchors also provide geometric constraints, supported by bidirectional epipolar geometry, to localize where corresponding content should appear in the intermediate frames. Experiments on four benchmarks demonstrate consistent improvements over strong baselines in long-horizon visual quality, geometric consistency, and multi-view coherence. These gains further translate into improved downstream planning performance under the same planners, highlighting the importance of drift-resistant, geometry-aware prediction for reliable navigation world models.

Pedestrian intention and trajectory prediction are critical for the safe deployment of autonomous driving systems, directly influencing navigation decisions in complex traffic environments. Recent advances in large vision-language models offer a powerful new paradigm for these tasks by combining high-capacity visual understanding with flexible natural language reasoning. In this work, we introduce PedestrianQA, a large-scale video-based dataset that formulates pedestrian intention and trajectory prediction as question-answering tasks augmented with structured rationales. PedestrianQA expresses richly annotated pedestrian sequences, in natural language, enabling VLMs to learn from visual dynamics, contextual cues, and interactions among traffic agents while generating concise explanations of their predictions without needing specialized architectures tailored for each task. Empirical evaluations across PIE, JAAD, TITAN, and IDD-PeD show that finetuning state-of-the-art VLMs on PedestrianQA significantly improves intention classification, trajectory forecasting accuracy, and the quality of explanatory rationales, demonstrating the strong potential of VLMs as a unified and explainable framework for safety-critical pedestrian behavior modeling.

Recently, world models have made significant progress in enhancing end-to-end driving systems through both future situation forecasting and improved scene understanding. However, existing driving world models are typically built upon dense scene representations, causing high computational costs and redundant information. In this paper, we present SparseWorld, a lightweight world model that focuses on predicting only the critical layout of the scene, enabling efficient future forecasting for end-to-end driving systems. SparseWorld first performs autoregressive rollout to forecast future map elements and surrounding agents, enabling the model to learn how driving scenarios evolve over time. It then leverages these predicted futures to refine downstream motion prediction and trajectory planning. Specifically, we propose a Sparse Dreamer that anticipates future instances in the latent space through joint temporal and spatial attention. By interacting with predicted future instances, the motion planner captures more accurate motion patterns and generates more informed and safety-aware trajectories. Extensive experiments demonstrate that SparseWorld significantly reduces collision risk and achieves state-of-the-art performance on the open-loop planning metrics of the nuScenes dataset with a collision rate of 0.05%. Moreover, it substantially outperforms the baseline method in closed-loop planning metrics on the Bench2Drive benchmark. Supplementary material is available at the project page: https://wryzju.github.io/SparseWorld/.

Current end-to-end autonomous driving systems are fundamentally limited by a mismatch between temporal causal reasoning and global trajectory consistency. Autoregressive (AR) models capture interaction-aware temporal dependencies via causal factorization, but their step-wise decoding leads to error accumulation and suboptimal global structure. In contrast, diffusion models optimize trajectories globally but lack explicit causal constraints, making them unreliable in interactive and safety-critical scenarios. This dichotomy reveals a deeper issue: existing methods treat causal modeling and global optimization as separate paradigms, without a principled way to unify them within a single trajectory distribution. To address this, we propose ChainFlow-VLA, which unifies causal generation and global refinement within a unified probabilistic framework. We formulate planning as a mixture over AR-induced modes and learn Vision-Language Model (VLM)-conditioned residual distributions over these modes. An autoregressive generator (Chain) produces a discrete set of causal trajectory modes, followed by a diffusion-based refiner (Flow) that leverages VLM hidden states as semantic priors to perform mode-conditioned correction in residual space while preserving causal structure. This straightforward conditioning seamlessly injects high-level scene understanding into fine-grained trajectory adjustments. Experiments demonstrate that ChainFlow-VLA achieves robust planning in ambiguous and long-tail scenarios, achieving a state-of-the-art score of 94.85 on the NAVSIM v1 leaderboard, matching human-level performance (94.8). Code will be available at https://github.com/AFARI-Research/ChainFlow-VLA.

Financial markets are characterized by extreme non-stationarity, low signal-to-noise ratios, and strong dependence on external information such as news, company fundamentals, and macroeconomic signals. Yet, existing approaches either abstract time-series into text or decouple forecasting from language-based reasoning, leading to a fundamental mismatch between qualitative reasoning and quantitative outcomes. To address this, we introduce StockR1, a time-series-enhanced LLM that unifies stock forecasting and financial reasoning through a verifiable forecast action. Based on a tool-call design, the model first emits a forecast action, which is a structured and interpretable representation of its qualitative market outlook. It then invokes a time-series decoder conditioned on this action to generate distributional future trajectories, leading to more informed question answering and financial reasoning. We optimize the full pipeline with reinforcement learning, where rewards jointly reflect answer validity, forecast accuracy, and consistency between generated actions and observed time-series dynamics. In addition, rewards are reweighted by a sample-level uncertainty scalar, encouraging the model to accommodate varying uncertainty in market dynamics. We evaluate StockR1 on financial question answering and stock forecasting over a large-scale 10-year benchmark. Our method consistently outperforms time-series baselines and general-purpose LLMs, improving reasoning accuracy by 17.7% (4B) and 25.9% (8B). These findings demonstrate that structuring the forecast actions establishes a powerful synergy between language reasoning and temporal prediction, enabling LLMs to reason through verifiable, interpretable, and numerically grounded decisions.

Existing Driving VLAs predict trajectories while largely ignoring their visual tokens -- a phenomenon we trace not to insufficient training but to a structurally ill-posed task formulation. We show that trajectory recovery, when viewed through the lens of inverse kinematics, requires both a current and a future visual state as boundary conditions; existing VLAs supply only the former, which encourages the model to shortcut through ego status and text commands alone. To address this, we re-design Driving VLA in the style of an inverse kinematics solver. First, a next visual state prediction objective that requires the LLM to predict the future visual scene provides dense visual supervision and suppresses shortcut paths. Second, a separate Inverse Kinematics Network (a cross-attention-based conditional diffusion model) that takes only the current and future visual states as input is designed to suppress reliance on ego status and textual shortcuts during trajectory decoding. With this simple prescription alone, our 0.5B-scale model recovers visual grounding and reaches trajectory planning performance comparable to 7B--8B VLAs more than an order of magnitude larger, on both the closed-loop NAVSIM-v2 and the nuScenes benchmarks. Extensive analysis further shows that this improvement stems from a recovered ability to exploit visual features, with the effect being most pronounced in dynamic driving situations such as turning.

Predicting how a person's first-person view will evolve (what action will follow, what plan completes a task, whether an in-progress shot will score) is fundamentally under-specified: the same context admits many plausible futures, and a model trained to minimize prediction error is forced to hedge or average across them, getting it wrong either way. Two findings shape our approach. First, the future camera trajectory, the path the head carves through space, lets the model commit to one of those futures: it carries the operator's intent in a form fine enough to determine how an action will unfold, substantially outperforming language as a conditioning signal. Second, this same intent makes the trajectory itself partially predictable from the context at hand, enough that trajectory need not be observed at test time to recover most of the gain. We instantiate these findings as TrajPilot, a model that predicts candidate future trajectories from egocentric context and uses them to pilot action prediction in an action-aligned embedding space where language shapes the structure but is never used as a conditioning input. TrajPilot beats VLM and structured-planner baselines on procedural planning across Ego-Exo4D atomic, Ego-Exo4D Keystep, Ego4D GoalStep, and EgoPER, with the trajectory advantage widening with horizon (exactly where prior planners collapse) and holding under RGB-only camera-pose estimation. With the goal masked at inference, the same model performs goal-free anticipation, beating VLM baselines on Ego-Exo4D atomic and extending to EPIC-Kitchens-100 and basketball shot-outcome prediction.

Learning generalizable trajectory representations from raw GPS traces remains difficult because the data is continuous, noisy, and irregularly sampled. Spatial tokenization is also challenging: fine grids yield sparse cells with weak embeddings, while coarse grids merge heterogeneous movement patterns into the same token. We present TrajTok, a trajectory encoder with a simple pretraining recipe for transferable trajectory embeddings. TrajTok first learns a multi-resolution hexagonal cell partition from the spatial distribution of GPS points, converting noisy GPS sequences into discrete cell tokens. To capture both geometry and kinematics, it uses a factorized transformer encoder with early per-modality self-attention blocks, cross-attention fusion layers, and spatiotemporal rotary position embeddings, ST-RoPE, to encode where and when each token occurs. TrajTok is pretrained with masked-token modeling that recovers both geometric structure and kinematic patterns from partial trajectory observations. On the Porto dataset, a frozen TrajTok encoder with lightweight task adapters achieves strong performance across trajectory similarity search, classification, estimated time of arrival, and full travel-time regression, outperforming multiple task-specific methods. The same frozen encoder supports both geometry-dominated and kinematics-dominated tasks, suggesting that TrajTok learns transferable trajectory structure rather than task-specific shortcuts. These results indicate that learned multi-resolution spatial tokenization combined with masked-token pretraining is a promising direction for general-purpose trajectory foundation models.

Language instructions offer a flexible way to specify task semantics but can become ambiguous in cluttered scenes containing multiple visually similar objects and candidate targets. We study Spatially Prompted Visual Trajectory Prediction (SP-VTP), an open-loop setting in which points or bounding boxes in the first egocentric frame specify an object--target pair and condition the prediction of future 3D end-effector (EE) trajectory chunks. To support this setting, we introduce EgoSPT, a controlled dataset comprising 2,841 egocentric fork pick-and-place episodes with first-frame object and target annotations and reconstructed 3D EE trajectories. SP-VTP evaluates whether a static task specification remains informative as the viewpoint and scene configuration evolve throughout execution. We also introduce SPOT, a spatially prompted object--target trajectory predictor that integrates first-frame visual and coordinate prompts with current visual observations and motion history to generate future trajectories. Rather than relying on an explicit object tracker, SPOT maintains a fixed representation of the first-frame task specification. Across three training seeds, spatial prompting consistently reduces translation and endpoint errors relative to a no-prompt baseline, while controlled prompt interventions reveal distinct roles for object and target cues at different stages of execution. Together, EgoSPT and SPOT provide a dataset and baseline for spatially conditioned egocentric trajectory prediction in open-loop pick-and-place settings.