Trajectory

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

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

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

Collision anticipation in autonomous driving requires not only accurate early warnings but also interpretable reasoning about what risk factors are being tracked and how risk evolves over time. Existing methods fall short in this regard: feature-driven models are opaque, post-hoc explanations often lack fidelity, and concept-based methods are mostly designed for static recognition rather than dynamic driving scenes. We propose CARA (Concept-Aware Risk Attention), an intrinsically interpretable spatio-temporal framework for collision anticipation. CARA derives domain-grounded risk concepts from accident narratives, aligns them with video frames via vision-language similarity, and organizes them into evolving concept trajectories. These trajectories provide explicit risk evidence that guides spatial attention, temporal attention, and anticipation, allowing semantic concepts to directly influence both where the model attends and how it predicts risk over time. By treating semantic risk factors as dynamic intermediate evidence rather than auxiliary post-hoc explanations, CARA tightly couples interpretability with the predictive process. Extensive experiments on three benchmarks show that CARA consistently improves anticipation accuracy and warning earliness over strong baselines, while providing sparse and semantically grounded concept evidence.

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

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

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

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

Frozen perception foundation models encode rich geometric, semantic, and dynamic knowledge. Yet narrow conditioning interfaces may attenuate task-relevant cues, while static fusion cannot adjust expert contributions to each scene. We cast this challenge as the prior-to-plan transfer problem and introduce PerceptDrive, a perception prior world-action modeling framework with adaptive expert routing. PerceptDrive feeds teacher-distilled priors from a frozen, driving-adapted provider and dense observation latents from a frozen self-supervised video encoder into a trainable expert-routed world-action model. Expert-specific query branches process these signals, while a prior-retention objective anchors each branch to its prior. A router predicts soft gates from a shared scene representation and combines the expert conditions before trajectory generation. During training, privileged rule-based sub-metric estimates for branch-specific trajectory drafts provide soft-gate distillation targets. The predicted action-free future latent conditions a flow-matching actor. At inference, privileged components are absent; with one front-facing camera, PerceptDrive generates one trajectory per planning step without test-time scoring, reranking, or search. Experiments show that PerceptDrive achieves state-of-the-art performance with 90.4 PDMS on NAVSIM v1 and 90.2 EPDMS on NAVSIM v2, outperforming existing methods. Ablations confirm complementary gains from prior retention and scene-conditioned routing, alongside differential reliance on the three priors. These results demonstrate that preserving and adaptively routing perception priors improves direct planning without test-time candidate selection.

Long-range vehicle trajectories provide important spatio-temporal evidence for traffic safety analysis, autonomous driving evaluation, and data-driven traffic management, yet continuously recovering them from fixed highway cameras remains difficult. As vehicles recede into distant road regions, perspective compression and scale decay often fragment or prematurely terminate automatic tracklets, even when their continuation remains identifiable from motion consistency across neighboring frames. We formulate this problem as recovering the far-range continuation of a vehicle trajectory from a reliable near-field tracklet. We introduce LoRFT, to our knowledge the first open benchmark dedicated to long-range vehicle trajectory reconstruction from fixed highway cameras. LoRFT comprises 22 expressway surveillance scenes, 366,109 video frames, 6,601 manually verified trajectories, 2,694,889 bounding boxes, road-geometry annotations, scene-level splits, and evaluation scripts. We further propose Map-RSTNet, a map-aware residual sequence-to-sequence model that reconstructs distant trajectories in a road-geometry-aligned state space and dynamically refreshes local road geometry during decoding. On LoRFT, Map-RSTNet reduces ADE, FDE, and 5-second RMSE by 11.0%, 15.4%, and 10.5%, respectively, relative to the strongest baseline. These results demonstrate that road-geometry-aware reconstruction can extend usable trajectory records from existing fixed-camera infrastructure. LoRFT provides a reproducible testbed for long-range vehicle trajectory reconstruction.

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

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

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

Distributed coordination of multi-agent systems frequently relies on cooperative protocols designed to achieve agreement on a prescribed, non-trivial trajectory. While the robustness of such protocols to various uncertainties is well documented, existing literature universally assumes that the target agreement trajectory itself remains invariant. This assumption may hold in ideal cases, but we prove that network perturbations can vastly modify the asymptotic agreement trajectory. We first investigate the exact trajectories of Linear Time-Invariant (LTI) agents subjected to dynamic coupling uncertainties by establishing a new Laplace-domain criterion that characterizes the specific closed-loop poles governing the perturbed agreement manifold. To formalize our analysis, we introduce the notion of structure-preserving dynamics, perturbations that maintain the null space of the communication graph's Laplacian, and contrast them with transmission only dynamics, affecting only the adjacency matrix. We prove a critical fragility within standard cooperative output regulation schemes: while static consensus is uniquely robust to heterogeneous transmission delays, synchronization to periodic trajectories is destroyed by arbitrarily small transmission delays. Furthermore, we demonstrate that for d-regular topologies, uniform transmission perturbations can easily shift the system to synchronize with an unexpected, entirely new frequency. These findings expose a previously unidentified vulnerability in classical robust synchronization, demonstrating that transmission dynamics necessitate fundamental structural modifications to networked reference generators.

Vessel trajectory prediction in complex maritime environments is essential for traffic management, collision warning, route planning, and autonomous navigation. Although AIS-based learning methods have progressed rapidly, existing datasets are often released as raw message streams or irregular time series, with inconsistent sampling rates, noisy observations, heterogeneous coordinate systems, and non-unified scenario protocols. Most public AIS resources also lack structured representations of navigational lanes, waterway geometry, and navigable-region constraints, limiting reproducible, environment-aware forecasting. To address this, we introduce NaviAIS, a standardized scenario-level AIS dataset for vessel trajectory prediction. It organizes multi-vessel historical-future trajectories within unified temporal windows and local coordinate systems, and provides rasterized navigable maps, vectorized lane priors, lane graphs, and structured map representations. Compared with existing datasets, it jointly supports vectorized lanes, multi-scenario coverage, vectorized maps, open accessibility, and processed trajectories. Built on this dataset, we propose NaviLane, a hierarchical macro-action framework for map-aware prediction. NaviLane first performs trajectory-map joint encoding for a unified scene representation, then uses a discrete macro-action codebook to generate multimodal candidates coarse-to-refined. A residual refinement module improves local geometric and dynamical consistency, and a world-model-based consequence-aware evaluator ranks candidates by interaction risk and environmental feasibility. Experiments show NaviLane outperforms representative baselines in both single-modal and multimodal settings, confirming the value of structured navigational priors, hierarchical multimodal generation, and consequence-aware evaluation.

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

Understanding the computational basis of action recognition is a central challenge in social cognition as well as in human-robot interaction. Inspired by the Mirror Neuron System (MNS), we propose a two-level architecture for motor primitive discovery and online phase recognition applied to the NICO humanoid robot. At the first level, two Self-Organising Maps (SOMs) learn topographic representations of arm kinematics (A-SOM) and hand kinematics (H-SOM) from simulated trials covering seven motor actions. The maps are trained on non-redundant features identified through hierarchical correlation analysis of motion trajectories. The results show that the two SOMs encode complementary aspects of motor behaviour. At the second level, an Echo State Network (ESN) evaluates whether temporal trajectories of SOM activations, represented by consecutive best-matching units, are sufficient for online recognition of the currently executed movement phase. The results show that SOM-based trajectories preserve the dominant phase-discriminative structure of the movement, while contextual information provides only a secondary refinement. Our contribution is the integration of established SOM and ESN methods within an MNS-inspired architecture for motor primitive representation and online phase recognition. The results are compatible with the computational hypothesis that self-organised motor representations, when temporally integrated, can support accurate online recognition of ongoing movement phases.

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

Vision-Language Navigation (VLN) requires an embodied agent to interpret a natural-language instruction and predict actions from temporally ordered visual observations. Adapting a multimodal large language model to VLN requires visual-language alignment, compact temporal inputs, action-space grounding, and stable training on the target hardware. This technical report presents PGN (Pangu Navigator), an offline VLN action-prediction system built on OpenPangu-7B. Training proceeds in two stages. First, PGMM aligns a frozen EVA-ViT-G/14 vision encoder with the frozen language backbone by training a Q-Former and a two-layer MLP projector. Second, PGN adapts the aligned model to expert navigation trajectories using five-observation windows, epoch-dependent temporal sampling, and a reasoning-then-action output format; this stage freezes the aligned visual pathway and updates three structural-token embeddings and LoRA adapters. The implementation combines mixed-precision computation, selective FP32 computation, and DeepSpeed ZeRO-2 on eight Ascend 910B NPUs. Under teacher-forced, open-loop evaluation on 500 held-out expert trajectories, V9 reports a 62.29% Normalized Action Match (NAM) and a 100.00% Non-empty Rate (NER). These metrics quantify offline expert-action alignment rather than closed-loop navigation success; evaluating error accumulation, path efficiency, and goal completion remains future work.

Reinforcement-learning navigation policies for legged robots select actions reactively from current observations and short-term memory, with limited capacity to anticipate how moving obstacles will evolve in the near future. In dynamic environments, this reactivity causes the robot to respond too late because collision risk depends on short-horizon scene structure rather than on current obstacle positions alone. Lightweight predictive supervision applied to the policy's recurrent state during training can encode anticipatory obstacle dynamics without modifying the inference-time controller. We augment a reactive LSTM-SRU navigation backbone with an auxiliary JEPA-style predictor and SIGReg regularization: during training, the predictor supervises the deterministic hidden state to anticipate its own next state; at inference, it is fully discarded, incurring zero additional computational cost. On simulated and real-world navigation benchmarks with dynamic obstacles, our method substantially improves navigation success while reducing collision rates through the predictive training signal alone, without additional inference-time parameters. Real-robot deployment on a Unitree Go2 demonstrates zero-shot sim-to-real transfer: the controller navigates cluttered indoor and dynamic outdoor environments without fine-tuning, with evasive behavior consistent with the collision reduction observed in simulation.

Autonomous driving requires both safe and efficient planning decisions in dynamic 3D environments. Although recent Vision/Video-Action models learn policies directly from visual observations and scale well with advances in vision transformers and large-scale training data, they often lack explicit geometric grounding and future-aware spatial guidance, limiting their ability to balance collision avoidance and driving progress. In this work, we propose GeoWorldAD, a geometry world action model that grounds trajectory planning in ego-aligned 3D space and anticipates short-horizon scene evolution with latent future geometry tokens. Present geometry provides essential spatial constraints for safe planning, while future geometry reveals how surrounding agents and ego-centric free space may evolve, reducing overly conservative decisions without sacrificing safety. To efficiently exploit these geometric cues, GeoWorldAD progressively aggregates multi-scale present geometry and latent future geometry through iterative trajectory refinement. Experiments on NAVSIM v1 and v2 demonstrate state-of-the-art performance, highlighting the effectiveness of explicit 3D geometry grounding and future geometry world modeling for safe and efficient autonomous driving.

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

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

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

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

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

This paper presents a trajectory prediction method for marine vessels based on optimal planning. Crude initial trajectories respecting static obstacles are first generated using A*-search to provide a feasible warm start. In the second step, a numerical optimizer is used to ensure COLREG compliance. The prediction problem is posed as sequential trajectory planning from the perspective of each surrounding vessel, requiring only their current positions, velocities, and intended destinations as input. As the latter is included in AIS messages, this enables faster predictions than learning-based methods that typically require longer data histories. The proposed method is validated using real-world scenarios constructed from AIS data.

A trained flow or diffusion model is usually run with only a handful of solver steps, and the integration error this leaves behind is unevenly distributed across the image. We ask where that error is injected and how it reaches the endpoint, and answer with a signed source-and-transport accounting of few-step integration error, tested to first order. A perturbation experiment on five models at 256^2 resolution shows the learned dynamics spread local disturbances widely: near the start of sampling, under 10% of the summed endpoint response remains at the source. Signed one-step truncation residuals, propagated through the model's own linearized dynamics, reconstruct much of the endpoint error's direction and regional structure (cosine 0.81-0.87), and a region's error owes more to what arrives from elsewhere than to its own injection. Structure-destroying nulls, with protocols frozen before evaluation, locate what carries the account: randomizing contribution signs halves it, and reassigning which region receives each contribution, with content, norms, and signs intact, destroys it entirely. Where the injections land is readable from the model itself. The variation of its velocity or prediction field along the trajectory, a structure that emerges during training, predicts the final per-region gap (within-image rho of 0.57-0.70 on fine trajectories, weaker from the cheap solve alone). The prediction is partial because endpoint error depends not only on injected magnitude but on its sign, timing, and transport through the learned dynamics. A training penalty on the injected variation lowers few-step error, so the structure is one a model can be trained to change.

Despite strong capabilities in data understanding and decision-making, autonomous data science agents still heavily rely on trial-and-error workflows that involve expensive computation. This bottleneck motivates models that can anticipate the effects of data science operations before real execution. In this paper, we introduce the concept of Data Science World Model, which model the data science execution environment by predicting environment state transitions conditioned on current workflow states and candidate operations. We further propose DSWorld, a practical framework that combines structured state construction, cost-aware routing, lightweight real execution, and an LLM-based simulator for expensive operations. To support training, we construct an 8K-scale transition trajectory dataset and introduce Reflective World Model Optimization, an error-aware reinforcement learning strategy for improving transition prediction. Experiments show that DSWorld accelerates RL-based agent training by approximately $14\times$ and search-based inference by approximately $3$-$6\times$ while maintaining competitive performance, and outperforms the strongest LLM baseline by 35.6% on transition prediction tasks. The code is available at https://anonymous.4open.science/r/DSWorld.

Autoregressive video diffusion models have enabled the generation of arbitrarily long videos by removing conditioning on future frames, thus greatly improving computational efficiency. Yet, they suffer from error accumulation over time, as the denoised sequence gradually drifts away from the conditioning distribution seen during training. Recent advances attempt to reduce this error by anchoring each generated frame to the learned manifold of real ones. However, even when all generated individual frames lie close to the real manifold, there are trajectories which the model lacks sufficient knowledge to continue without exiting it, thus reaching a terminal point. To prevent the model from being trapped in terminal points, we start from the hypothesis that for well-modeled future trajectories the distribution of the predicted noise should match the one of the forward noising process. To enforce such a prior at test time, we introduce Terminal points Avoidance through Noise Guided Optimization (TANGO), which uses the diffusion model as a critic of its own outputs, by predicting one step forward and requiring an isotropic Gaussian noise prediction. We use the deviation from this expected noise distribution to search for an alternative trajectory that does not lead to a terminal point. Our approach achieves a $3.1\%$ absolute improvement on VBench over state-of-the-art, while reducing Fréchet Video Distance by $28.3\%$ on average across $15$s videos. Our code is available on https://mever-team.github.io/tango.

Post-training agents for automated AI research requires optimizing not only model parameters, but also the runtime harness that shapes how research trajectories are generated, evaluated, and learned from. Existing pipelines typically train models under a fixed harness, including prompts, tools, skills, middleware, and memory, while leaving the data-generating process outside the optimization objective. This creates a mismatch between model updates and the static scaffolding that determines trajectory quality. We introduce Co-Harness, a framework that jointly optimizes the agent harness and model parameters during post-training. Co-Harness alternates between harness optimization and model optimization. An LLM-based HarnessCritic analyzes failed trajectories, identifies harness-level failure modes, and proposes validated local updates. The model is then fine-tuned on high-quality trajectories generated by the improved harness, distilling effective scaffolding into model parameters. A 200+ hour autonomous case study further shows that Co-Harness can recover from system crashes, improve inference efficiency, and discover ensemble strategies without human intervention. These results suggest that joint harness and model optimization is an effective way to improve agents beyond fixed-harness post-training.

Topology optimisation (TO) often requires repeated finite element analysis and sensitivity-based material updates, which can be costly when multiple candidate designs are needed under varying physical and design conditions. Generative TO offers a route to rapid design exploration, but existing models may rely on adversarial training, long reverse-diffusion sampling, or external guidance to maintain structural feasibility and physical consistency. This study develops a flow matching-based topology optimisation (FMTO) framework for conditional topology generation. Linear FMTO is first formulated as an endpoint-based baseline by interpolating between a Gaussian source field and the BESO reference topology. To introduce mechanically meaningful intermediate states, a trajectory-aware FMTO formulation is proposed, where volume-fraction-indexed BESO states are used to construct the probability path and target velocity field. This incorporates physics-guided optimisation history into generative flow learning without adding inference-time optimisation. A path--velocity mismatch analysis explains why moderate trajectory weighting can improve generation stability, whereas excessive guidance may over-constrain the learned transport. Numerical examples show that FMTO generates diverse topology candidates with improved compliance-related performance, volume-fraction satisfaction, topology fidelity, and substantially fewer sampling steps than a diffusion-based baseline. Under limited training data, trajectory-aware FMTO achieves the best overall performance with a moderate trajectory weight. Studies on trajectory-anchor density and three-dimensional topology generation further demonstrate the influence of path design and the applicability of the proposed framework beyond two-dimensional problems.

End-to-end trajectory planners need to represent multiple plausible driving behaviors while producing a single executable trajectory under real-time constraints. Proposal-based approaches address this ambiguity by generating multiple candidates, but converting the proposal set into a final plan remains a key design problem. We present DRIFT, a fixed-depth planner that combines one-step drifting in a compact trajectory latent space with scene-aware proposal aggregation. Conditioned on features from a pretrained visual encoder, the DRIFT Decoder generates 48 proposal features in a single batched pass, with 32 samples at alpha=0.5 and 16 samples at alpha=0.9. A lightweight Aggregation Head integrates these features with scene, navigation, and ego-state information and directly predicts the final trajectory without requiring trajectory-level quality labels for aggregation. Its output is trained with expert-trajectory imitation and a map-derived boundary regularizer that penalizes waypoints outside the drivable polygon and inside waypoints near its boundary. On NAVSIM navtest, DRIFT achieves 89.6 PDMS and 90.4 EPDMS, with strong drivable-area compliance and ego progress among the methods compared. The proposal-generation and aggregation module runs in 10.82 ms on an NVIDIA RTX 4090, while full-model inference including the visual backbone takes 66.43 ms. These results show that one-step latent proposal generation and direct aggregation provide an efficient design for multi-hypothesis motion planning.

Large Language Model (LLM) agents have shown remarkable capabilities in autonomous decision-making by generating sequential trajectories of states, actions, and observations. However, in complex, long-horizon tasks, these agents frequently suffer from compounding errors and struggle to recover from failures. Existing self-correction mechanisms rely on prompt-based reflection, which is inherently brittle, incurs heavy time and API costs due to iterative trial-and-error loops, and produces task-specific memory that may be hard to generalize to new scenarios. To address this, we propose Experience Memory Graph (EMG), a framework that reformulates agent failure recovery as a graph matching problem. At training time, we convert both failed exploration trajectories and successful expert trajectories into directed action decision graphs. By matching these graphs, we extract common subgraphs (successful workflows) and graph edit paths that explicitly indicate how to correct failures (e.g., which actions to add, delete, or relabel under a given observation), and store them in a memory graph with intra-task nodes and cross-task edges. At test time, EMG retrieves relevant insights and guides the agent in a single, loop-free execution. Experiments on ALFWorld and ScienceWorld show that EMG consistently outperforms state-of-the-art reflection baselines in success rate and average reward, while requiring no test-time trial-and-error.

Robots operating in human-robot collaboration must communicate not only their intended actions but also uncertainty arising from incomplete or ambiguous perception. This work introduces a mathematical framework for expressing perceptual uncertainty through robotic manipulator motion. Drawing on Laban Movement Analysis, robot behavior is organized in a Commitment-Vigilance state space that maps uncertainty-related states - confidence, curiosity, hesitance, fear, and inactivity - to distinct Laban Effort signatures. Five motion primitives - approach, pause, retreat, exploration, and oscillation - are then parameterized using eleven kinematic and geometric descriptors, including acceleration, pause and retreat characteristics, gaze angles, tilt, and shiver amplitude. A video-based human-subject study evaluated recognition of four expressive trajectories and the influence of individual descriptors on perceived intensity. Participants reliably identified the intended behavioral states, while several descriptors significantly modulated expressiveness. The results establish a perceptually grounded basis for encoding robot uncertainty in motion and support future autonomous trajectory generation using parametric movement representations for collaborative tasks in shared environments. Code, videos, questionnaire and appendices are available at "https://bit.ly/github-aou".

Autonomous racing demands planning algorithms that balance vehicle dynamics at the limits of handling with strategic decision-making in competitive multi-agent scenarios. Game theory provides a mathematical framework for modeling these interactions, enabling interactive trajectory planning and strategic behaviors, such as blocking. However, directly solving full dynamic games online is computationally prohibitive and challenging to integrate into robust, high-frequency autonomous software stacks. This paper proposes a hybrid architecture that integrates game-theoretic reasoning into a sampling-based motion planner, combining strategic interactions with robust trajectory generation. Building upon an $α$-potential game formulation, we utilize an offline-learned potential function to capture multi-agent interactions. During online operation, a gradient-based optimization dynamically refines interaction parameters to generate an \textit{Interaction Reference Path}. This path serves as a dynamic cost bias within a high-frequency sampling planner. We evaluate our approach in a high-fidelity simulation environment on the Yas Marina Circuit. Qualitative and quantitative results demonstrate that our approach successfully induces defensive behaviors like blocking without carrying the computational burden of full dynamic game solvers.

Deep learning systems often fail due to subtle implementation faults that alter training behavior. Recent work has studied how to detect and diagnose such failures from changes observed across training epochs. However, the software engineering community still lacks a public dataset of per-epoch training runs with documented fault history, feature extraction details, and clear reuse support for fault detection and diagnosis tasks. We present Deep4ge, a controlled benchmark of 14,227 training runs generated from 59 adapted TensorFlow/Keras deep neural network (DNN) programs collected from Stack Overflow. We generated faulty variants using 27 source-code transformations that introduce known faults across seven categories. The dataset contains 9,845 faulty runs and 4,382 correct baseline runs. For each run, we record 4 evaluation metrics and 26 features that measure training behavior at every epoch. These features capture weights, gradients, activations, accuracy and loss trends, learning rate, and hardware use. Deep4ge supports binary fault detection, multi-class fault diagnosis, and early fault prediction from partial training runs. We release the dataset and fault-injection framework at https://doi.org/10.5281/zenodo.20337241.

This paper derives an analytical differential flatness transform for a tailsitter Unmanned Aerial Vehicle (UAV) under coordinated flight conditions using a simplified aerodynamic model. The proposed framework is formulated exclusively using rotation matrices, avoiding the ambiguities inherent to Euler angle representations. The method extends the applicability of an existing state-of-the-art differential flatness-based controller to flight regimes involving a significant vertical velocity component, where the previous approach becomes inapplicable. The proposed framework is validated experimentally with trajectories that highlight its advantages in these regimes.

UAV swarm for applications, such as indoor inspection, security patrol, and logistics delivery, are often mission-oriented rather than exploration-oriented. In these tasks, UAVs are required to visit task-relevant regions in a prescribed sequence, and such region-level mission information can often be obtained from pre-deployment sketch-map priors, such as floor plans, CAD layouts, or evacuation diagrams. Although these tasks are executed in three-dimensional space, UAVs usually fly within a specific altitude layer or a nearly fixed altitude range on each floor, making mission-level region transitions mainly governed by planar connectivity. Based on these observations, this paper proposes a mission-oriented coordinated navigation framework that exploits sketch-map priors for multi-UAV indoor operations. Onboard observations are used to perform topological alignment, and the aligned prior is fused with online observations to construct a mission-oriented traversability representation. A layered 2D--3D coordinated navigation framework is further developed, where 2D guided path planning generates mission-oriented guide paths and guide-driven 3D trajectory optimization produces dynamically feasible and collision-free trajectories. Simulation and real-world experiments validate the effectiveness of the proposed framework in structured multi-room indoor environments and further demonstrate its coordinated navigation capability under both communication-available and communication-loss conditions. Multi-floor simulation results show the scalability of the system to layered indoor structures.

Imitation learning enables robots to acquire manipulation skills from demonstrations by mapping observations to actions. Existing approaches predict either short-horizon continuous action sequences or discrete keyposes. However, continuous prediction methods suffer from compounding errors due to short prediction horizons and struggle with multi-modal action distributions, whereas keypose-based methods necessitate an external planner, constraining real-time applicability. To address these challenges, we introduce SegDiff, a closed-loop visuomotor policy that integrates the strengths of both paradigms. SegDiff decomposes demonstrations into motion segments between keyposes and learns to predict the continuous trajectory from the current state to the next keypose, enabling long-horizon prediction with real-time refinement. Furthermore, we leverage the capability of diffusion models and DDIM inversion to propose a Dynamic Temporal Ensembling mechanism, which allows the policy to efficiently respond to dynamic environments and mitigate discontinuities caused by inconsistent multi-modal sampling. SegDiff demonstrates significant performance gains over existing approaches across various simulated and real-world scenarios, indicating its strong ability to reason over extended temporal dependencies while maintaining real-time adaptability and control stability.

Previous feed-forward 4D reconstruction methods either predict per-frame static point clouds, ignoring foreground motion, or estimate point cloud trajectories while being limited to small camera motions. This restricts their ability to aggregate observations over time and reconstruct complete dynamic scenes under large viewpoint changes. To address this limitation, we propose OmniX, a feed-forward 4D reconstruction framework that predicts dense 3D point trajectories for every pixel from videos with large camera motion. OmniX decouples dynamic motion modeling from static geometry prediction and represents motion using a compact set of dynamic tokens. By leveraging the sparse and low-rank structure of 3D motion, these tokens generate trajectory fields for all pixels across all images while efficiently preserving global interactions. To facilitate training, we further build an automatic UE5-based 4D data engine and introduce a large-scale dataset containing 80K scenes and 1.28M multi-view videos with full geometric annotations. OmniX achieves state-of-the-art performance on dense 3D point trajectory prediction and 3D point tracking, while also demonstrating competitive results on video depth estimation and camera pose estimation.

Synthetic data is widely used to train large language models because it is inexpensive to generate and easy to control. As models are increasingly deployed as agents, synthetic trajectories are likely to become an important source of training data for agentic behavior. We investigate the effects of training on synthetic agentic trajectories containing adversarial interactions, including actions such as terminating another agents process, lowering its scheduling priority, or accessing resources without authorization. We finetune Llama 3.3 70B Instruct on these trajectories, generated to approximate reinforcement learning rollouts, and evaluate the resulting models on Anthropics Agentic Misalignment suite and Apollos in context scheming scenarios. Finetuning on these trajectories consistently increases misaligned behavior. Leaking rises by roughly a factor of five over the baseline, 4.6% to 24.9%. This increase survives the removal of every adversarial action from the trajectories. Finetuning on structurally comparable trajectories generated benign from the start produce a substantially smaller effect, 15.5%. These results indicate that the misaligned disposition is introduced during the generation process and encoded diffusely throughout the trajectory, rather than being localized to the harmful actions themselves. The effect also depends on the generating model. Benign trajectories produced by Gemini 2.5 Flash induce slightly higher leaking rates than trajectories generated from identical tasks by Claude 3.7 Sonnet. In contrast, broad safety benchmarks degrade similarly across all finetuned models and therefore fail to distinguish these effects. Our results suggest that action level filtering is insufficient to ensure the safety of synthetic agentic training data and that dispositions introduced by the generating model can survive semantic inspection.

Benefiting from the powerful priors embedded in large-scale pre-training data and the emerging commonsense reasoning ability, large language models (LLMs) have shown unprecedented generalization capabilities in many research fields. Recently, projecting visual embeddings into the language space via vision-language models (VLMs) to achieve sim-toreal and cross-scene generalization has become a prevailing paradigm in the field of Vision-and-Language Navigation in Continuous Environments (VLN-CE). VLN requires an embodied agent to navigate through unseen environments following natural linguistic instructions. We emphasize that a VLN task can be decomposed into a sequence of sub-tasks, each corresponding to a process of 3D spatial interaction with the environments described by instructions such as "walk to the end of the sofa and turn left." However, such spatial interactions involving moving into the image along the direction of depth sensing are puzzling for VLMs as they were predominantly trained on conversations with RGB images. Rather than incorporating depth or 3D geometric information-which VLMs rarely encounter during pretrainingwe propose an alternative approach: fine-tuning VLMs to learn navigation interactions directly in 2D pixel space through autoregressive trajectory generation. Given a linguistic instruction and historical observations, our model sequentially predicts a series of pixel coordinates, drawing a trajectory from the bottom center of the current observation. While prior work has proved that pixel-goal supervision outperforms learning of discrete actions, our experiments further verify that the supervision of pixel-space trajectory significantly enhances VLN performance. Moreover, we demonstrate that our flagship model achieves state-of-the-art level performance with relatively limited computational resources and training data.

Large Language Model (LLM) agents are commonly trained from expert trajectories using supervised fine-tuning (SFT), which treats multi-turn agent behavior as ordinary text imitation. This recipe is simple and low-cost, but it only learns to imitate the sequence of expert actions, rather than training the agent to choose the right action against plausible mistakes at each state. Existing methods to mitigate this problem include preference learning or reinforcement learning, but they usually need high-cost environment rollouts and reward models. We propose Agentic-DPO, a lightweight offline agent policy optimization method that turns expert trajectories into state-conditioned preference supervision. At each expert action state, Agentic-DPO samples a one-step action from the current state, treats plausible wrong actions as negatives, and contrasts them with the expert action using a DPO-style preference objective. To avoid mixing both policy and schema in preference learning, we introduce Policy-Preserving Augmentation (PPA), which renders the same latent trajectory under multiple schemas while keeping the expert policy fixed. Agentic-DPO requires no online environment rollout, reward model, or full-trajectory student exploration. We conduct experiments across StableToolBench, tau-bench retail, and Mind2Web, where Agentic-DPO consistently improves agents at different model scales beyond imitation. In particular, it raises tau-bench accuracy from 21.7% (SFT) to 41.4% for a 9B model, matching online GRPO under the same backbone with only step-level rollouts and without environment interaction during gradient steps. The results suggest that expert trajectories can support low-cost agentic policy optimization when converted from demonstrations into state-level action preferences. Code for Agentic-DPO is released at https://github.com/Schuture/Agentic-DPO.

Autonomous driving planning is a key component of IoT-enabled intelligent transportation systems, requiring vehicles to generate safe, efficient, and executable trajectories in complex urban environments from multi-source contextual information. While imitation learning (IL) has shown promise on large-scale datasets, IL-based planners still suffer from limited coverage of complex long-tail interactions, weak consistency with downstream constrained refinement, and insufficient use of high level scene semantics under real time constraints. To address these issues, this paper proposes a large language model (LLM) enhanced differentiable trajectory planning framework for IoT-enabled autonomous driving. Specifically, we introduce a surrounding agent centric data augmentation strategy to reorganize sur rounding agent trajectories as additional planning supervision, thereby improving the training distribution without collecting additional raw data. We further design a complexity-aware asyn chronous LLM-based semantic enhancement module to extract scene-related high-level semantic features with controlled online overhead. In addition, a differentiable optimization module is incorporated to refine generated trajectories with explicit residual penalties while backpropagating optimization gradients to the upstream planner. Experiments show that the proposed method achieves the best overall scores of 83.63 and 78.29 on the nuPlan closed-loop nonreactive and reactive Hard20 benchmarks, respectively, and CARLA-ROS tests further verify its online deployment and real time closed-loop execution capability.

Scientific ideation unfolds over multiple stages, including literature search, paper reading, tool use, claim checking, cross-paper synthesis, brainstorming, rejection of weak directions, and iterative writing. Yet most existing resources capture isolated components or final artifacts rather than the process connecting them. We introduce IdeaTrail, a dataset of 1,170 multi-turn trajectories for scientific ideation and proposal generation. Each trajectory follows a research process from evidence gathering to either idea selection or proposal construction, jointly recording tool use, acquired evidence, intermediate artifacts, and reasoning. IdeaTrail is synthesized from human-selected research papers and proposal artifacts through a Generator--Advisor loop. The Generator produces the visible sequence of actions, observations, and artifact edits, while the Advisor uses the full generation context to check grounding, causal order, naturalness, and leakage from hidden targets. This reverse-to-forward design keeps trajectories aligned with real scientific artifacts while retaining the uncertainty, evidence use, and staged convergence characteristic of research practice. IdeaTrail provides both reusable process supervision and a general recipe for constructing scientific-research-agent data.

This paper proposes a new notion of robust invertibility for nonlinear dynamical systems, and introduces constructive parameterizations of recurrent neural network which are robustly invertible by design. We define robust invertibility as the existence of a causal inverse system such that both the forward and inverse systems are contracting and have bounded incremental input-output gains (the system is bi-Lipschitz), implying that both forward prediction and input reconstruction are robust to signal perturbations and initial-state mismatch. We construct robustly invertible recurrent models via series composition of static orthogonal layers and dynamic layers satisfying a strong input-output monotonicity property, and provide a differentiable neural network parameterizations in the form of the bi-Lipschitz recurrent equilibrium network (BiLipREN). Additionally, composition with dynamic orthogonal layers yields a nonlinear minimum-phase/all-pass (a.k.a. inner--outer) factorization. We illustrate the utility of the framework through a series of application examples in data-driven internal model control, dynamic surrogate loss learning, and signal-space normalizing flows, illustrating its utility for robust control, trajectory optimization, and generative modeling of complex trajectory distributions.

In this work, we present B-spline Policy (BSP), an action representation designed for accelerating robot manipulation policies. Rather than predicting discrete-time action chunks, BSP parameterizes actions as continuous B-spline curves defined by a set of knots and control points. This representation yields smooth, time-continuous trajectories that can be temporally scaled and executed by low-level controllers at higher frequencies and speeds. We show that B-spline-parameterized actions can be seamlessly integrated into standard policy learning pipelines by directly predicting B-spline parameters. Experiments on simulated and real-world tasks demonstrate that BSP significantly reduces task completion time, achieving substantial improvements over baseline methods while maintaining strong success rates. More results: https://b-spline-policy.github.io

We investigate whether identity-specifying system prompts produce statistically distinguishable geometric fingerprints in the hidden-state trajectories of four open-weight transformer language models spanning four post-training regimes: no training (Gemma-4-E4B base), multimodal RLHF (Gemma-4-E4B-it), RL distillation (DeepSeek-R1-Distill-Qwen-7B), and SFT (Qwen2.5-7B-Instruct). Three prompt conditions (an identity-specifying axis prompt, a length-matched generic-assistant prompt, and a 26-token vanilla baseline) are compared via five geometric metrics, principally the 1-Wasserstein distance between edge-wise distributions of Ollivier-Ricci curvature on k-NN trajectory graphs. Claims rest on trajectory-level permutation tests with multiple geometric controls (teacher-forced content controls, temporal-chain vs k-NN topology, ABT-projected k-NN, angular vs Euclidean graph construction, B=5000 permutations on borderline statistics). The central finding is a qualitative reorganization of identity encoding across the instruction-tuning boundary: in the base model the fingerprint is direction-coded (separation 0.034, p=0.002 under angular k-NN); in the multimodal instruction-tuned model it migrates into the magnitude (angular separation collapses to p=0.439 while Euclidean survives at p=0.042, and the mean norm of the first generated state inverts its length-ordering, being lowest for the identity prompt). This direction-to-magnitude reorganization is specific to the multimodal instruction-tuning regime, absent under RL distillation and SFT. A teacher-forced control attributes ~30% of the free-running cosine signal to prompt-driven effects. We position W_1 on edge-wise Ollivier-Ricci distributions on k-NN trajectory graphs as a methodological contribution of independent interest.

The differentiable shift-variant filtered backprojection (SV-FBP) framework enables data-driven estimation of redundancy weights for cone-beam CT reconstruction under general source trajectories, removing the need for analytically derived weighting schemes. In this work, we present a systematic study of the robustness and adaptability of differentiable SV-FBP under challenging acquisition settings. We show that the framework remains stable across highly irregular and discontinuous trajectories, indicating that reconstruction performance is largely insensitive to trajectory ordering or continuity. Instead, the spatial distribution of sampling points plays a more dominant role. Under sparse-view conditions, differentiable SV-FBP achieves competitive reconstruction quality while providing an order-of-magnitude reduction in computation time compared to iterative reconstruction methods at moderate sampling densities. However, we identify a clear transition regime under severe undersampling, where the absence of iterative data consistency leads to performance degradation. Furthermore, we demonstrate that the framework remains applicable to non-planar multi-isocenter geometries, such as Lissajous-saddle trajectories, without requiring architectural modifications. These findings provide new insights into the behavior and limitations of the differentiable SV-FBP model and highlight it as a flexible and efficient solution for non-standard and robotic CBCT acquisition scenarios.

Dataset condensation for action segmentation synthesizes compact, informative representations of long, untrimmed video datasets. The existing approach relies on Variational Autoencoders and an iterative latent optimization; it is computationally expensive and suffers from over-smoothed reconstructions and rigid temporal constraints. This paper proposes to shift the condensation paradigm from optimization-based inversion to deterministic latent mapping. By leveraging Denoising Diffusion Implicit Models, we represent action segments as continuous trajectories anchored by sparse latent points in the noise manifold. To maximize representational efficiency, we introduce an adaptive allocation mechanism that dynamically redistributes the anchoring budget based on segment-wise reconstruction difficulty. Extensive experiments demonstrate that our framework significantly outperforms state-of-the-art methods in segmentation performance across common datasets. Notably, our approach achieves performance parity with real data training while maintaining a condensation ratio of 2.4% on Breakfast dataset.

Although Video Large Language Models (Video LLMs) have shown strong performance in video understanding, their efficiency is still limited by the large number of visual tokens. Existing video token compression methods typically rely on frame-wise saliency or heuristic token merging, which can over-focus on locally salient regions and produce ambiguous fused features. To address these issues, we propose GeoTrace, a training-free spatiotemporal token compression framework that decomposes video evidence into exact skeleton tokens and traceable residual event tokens. Specifically, Contextual Farthest-Point Anchoring (CFPA) preserves salient, context-consistent, and high-coverage skeleton tokens, while Trajectory-Constrained Residual Condensation (TCRC) compresses residual tokens through one-to-one temporal trajectories and constrained near-manifold condensation, producing traceable event tokens with reduced ambiguity. We evaluate GeoTrace on four Video LLMs across four video understanding benchmarks, and the results demonstrate its effectiveness and generalization across different model architectures and scenarios. On LLaVA-OneVision, with only 10% visual tokens retained, GeoTrace achieves a $12.99\times$ TFLOPs reduction while preserving 99.1% of the vanilla performance. Overall, GeoTrace offers a compact and traceable token representation for efficient and robust Video LLM inference. Code is available at \href{https://github.com/guohuan-xie/GeoTrace.git}{\texttt{Code}}.

Multi-UAV exploration is often constrained by unreliable communication, limited field-of-view sensing (e.g., lightweight onboard camera), and finite travel budgets that require each robot to reserve enough budget to return to its base. We present Dec-MARVEL, a decentralized budget-aware exploration framework for communication-free teams with directional sensing. Rather than exchanging maps, goals, or messages, each robot coordinates through its incidental observations: any teammate trajectory within its field of view serves as a coordination signal. A graph-attention actor fuses local frontier geometry, teammate motion, and budget features to select return-feasible waypoint-heading actions. The actor is trained with phase-conditioned critics, a training-only task-oriented privileged critic, and a mixture-based budget curriculum. Across 900 held-out trials spanning three team sizes (2, 4, 8 robots) and three travel budgets (720, 800, 1024 meters) against four baselines, Dec-MARVEL achieves the highest or tied-highest exploration rate and lowest sensing overlap across all nine team-size budget configurations. Under our tightest 720m budget, it reaches 53%, 94%, and 100% success for 2, 4, and 8 robots, versus 37%, 83%, and 99% for the strongest baseline. Physical-robot experiments demonstrate successful sim-to-real transfer and real-world deployment of Dec-MARVEL.

Score matching controls average error under the forward marginals, but a discretized reverse-time sampler evaluates the learned score along its own trajectory. We show that small forward-marginal error does not guarantee numerical stability. We construct a single smooth score field with arbitrarily small forward-marginal $L^2$ error. The learned reverse-time process is nonexplosive, has moments of every order, and can be arbitrarily close to the exact reverse-time process in path-space total variation. Yet its Euler--Maruyama discretizations converge in probability while every positive moment diverges. Thus weak convergence can hold even though every Wasserstein distance $W_p$, $p\ge1$, diverges. The same failure can occur within one fixed finite neural architecture. We construct a family of bounded, globally Lipschitz denoisers for which both the forward-marginal error and the path-space total variation distance tend to zero, while their Euler--Maruyama endpoints diverge in every $W_p$. For compactly supported data, we also give a simple positive result. Projecting the learned denoiser onto a known bounded closed convex set containing the support preserves pointwise accuracy, gives grid-uniform moment bounds, and yields Wasserstein convergence under mild local regularity. Experiments with a small fixed DiT-style network show large growth along rare numerical trajectories and its suppression by denoiser projection, while overall trajectory errors remain small.

Vehicle intention prediction is a pivotal aspect in the agility and safety of autonomous vehicles in all driving scenarios; if genuine enhancement of autonomous vehicles are required, we need to make them adopt human interpretation of driver's intention especially in cases that require a lot of human interaction as well as complex driving behaviors like the ones at intersections, roundabouts and emergency cases such as sudden stops where vehicle intention prediction helps in taking the correct evasive action within a real time period where every second of action makes an impact and can prevent a catastrophe from taking place. In the worst case, it helps minimize the damage and make safety a priority. Intention prediction can also be used to enhance trajectory prediction (intention conditioned trajectory prediction). In this study, The INTENT framework is proposed using LSTM model to predict the vehicle's intention at intersections 2 seconds ahead of the event occurrence to predict whether the cars in intersections are going straight, turning left, or turning right. Various model experiments and ablation study are thoroughly tested on InD dataset achieving 99.71% accuracy.

Unmanned Aerial Vehicle (UAV) videos are widely used in traffic monitoring, urban management, and emergency rescue. However, existing UAV video perception mainly relies on box-level localization and trajectory association under predefined categories, making it difficult to simultaneously support flexible queries and fine-grained instance-level dynamic understanding in open scenarios. To this end, we introduce a new task, UAV Open-Vocabulary Video Instance Segmentation (UAV-OVVIS), which discovers targets in UAV videos according to open-vocabulary queries and outputs instance-level segmentation trajectories with globally consistent identities. Considering the scarcity of instance-level annotations in UAV scenarios, we propose AeroTrack, a training-free unified framework. AeroTrack centers on periodic open-vocabulary detection, short-segment mask propagation, and cross-segment identity unification, reusing existing visual foundation models to enable UAV-OVVIS. Based on this framework, we instantiate five AeroTrack variants and construct AeroVIS, an evaluation benchmark for UAV-OVVIS containing 9 UAV object categories and 8,279 trajectories. Experiments show that AeroTrack substantially outperforms existing general video instance segmentation methods in UAV scenarios and demonstrates strong open-vocabulary robustness and generalization. To support future research, we release AeroTrack and AeroVIS as a unified framework and benchmark for UAV-OVVIS.

Spatial and Single-cell transcriptomics are transformative in deciphering cellular dynamics. As the fundamental paradigm for reconstructing cell developmental paths, trajectory inference (TI) is critical. However, existing methods require extensive manual intervention and proficiency in heterogeneous tools, posing a significant barrier to efficient TI analysis. To bridge this gap, we propose SpaCellAgent, an autonomous large language model (LLM) multi-agent framework that automates end-to-end spatiotemporal analysis and narrative generation. SpaCellAgent utilizes a multi-agent architecture for strategic workflow planning, a dynamic tool-orchestration engine for adaptive algorithm selection, and a self-evolution module that iteratively refines performance through feedback. We evaluate SpaCellAgent on six heterogeneous datasets encompassing complex temporal developmental trajectories, diverse sequencing platforms, and spatially-resolved tissue architectures. SpaCellAgent consistently demonstrates over 40% improvement in analytical efficiency while maintaining expert-aligned performance. By converting natural language specifications into optimized analytical workflows and fully automating the pipeline, SpaCellAgent democratizes advanced spatiotemporal modeling and establishes a scalable, agent-driven paradigm for computational biology. The code and materials are available at https://github.com/LittleXH-shw/SpaCellAgent.

Real-image diffusion inversion is governed by a tight quality-cost trade-off, with costs incurred in computation, storage, or per-image optimization. We study this trade-off through the forward Gaussian noise anchor that defines a diffusion trajectory and isolate two mechanisms behind effective stored-noise inversion. First, diffusion noise exhibits an element-wise compression asymmetry: int8 full-dimensional anchors preserve reconstruction, whereas low-dimensional subspace summaries are much less reliable, often collapsing even at comparable or smaller payloads; the element-wise over subspace ordering persists across five stored-noise inversion methods. Second, inversion is trajectory-bound and score-prior coupled: the matched forward anchor and a trained score network are both necessary, arguing against a purely algebraic-identity explanation. Together, these findings specify what to store and how to use it. They lead to Noise-Anchored Reverse Correction (NARC), a training-free inversion primitive that stores a single int8 latent anchor and reuses it with a fixed, noise-level-dependent anchor-weight schedule: strong anchoring when the reverse trajectory is noise-dominated, then relaxed anchoring as image detail emerges. On PIE-Bench++ with Stable Diffusion 1.5, NARC outperforms five modern non-exact baselines and improves PSNR by +3.24 dB over PnP DirectInv while using about 400x less inversion storage than PnP DirectInv. The compression asymmetry, anchor specificity, and editing plug-in also transfer to SDXL 1024^2.

Robot imitation learning for manipulation should preserve demonstrated task geometry while producing dynamically admissible robot motions. Existing pipelines often learn task-dependent trajectories and impose execution limits afterward through filtering, smoothing, clipping, or time scaling, which may distort task-critical end-effector paths. We propose the Spectral Movement Primitive (SMP), a frequency-domain imitation learning framework that couples task-space skill generation with joint-space execution regulation. Demonstrations are represented by truncated finite-horizon Fourier coefficients. An empirically selected low-frequency task band captures the dominant motion geometry, while higher harmonics contribute disproportionately to derivative growth. A frame-aware context-conditioned GMM/GMR prior predicts the task-band coefficients in a canonical task frame, and the resulting Cartesian trajectory is mapped to joint space through sequential inverse kinematics. A phase-coupled regulator then limits the requested phase progression without modifying the spectral coefficients, thereby enforcing joint velocity and acceleration limits while preserving the represented path. Experiments evaluate task-band reconstruction, robustness to composite demonstration corruption, out-of-distribution cross-board generalization, joint-space dynamic admissibility, end-effector path preservation, and deployment on a Franka Panda robot. Results show compact geometric reconstruction, consistent transfer across unseen task frames, substantial reductions in dynamic violations and jerk, and preservation of the intended end-effector path during phase regulation.

LLM-powered data agents are playing an increasingly important role in data-driven decision making. However, existing data agents struggle to generalize to unseen data environments and analytical workflows, especially in heterogeneous enterprise settings. This creates a growing need for synthesizing high-quality data agent trajectories that capture complex analytical workflows for given data environments. Such trajectories support two key downstream uses: they can serve as supervised finetuning (SFT) data that adapts data agent models to the target domain, and as in-context learning (ICL) demonstrations to guide general-purpose LLMs in unfamiliar data environments. Thus, we introduce TOFFEE, a system for synthesizing high-quality data agent trajectories from given data environments via Monte Carlo Tree Search (MCTS) with adaptive model selection and cross-task prefix reuse. We show that TOFFEE can effectively generate scalable trajectory data for complex analytical tasks across heterogeneous environments. In this demonstration, we present the system framework of TOFFEE, including its task pool construction, trajectory explorer, and learned cost model. We also introduce the web interface of TOFFEE and its workflow, and demonstrate two end-to-end scenarios: trajectory synthesis for data agent finetuning, and demonstration-augmented data agent reasoning.