Trajectory Prediction

We study trajectory selection for reasoning distillation, where teacher-generated reasoning trajectories are selectively used as supervision for a student model. Existing methods rely on heuristics such as trajectory quality or model confidence, but they often overlook whether a trajectory is learnable by the student. In this paper, we present LARK, a learnability-grounded method for reasoning trajectory selection. LARK selects trajectories that the student can learn efficiently while preserving the generalization of the full training distribution. At the core of LARK is a learnability factor $ρ$, which characterizes the rate at which the student's training loss decreases. To estimate this rate efficiently and maintain generalization, we introduce a learnability proxy and a $χ^2$-regularized selection policy that balances learnability and distributional coverage, both with strong theoretical guarantees on their estimation error. Empirically, LARK consistently outperforms data selection baselines across multiple base models and reasoning tasks. Diagnostic analyses show that the LARK score predicts downstream training utility and that LARK-selected trajectories induce faster supervised fine-tuning loss reduction. Our code is available at https://github.com/Tianrun-Yu/LARK.

Inferring dynamics from population snapshots is a fundamental challenge in machine learning and biology. In scRNA-sequencing (scRNA-seq), destructive measurements preclude direct tracking of individual cells across time, making trajectory inference underdetermined. Optimal Transport (OT) provides a principled framework for snapshot alignment, but a long-standing modeling question is which cost functions yield biologically meaningful couplings. Standard OT approaches rely on gene-expression distances, implicitly treating cells as independent points and neglecting structured cell-cell communication mediated by ligand-receptor signaling. We introduce CellBRIDGE (Cell-Based Regularized Interaction-Driven Gene Expression), which augments feature-based OT with a directed, typed interaction cost derived from ligand-receptor activity. By explicitly modeling cell-cell communication, CellBRIDGE improves cross-snapshot couplings and downstream trajectory estimates across synthetic and real scRNA-seq datasets relative to feature-only baselines. Notably, CellBRIDGE enables mechanistically interpretable in silico perturbations: on lung cancer data, silencing specific ligand-receptor pairs induces trajectory shifts that recapitulate expected effects of targeted pathway inhibition.

Inferring continuous probability paths from sparse snapshots is a fundamental challenge in domains like single-cell biology, where high-fidelity data acquisition is often destructive and constrained by prohibitive sequencing costs. This motivates the need for active learning strategies to strategically select optimal measurement times. However, designing active learning policies for this setting remains an open problem: the target objects reside on the infinite dimensional Wasserstein space where standard Euclidean metrics are ill-defined, and current interpolation methods lack epistemic uncertainty quantification. We introduce a framework which extends active experimentation to the space of measures. By leveraging Linearized Optimal Transport (LOT), we map distributional snapshots into a tangent space amenable to Gaussian Process modeling, allowing us to construct a tractable probabilistic surrogate for the underlying probability path. This yields an acquisition policy that iteratively selects measurement times to minimize uncertainty. Empirical results demonstrate that our strategy outperforms uncertainty-agnostic baselines on both synthetic and real-world datasets.

LLM-based agents have demonstrated strong capabilities in solving complex tasks through multi-step reasoning and tool use. However, existing evaluation protocols primarily focus on task success, overlooking a critical aspect of agent behavior: execution efficiency. In practice, agent trajectories often contain redundant steps that consume substantial resources while contributing little to task completion. In this work, we propose and formulate a new research area: \textbf{redundant step detection} for agent trajectories. To support this initiative, we introduce \textbf{RedundancyBench}, a new benchmark that contains diverse tasks with carefully annotated trajectories, where each step is labeled according to its contribution to task completion. Using RedundancyBench, we develop and evaluate 3 representative methods to answer whether a step within trajectory is redundant or necessary. Our results show that even the best-performing method achieves only 24.88% score in detecting redundant steps, while some methods perform worse than random guessing. These results highlight the task's complexity and the need for further research in this area. \footnote{Code and dataset in this paper are both available in \href{https://anonymous.4open.science/r/RedundancyBench}{https://anonymous.4open.science/r/RedundancyBench}.}

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

Task success can hide process anomalies in real-world agent executions. An agent may pass the final task oracle while still accumulating unresolved ambiguity, unsafe external writes, ignored errors, weakly grounded commitments, or capability-boundary overcommitment. We study this mismatch as the Outcome-Process Gap and introduce OpenClawBench, a large-scale dataset for measuring and supervising process-side anomalies in real agent execution processes. OpenClawBench is built from BFCL-driven OpenClaw sessions produced by 6 source models and contains 31,264 annotated trajectories. It aligns task-oracle outcomes with structured process evidence. FullTax converts the aligned trajectories into structured anomaly supervision: binary labels, supporting evidence, onset/span localization, severity, recoverability, and a 5-class anomaly taxonomy. Using OpenClawBench, we make the Outcome-Process Gap measurable. Among 31,135 oracle-passing executions, 2,904 are still labeled process-anomalous under FullTax. These results show that success-only evaluation misses a concrete class of process-side failures in real agent executions. A LoRA-fine-tuned Gemma 3 12B detector trained on the high-confidence FullTax supervised pool reaches binary F1=0.729 on the cleaner-labels held-out test split. Together, OpenClawBench turns real agent execution logs into auditable and reusable supervision for studying, diagnosing, and operationally monitoring runtime agent reliability.

Diffusion-based and iterative methods have become effective tools for solving imaging inverse problems. Their reconstruction process naturally forms a trajectory of intermediate estimates. Although these intermediate estimates define a reconstruction trajectory, most methods do not explicitly regularize the transitions between consecutive states. To address this limitation, we introduce TRACE, a training-free TRAjectory-Constrained rEconstruction framework that stabilizes the reconstruction path by coupling adjacent states along the trajectory. This gives a trajectory-level model that can be interpreted as a sequence of proximal updates. Since the exact proximal update is generally intractable, we approximate it with a neural mapping. This yields a diffusion-like reconstruction process with an explicit coupling between neighboring states. We provide a stability analysis showing that temporal coupling bounds trajectory variation and that this control is preserved under untrained network updates. Experiments on linear and nonlinear image reconstruction tasks show that TRACE improves reconstruction quality. Trajectory-level analyses and ablations confirm that temporal coupling directly affects state transitions along the reconstruction path.

Fast catching of free-flying objects is difficult because of short reaction time, impact uncertainty, and kinodynamic constraints. We use reinforcement learning in simulation to collect successful catching trajectories and learn a low-dimensional kinodynamic trajectory manifold. At run time, the estimated object initial state is mapped directly to a reference catching trajectory without online nonlinear optimization. The trajectory is tracked with compliant control near contact for improved impact absorption and capture stability.

Sampling-based motion planners offer a practical and scalable approach to kinodynamic motion planning, notably for high-dimensional, underactuated, or non-holonomic systems. However, these planners are typically used offline, requiring execution to begin only after the trajectory has been computed. In addition, the planned trajectory may not be accurately tracked in the presence of motion uncertainty, leading to deviations from the nominal solution. In this work, these limitations were addressed within a unified framework, \method, an asymptotically-optimal meta-planner framework that improves both path quality and tracking performance during execution. In addition to the main execution thread, this framework comprises a replanning method that continuously explores the state space and refines the trajectory during execution, and an optimization process that refines future control inputs to reduce tracking error. Together, these components enable \method to leverage asymptotically optimal planning online while improving execution accuracy under uncertainty. The proposed approach is evaluated in both simulation and real-world environments across multiple systems, demonstrating consistent improvements in trajectory quality, tracking accuracy, and overall performance compared with baseline methods.

Low-thrust trajectory design relies heavily on repeated evaluations of fuel consumption and transfer feasibility, which require expensive optimal control solutions. In this work, we show these quantities can be accurately approximated by machine learning surrogates, enabling fast and scalable evaluation across a wide range of scenarios. By increasing both dataset size and model capacity, we observe that low-thrust trajectory optimization follows a scaling law, with performance improving linearly with the logarithm of training data and network parameters, and no evidence of saturation within the explored regime. Guided by this observation, we construct a large-scale dataset using the proposed homotopy-ray strategy tailored to mission design requirements. A key is the introduction of a self-similar transformation, which allows generalization across semi-major axes, inclinations, and central bodies avoiding retraining. As a result, the same neural approximator can be applied to diverse orbital environments and mission classes. The proposed models accurately predict optimal fuel consumption and minimum transfer time for single- and multi-revolution transfers. Their performance and generalization are demonstrated on a public dataset, a multi-asteroid flyby problem from the Global Trajectory Optimization Competition, and an asteroid rendezvous mission design. The models and datasets are released as open-source to support the space community.

Personalized generation with frozen large language models requires a conditioning signal that is both compact and current. Existing personalization methods typically retrieve or summarize user histories in text, or compress them into static latent profiles and soft prompts. These approaches are efficient, but they treat a user's past behavior as an aggregate profile and therefore mix stable identity, recent drift, and item content in the same representation. We propose LAtent Trajectory Tracking and Extrapolation (LATTE), a framework that represents personalization as forecasting a peer anchored relative preference state. For each historical session, LATTE subtracts a time masked baseline formed from comparable users who responded to the same item, producing a state that measures how the target user differs from peers under a shared item context. A lightweight sequence predictor then forecasts the next state in this trajectory, and a State to Token Bridge injects the forecast into a frozen instruction tuned LLM through a single anchored soft token. We provide a latent factor analysis showing when peer anchoring cancels shared item variation and why temporal forecasting trades off stale averages against noisy recent states. Experiments on Amazon Reviews 2023 and MemoryCD show that LATTE consistently outperforms retrieval, summary memory, static latent profiles, difference aware latent profiles, and soft prompt compression baselines. On Amazon Reviews 2023, LATTE improves average ROUGE-L from 0.219 for a static latent profile and 0.245 for the strongest added latent compression baseline to 0.259. Additional pairwise comparisons and diagnostic analyses suggest that the improvement is mainly due to forecasting user-specific trajectory information, rather than merely adding a soft prompt interface.

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.

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.

Autonomous driving stacks must pick one trajectory from a multi-modal candidate set; choosing by model confidence ignores safety, traffic-law, and comfort constraints. We present \textsc{RECTOR} (Rule-Enforced Constrained Trajectory Orchestrator), a post-generation reranking layer that scores candidates against a tiered rulebook (Safety~$\succ$Legal$\succ$Road$\succ$Comfort) via differentiable proxies and a scene-conditioned applicability mechanism, then selects with a deterministic $\varepsilon$-lexicographic rule that preserves cross-tier priority by construction -- without retraining the predictor. On the Waymo Open Motion Dataset \texttt{validation_interactive} split (43{,}219 augmented instances, $K{=}6$), under ProtocolB (28-rule proxy catalog, oracle applicability) rule-aware selection cuts Safety+Legal violations from 28.58% to 20.42% and Total from 40.32% to 32.41% versus confidence-only on the same candidates. A uniform-weight weighted-sum baseline matches binary compliance on this benchmark -- the empirical lift comes from rule-aware ranking, while the lexicographic guarantee is the structural differentiator no weight calibration can replicate. Under adversarial confidence corruption, confidence-only selection fails in 100% of scenarios while both rule-aware selectors reject the injected mode in $\sim$96%. All figures are proxy-evaluator results (not a safety certificate), open-loop, 5,s horizon, U.S.\ rules, validation split.

A small number of methodological contributions, including word2vec, the Transformer, large-scale pre-training, and reinforcement learning from human feedback, have reshaped NLP and AI research over the past decade. OpenReview now makes numeric reviewer scores and accept/reject decisions public for every ICLR submission. Whether such review signals identify trajectory-changing papers at submission time, however, remains untested at corpus scale. We answer this question on $36{,}113$ papers from ICLR 2017--2025, identifying \emph{catalysts}: papers whose descendants measurably redirect future research. We compare four disruptiveness measures (the Consolidation/Destabilization (CD) index, node2vec, the direction-aware Embedding Disruptiveness Measure (EDM), and an LLM-based semantic rater) and define a five-type operational catalyst taxonomy (topic initiator, topic bridge, within-topic redirector, simultaneous, and recognition-misaligned). EDM leads at identifying highly cited ICLR papers (AUC $0.83$ vs.\ $0.60$ for CD, $0.49$ for node2vec, and $0.42$ for the LLM rater). Topic initiators precede a $7.55{\times}$ topic-share growth and topic bridges precede an $11.52{\times}$ growth in cross-topic citation flow versus year-matched controls. We found that the peer review scores are essentially orthogonal to future disruptiveness ($|ρ|{\leq}0.005$; accepted and rejected papers have indistinguishable mean EDM, $p{=}0.11$).

Model Predictive Control (MPC) for autonomous navigation faces a fundamental trade-off between model accuracy and real-time efficiency. High-fidelity dynamics models can accurately predict complex vehicle-terrain interactions during trajectory rollouts, but incur significant computational cost, increasing inference latency and reducing control frequency. Conversely, lightweight models enable fast updates and dense sampling, yet may produce erroneous predictions under safety-critical conditions, potentially leading to catastrophic failures such as vehicle rollover. To address this trade-off, we propose Adaptive Dynamics Orchestration (ADO), a framework that dynamically selects the most appropriate dynamics model for the current navigation context. ADO maintains a library of models spanning diverse accuracy-efficiency profiles and continuously refines terrain-conditioned performance estimates using residual errors from online counterfactual rollouts, where executed control actions are replayed across the model library to assess predictive discrepancy. These estimates guide model selection in real time, balancing computational efficiency and predictive accuracy. Real-world experiments on an off-road ground robot demonstrate that ADO significantly reduces modeling error compared to a fixed low-latency baseline, while approaching the accuracy of the highest-fidelity model without incurring its computational cost, resulting in more reliable and effective navigation in challenging terrain.

We study the problem of identifying dynamically distinct basins of attraction in high dimensional time-homogeneous Markov processes using only trajectory sampling. This problem is fundamental in the analysis of metastable dynamical systems, where the process rapidly mixes within basins while transitions between basins occur rarely on the timescale of interest, or even when the state space is reducible. Existing approaches typically rely on spatial discretization or spectral analysis of estimated transition operators, which can become unreliable in high dimensional settings or when the underlying basin geometry is highly nonlinear. We propose a discriminative approach to basin identification based on marginal trajectory distribution comparison. We prove a simple risk separation result: if two initial states belong to the same basin, the Bayes-optimal classifier distinguishing their marginal trajectory distributions achieves risk close to 1/2, whereas if they lie in distinct basins, the optimal risk is close to zero. This observation reduces basin detection to a two-sample discrimination problem between marginal trajectory distributions. Motivated by this principle, we develop a neural algorithm that receives a set of candidate basin representatives and iteratively merges them by estimating classification risk with a neural network that approximates the Bayes classifier. We evaluate the method on various metastable systems. These include synthetic systems constructed by embedding low-dimensional dynamics into high dimensional noisy ambient spaces. In these settings, standard spectral and clustering-based methods often fail, while our approach accurately recovers the underlying basin structure. These results display a shortcoming of existing methods and highlight trajectory discrimination as an effective tool for identifying dynamical basins in high dimensional stochastic systems.

Single-cell RNA sequencing (scRNA-seq) provides high-dimensional profiles of cellular states, enabling data-driven modeling of cellular dynamics over time. In practice, time-resolved scRNA-seq is collected at only a few discrete time points as unpaired snapshot populations, leaving substantial temporal gaps. This motivates trajectory inference at unmeasured time points. Existing methods mainly follow two directions, optimal-transport (OT) alignment provides distribution-level matching between observed snapshots, while continuous-time generative models support forecasting via learned dynamics. However, two challenges remain: (i) unpaired snapshots render local transitions between adjacent time points ambiguous, leading to unstable supervision; and (ii) long-horizon prediction relies on repeated integration, where small modeling errors compound and cause distribution drift. To address these challenges, we propose single-cell Flow Matching (scFM), a latent generative framework based on coupling-conditioned flow matching. First, we compute entropically regularized OT couplings between adjacent snapshots and use them to construct soft, weighted flow-matching targets for learning time-dependent velocity fields. Second, we learn bidirectional velocity fields and leverage their consistency to refine couplings and improve temporal coherence under sparse supervision. Third, we introduce distribution-level alignment and latent dynamic regularization to anchor long rollouts and mitigate drift. Experiments on real-world time-series scRNA-seq datasets show that scFM consistently improves distributional prediction performance for both temporal interpolation and extrapolation. Moreover, scFM yields more accurate trajectory reconstruction and temporally coherent visualizations where intermediate time points are absent, indicating a more faithful recovery of underlying temporal gene expression dynamics.

Latent world models can learn representations that contain information needed for control, while the downstream controller may still rank candidate actions poorly when it relies on terminal latent distance alone. We study this failure in a fixed encoder and introduce trajectory reachability metrics (TRM), a small temporal pairwise cost trained from logged trajectories and used to rank predicted endpoints of a candidate action sequence against a goal. In the TwoRoom evaluation on 100 episodes from a high distance range, the original controller with LeWorldModel reaches 7.0% mean success. Temporal TRM trained after excluding all evaluation episodes reaches 96.7%, shuffled label controls stay at 0.0%, and TRM also improves PLDM from 32.7% to 84.0%. TopoNav, a separate pixel navigation task, shows the same link between repaired ranking and closed loop control. The selection audit with shared candidates (SASC) and rowspace interventions show that the gain comes from reweighting latent directions carrying the action decision. The XY rowspace contributes less than 1% of terminal latent MSE but carries most of the information needed for control. Coverage and boundary tests define the scope. Balanced doorway coverage restores a 0.0% coverage failure to 100.0% success, while an unseen wall orientation and contact rich PushT expose layout, dynamics, and recovery limits.

While flow-matching text-to-speech (TTS) achieves strong zero-shot speaker similarity and naturalness, it remains susceptible to content fidelity issues, particularly skip and repeat errors from imperfect alignment. We propose RobustSpeechFlow, a training strategy that improves alignment robustness by extending contrastive flow matching with length-preserving repeat and skip latent augmentations. Requiring no external aligners or preference data, our method directly penalizes realistic failure modes and readily integrates into existing pipelines. On Seed-TTS-eval, it reduces the word error rate (WER) from 1.44 to 1.38 using only 0.06B parameters. On our ZERO500 benchmark, it delivers consistent intelligibility improvements across diverse speaker and prosody conditions; at NFE=24, it reduces English character error rate (CER) from 0.48% to 0.35% and Korean CER from 0.81% to 0.57%. Audio samples: https://robustspeechflow.github.io/

Supervised fine-tuning (SFT) on long teacher trajectories is the dominant way to instill investigation and reasoning in open software-engineering (SWE) agents. Since every retained response becomes an imitation target, the student inherits the final outcome and intermediate flaws, including ungrounded leaps and redundant loops. High-quality training data must be effective(each step is grounded and narrows the agent's epistemic gap to the correct fix) and efficient(each step is information-bearing rather than redundant or looping). Existing recipes filter or relabel teacher rollouts using only a binary terminal verifier, which does not directly target these axes and provides no supervision on instances where the teacher fails. Most real issue includes a developer-authored reference patch, $p^\star$, revealing the file paths, runtime behaviors, and coding conventions presupposed by the correct fix, yet standard pipelines discard it. We propose Patches-to-Trajectories (P2T), which uses $p^\star$ as privileged information during curation and formulates trajectory construction as bi-objective optimization over per-step effectiveness and trajectory length. A reverse phase distills $p^\star$ into a latent process graph, $G^\star$, of contextual facts and solution milestones. A forward phase curates trajectories from blinded teacher continuations by scoring per-step progress against $G^\star$ under a leakage-blocking groundedness check and retaining the shortest effective segments. Using only 1.8k curated SWE-Gym instances, P2T improves effectiveness and efficiency over outcome-filtered SFT and its tool-error-masking variant. On SWE-bench Verified, it raises Pass@1 by up to 10.8 points while reducing per-instance inference cost by ~15%, with consistent gains on SWE-bench Lite. Size-matched ablations and qualitative analysis further isolate trajectory quality from data scale.

Video anomaly detection is critical for public safety and security, yet remains highly challenging despite extensive research due to large variations in appearance, viewpoint, and scene dynamics. Among existing approaches, human pose-based methods have emerged as a major line of research, showing strong performance since many anomalies in public datasets involve humans and pose representations are robust to appearance changes while providing compact motion descriptions. However, these methods often overlook bounding-box trajectories, although such information is inherently available in pose-based pipelines. In this paper, we explicitly leverage these trajectories as a primary anomaly cue. We present TrajVAD, a framework that models multi-class bounding-box trajectories using normalizing flows to learn normal kinematic patterns. Its trajectory-only variant, TrajVAD-T, eliminates pose estimation, reaches 87.7 AP on ShanghaiTech, and achieves the best results on MSAD among compared methods. TrajVAD-P adds a reliability-gated pose branch and improves performance to 88.6 AUROC and 90.9 AP on ShanghaiTech, establishing bounding-box trajectories as an effective modality for video anomaly detection.

The efficient Test-Time Scaling (TTS) paradigm offers a promising perspective for enhancing the generation performance of diffusion models. However, current solutions are limited to a static, pre-defined noise pool and suffer from inflexible noise exploration across the denoising trajectory. To bridge this gap, we propose RTS, a novel Reward-guided Trajectory Scaling method to fully unlock the generative potential of diffusion models. Unlike existing methods, RTS facilitates the synthesis of refined, high-fidelity images via two core innovations: 1) a reward-guided noise optimization strategy to actively direct the search towards promising regions; and 2) a sparse test-time scaling framework together with a PCA-driven curvature analysis scheme to prioritize key intermediate steps in the entire denoising space, effectively compressing the search space. Experiments show our approach outperforms baselines by 15.6% across GenEval Score, and a 60.4% enhancement in ImageReward score, setting a new SOTA while providing a practical guideline for more effective test-time scaling across diffusion-specific architectures.

Reinforcement learning with verifiable rewards (RLVR) has become a dominant paradigm for improving reasoning in large language models (LLMs), yet the underlying geometry of the resulting parameter trajectories remains underexplored. In this work, we demonstrate that RLVR weight trajectories are extremely low-rank and highly predictable. Specifically, we find that the majority of downstream performance gains are captured by a rank-1 approximation of the parameter deltas, where the magnitude of this projection evolves near-linearly with training steps. Motivated by this, we propose a simple and compute-efficient method RELEX (REinforcement Learning EXtrapolation), which estimates the rank-1 subspace from a short observation window and extrapolates future checkpoints via linear regression, with no learned model required. Across three models (i.e., Qwen2.5-Math-1.5B, Qwen3-4B-Base, and Qwen3-8B-Base), RELEX produces checkpoints that match or exceed RLVR performance on both in-domain and out-of-domain benchmarks, requiring as few as 15% steps of full RLVR training. Remarkably, RELEX is able to extrapolate far beyond the observation window at no training cost, predicting checkpoints up to 10-20$\times$ beyond the observed prefix with continued improvement (e.g., observe only the first 50 steps and extrapolate to 1000 steps). Our ablation analysis confirms the minimalist sufficiency of RELEX: neither increasing the subspace rank nor employing non-linear modeling yields further gains in extrapolation. Finally, we show that RELEX's success stems from a "denoising" effect: by projecting updates onto the rank-1 subspace, the model discards stochastic optimization noise that would otherwise degrade performance during extrapolation. Our code is available at https://github.com/weizhepei/RELEX.

The maximum softmax probability (MSP) represents a default approach when evaluating uncertainty quantification for language model generation with structured output. Although cheap, it is often miscalibrated. Methods that probe the model's internal activations feed raw hidden states into opaque classifiers, reading activations as static snapshots and leaving implicit the layer-wise trajectory by which a representation is formed. Yet, similar endpoints can arise from very different paths, and how evidence accumulates, reinforces, or reverses across depth might reveal uncertainty that final probabilities obscure. We extract eleven scale-invariant geometric features, tracing the cumulative path of per-layer MLP updates, and feed them to a sparse linear probe. The probe outperforms MSP under selective abstention, with gains scaling with baseline miscalibration up to 21 AURC points. Because every feature has a closed-form geometric meaning, the probe's coefficients trace how and where along depth errors take shape -- which layers commit prematurely, which contradict the running state, where trajectories drift away from their endpoint.

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.

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

High-resolution 3D medical image generation remains challenging because fully volumetric models are computationally expensive, while efficient 2D slice generators often fail to preserve anatomical consistency across the third dimension. We propose LiFT, a framework for Lifted inter-slice Feature Trajectories that factorizes 3D volume synthesis into per-slice image generation and inter-slice trajectory learning. Rather than modeling the volumetric distribution end-to-end, LiFT treats a volume as an ordered trajectory in feature space, capturing how anatomical structures appear, transform, and disappear across depth. A tri-planar drifting loss aligns the trajectory of generated slices with the trajectories of real volumes, enabling distributional learning over inter-slice progressions in unconditional generation; in paired translation, a bidirectional $z$-context mixer trained against the registered target supplies through-plane coherence while preserving per-slice fidelity. We evaluate LiFT on BraTS 2023 (unconditional and missing-modality MR) and SynthRAD2023 (MR-to-CT). Across these settings, LiFT preserves per-slice quality, approaches the reported cWDM missing-MR reconstruction quality at \sim$$135\times lower inference cost (without formal equivalence testing), and improves through-plane coherence on MR-to-CT relative to a no-mapper ablation, demonstrating that lightweight inter-slice trajectory learning is a viable route to high-resolution 3D medical synthesis.

Accurately forecasting human trajectories from an egocentric perspective plays a central role in applications such as humanoid robotics, wearable sensing systems, and assistive navigation. However, progress in this direction remains limited due to the scarcity of egocentric trajectory datasets collected in real-world environments. Addressing this need, we introduce EgoTraj, an egocentric multimodal open dataset recorded using Meta Quest Pro (MQPro). EgoTraj contains 75 sequences of human navigation collected from multiple MQPro wearers in real-world urban environments. Each recording provides synchronized RGB video along with ground-truth data, including continuous time-synchronized 6-degree-of-freedom head poses, per-frame 3D eye gaze vectors, scene annotations. To the best of our knowledge, EgoTraj differs from typical egocentric trajectory datasets by capturing long-horizon, self-directed navigation across diverse urban routes with broad participant diversity. To demonstrate the potential of the dataset, we benchmark several state-of-the-art methods for egocentric trajectory prediction and conduct ablation studies to analyze the contributions of gaze, scene, and motion cues. The results highlight the utility of EgoTraj for AR-based perception, navigation, and assistive systems. The EgoTraj dataset, code, and EgoViz Dashboard are publicly available at https://github.com/yehiahmad/EgoTraj.

Equipping LLMs with tool-use capabilities via Agentic Reinforcement Learning (Agentic RL) is bottlenecked by two challenges: the lack of scalable, robust execution environments and the scarcity of realistic training data that captures implicit human reasoning. Existing approaches depend on costly real-world APIs, hallucination-prone LLM simulators, or synthetic environments that are often single-turn or depend on pre-collected documents. Moreover, synthetic trajectories are frequently over-specified, resembling instruction sequences rather than natural human intents, reducing their effectiveness for RL training. We introduce EnvFactory, a fully automated framework that addresses both challenges. EnvFactory autonomously explores and verifies stateful, executable tool environments from authentic resources, and synthesizes natural multi-turn trajectories through topology-aware sampling and calibrated refinement, producing grounded queries with implicit intents. Using only 85 verified environments across 7 domains, EnvFactory generates 2,575 SFT and RL trajectories. Despite using significantly fewer environments than prior work, which are often 5 times more, EnvFactory achieves superior training efficiency and downstream performance, improving Qwen3-series models by up to +15% on BFCLv3, +8.6% on MCP-Atlas, and +6% on conversational benchmarks including $τ^2$-Bench and VitaBench. By fully automating both environment construction and trajectory synthesis, EnvFactory provides a scalable, extensible, and robust foundation for Agentic RL.

Single-cell trajectory inference from destructive time-course snapshots is fundamentally ill-posed: neither cross-time cell correspondences nor continuous trajectories are observed, so the snapshot distributions alone do not uniquely determine the underlying dynamics. Existing optimal transport and flow-based methods typically couple cells by Euclidean proximity at observed clock times, which can misalign trajectories when development is asynchronous and cells sampled at the same experimental time occupy different latent pseudotime stages. We propose PACE, a trajectory inference framework that recovers geometry-consistent continuous transport dynamics from destructive time-course snapshots through three coupled components. First, PACE constructs a state- and time-dependent anisotropic Riemannian metric that assigns low transport cost along locally supported tangent directions while penalizing normal velocity components. Second, it alternates between refining cross-time couplings under the induced path-action cost and fitting endpoint-preserving neural bridges between adjacent snapshots. Third, it distills the learned bridge dynamics into a global continuous-time velocity field over cellular states. Across seven controlled and biological datasets covering nine held-out reconstruction experiments, PACE achieves the strongest overall reconstruction performance, reducing MMD, Wasserstein-1 distance, and Wasserstein-2 distance by 23.7% on average relative to the strongest competing baseline. PACE also improves RNA-velocity alignment by 15.4% on an embryoid body differentiation benchmark, without requiring explicit cell pairing, lineage tracing, or RNA-velocity supervision during training. Code is available at https://github.com/AI4Science-WestlakeU/PACE.

Understanding customer movement within retail spaces is essential for optimizing store layouts. Real-world trajectory data can provide highly accurate insights, but collecting it is costly and often infeasible for many retailers. Heuristics such as Travelling Salesman Problem (TSP) and Probabilistic Nearest Neighbours (PNN) are commonly used as inexpensive approximations, but actual customer trajectories deviate by an average of 28% from shortest paths, highlighting a tradeoff between accuracy and practicality. We propose an agent-based modelling framework that casts customer trajectory prediction as a maximum entropy reinforcement learning (RL) problem, balancing reward maximization with stochasticity to better reflect customers with bounded rationality. Using real-world trajectory data from a convenience store, we show that RL-generated trajectories align more closely with customer behaviour than TSP and PNN, providing more accurate estimates of impulse purchase rates and shelf traffic densities. Furthermore, only RL-based predictions yield repositioning decisions for impulse products that align with those derived from actual trajectory data, resulting in comparable estimated profit gains. Our work demonstrates that RL provides a practical, behaviourally grounded alternative that bridges the gap between oversimplified heuristics and data-intensive approaches, making accurate layout optimization more accessible. To encourage further research, the source code is available on GitHub.

While 3D Gaussian Splatting (3DGS) has revolutionized real-time photorealistic view synthesis, its fundamental reliance on symmetric Gaussian distributions introduces visual artifacts that hinder accurate spatial data exploration. Specifically, symmetric kernels struggle to capture shape and color discontinuities , which cause blurriness and primitive redundancy that mislead human perception during visual analysis. To address these visualization barriers, we introduce 3D Skew Gaussian Splatting (3DSGS), a novel framework that significantly enhances the structural fidelity and compactness of explicit scene representations. Our key insight lies in extending the standard primitive to a general Skew Gaussian counterpart. This generalized primitive inherits the highly efficient rasterization properties of standard Gaussians while gaining intrinsic asymmetric modeling capabilities. We couple this with an enhanced opacity representation to better handle complex transparency, alongside a depth-aware densification strategy that intelligently manages primitive allocation. Furthermore, to make these advancements actionable for real-world visual analytics, we re-derive the CUDA rasterization pipeline to universally support both symmetric and skew Gaussians, integrating it into a decoupled, free-camera interactive visualization engine. Extensive experiments demonstrate that 3DSGS achieves superior rendering quality and structural compactness, particularly in regions with intricate details, while maintaining the real-time frame rates necessary for fluid interactive exploration. Supplementary derivations and visual results are available at \textbf{\textit{https://3d-skew-gs.github.io/}}.

Accurate pedestrian trajectory prediction is crucial for autonomous systems operating in complex environments, such as modular buses and delivery robots in suburban or semi-structured areas. Social Spatio-Temporal Graph Convolutional Neural Networks (Social-STGCNN) have shown strong performance by modeling social interactions; however, producing diverse and well-calibrated future trajectories remains challenging. In this work, we build on a Social-STGCNN backbone and introduce a Conditional Variational Autoencoder (CVAE)-based probabilistic formulation to explicitly model multimodal future trajectories. We evaluate the method on the ETH and UCY pedestrian trajectory datasets as well as on a real-world pedestrian dataset collected by a mobile robot. Results show moderate gains on public benchmarks, but more consistent endpoint accuracy and improved trajectory diversity across different crowd configurations. Evaluation on robot-collected data further demonstrates the approach's effectiveness beyond curated benchmarks and supports its applicability in practical deployments.

Generalizable agents should adapt to diverse tasks and unseen environments beyond their training distribution. This position paper argues that such generalization requires environment scaling: expanding the distribution of executable rule-sets that agents interact with, rather than only increasing trajectories or tasks within fixed benchmarks. Current scaling practices largely focus on collecting more experience or broader task sets under fixed interaction rules, leaving agents brittle when underlying interfaces, dynamics, observations, or feedback signals change. The core challenge is therefore a world-level distribution shift: agents need systematic exposure to environments with meaningfully different executable rule-sets. To clarify this challenge, we propose a unified taxonomy that separates trajectory scaling, task scaling, and environment scaling by their primary deliverables and by what changes in the executable rule-set. Building on this taxonomy, we synthesize construction paradigms for scalable environments, contrasting programmatic generators that prioritize controllability and verifiability with generative world models that offer broader coverage and open-endedness. We further outline how environment scaling can be coupled with stateful learning mechanisms, emphasizing learned update rules for cross-environment adaptation. We conclude by discussing alternative perspectives and argue that scalable environments provide the essential substrate for measurable and controllable progress toward robust general agents.

Hallucination correction is not a one-direction problem. We show that intermediate layers are neither uniformly more truthful than final layers nor uniformly less trustworthy. Yet hallucination reduction is usually instantiated through one fixed intervention form: contrast one layer against another, steer along a truthfulness direction, or defer to external evidence. This framing is structurally incomplete. Cross-layer factual evidence does not evolve uniformly: in some failures truthful support is present internally and later suppressed, whereas in others candidate competition remains genuinely multi-directional across depth, so no single signed scalar family is generally sufficient. We introduce Trajectory Correction from Cross-layer Evidence for Hallucination Reduction (TRACE), a deterministic, training-free algorithm which corrects hallucinations at inference time by deriving both the corrective layer and the appropriate correction operator from each input's cross-layer candidate trajectory inside the LLM's own forward pass. Under one frozen hyperparameter setting, TRACE selects among scalar reversal, earlier-state recovery, and candidate-space correction using only model-internal evidence. Evaluated as a single universal algorithm across 15 models, 8 model families, and 3 factuality benchmarks, TRACE improves every evaluation cell, yielding mean gains of +12.26 MC1 points and +8.65 MC2-style points with no regressions, with gains reaching +47.20 MC1 and +43.38 MC2-style points. The method uses no labels, retrieval, pretraining, finetuning, or per-model calibration.

Recent aerial vision-language navigation (VLN) datasets have grown rapidly, but they primarily address goal-oriented navigation to static destinations, leaving UAV visual tracking -- continuously following a moving target while maintaining visibility -- largely without dedicated training data. We introduce CosFlyTrack, a large-scale multi-modal dataset and scalable generation pipeline for UAV visual tracking in urban environments. The dataset provides approximately 12,000 expert and perturbed UAV trajectories generated from 6,000 pedestrian paths, comprising 2.4 million timesteps (approximately 334 hours) with seven aligned data channels: RGB, metric depth, semantic segmentation, six-degree-of-freedom drone pose, target state with visibility flag, bilingual (Chinese-English) instructions, and trajectory-pair metadata. To generate high-quality expert trajectories, we develop MuCO, a multi-constraint optimizer that plans directly in continuous three-dimensional space with BVH-accelerated collision and visibility queries, jointly enforcing target visibility, viewpoint quality, collision avoidance, smoothness, and kinematic feasibility, avoiding the discretization artifacts and post-hoc smoothing of grid-based planners. Fine-tuning experiments on seven vision-language models show that CosFlyTrack improves tracking performance to 78.3 to 95.6 percent SR@1 meter, a 53 to 69 percentage point gain over zero-shot baselines, supporting the dataset as a training resource for dynamic target-following agents. The dataset is publicly available at https://huggingface.co/datasets/AutelRobotics/CosFly; evaluation scripts and pre-trained checkpoints are hosted at https://huggingface.co/AutelRobotics/CosFly-Track.

Recent progress in Reinforcement Learning (RL) provides a principled approach to optimizing Vision-Language-Action (VLA) models, facilitating a shift from trajectory imitation to active learning in the task environment. Despite improvements in control precision, most RL optimizers remain task-specific, which reduces VLA models from generalist controllers to policies that overfit to a narrow set of tasks. In this study, we conduct an in-depth analysis of this phenomenon and highlight the importance of cross-task feature representations for improving the generalizability of VLA models. Motivated by this finding, we introduce DyGRO-VLA, a two-stage optimization framework that 1) effectively captures cross-task latent representations based on information-theoretic principles, and 2) dynamically refines policy optimization via a mixture-of-RL-residuals. DyGRO-VLA enables the RL optimizer to exploit task-relevant latent information while strategically mitigating adverse interference on the learned representations throughout the optimization process. We evaluate our approach on LIBERO, RoboTwin2 benchmarks, and further validate it on real world, demonstrating consistent improvements over strong baselines under multi-task training and distribution shift.

Flexible robotic manipulators (FRMs) offer advantages in lightweight design and large workspace, but their structural flexibility induces vibrations, accelerates fatigue, degrades tracking performance, and limits operational speed. These challenges are further amplified in multi-link serial manipulators, where increased overall length leads to greater structural flexibility. This article presents a backstepping output-feedback framework for fast vibration suppression and tip tracking of an n-degree-of-freedom serial flexible manipulator robot (nDSFMR), with a DeepONet-based approximation for practical deployment. Each link-joint is modeled as a Timoshenko beam coupled with an ODE and transformed into a canonical hyperbolic PDE with boundary dynamics. A backstepping-based boundary controller at the joint is developed to equivalently inject distributed damping along the beam, enabling rapid vibration suppression and trajectory tracking, only using available boundary measurements. To enable real-time implementation and scalability, a DeepONet neural operator is introduced to approximate the backstepping kernels, significantly reducing computational cost and facilitating fast controller updates under varying operating conditions. Experiments on a two-link flexible manipulator demonstrate faster vibration suppression and convergence of the end-effector to the desired trajectory, compared with a linear quadratic regulator (LQR) with feedforward control.

Despite substantial advances in large language models (LLMs), generating factually consistent responses for knowledge-intensive question answering remains challenging. These difficulties are primarily due to hallucinations and the limitations of LLMs in bridging long-tail knowledge gaps. To address this, we propose AMATA, an Adaptive Multi-Agent Trajectory Alignment framework that dynamically integrates external knowledge to improve response interpretability and factual grounding. Our architecture leverages six specialized agents that collaboratively perform structured actions for complex question reasoning. We formalize multi-agent collaboration with external tools as a trajectory preference alignment problem, incorporating question-aware agent customization and inter-agent preference harmonization. AMATA introduces two principal innovations: (1) Intra-Trajectory Preference Learning, which learns objective-oriented preferences to prioritize critical agents, and (2) Inter-Agent Dependency Learning, which captures cross-agent tool dependencies through a novel dependency-aware direct preference optimization technique. Empirical results show that AMATA consistently outperforms baseline approaches, knowledge-augmented frameworks, and LLM-based trajectory systems on five established knowledge-intensive QA benchmarks. Further analysis demonstrates the efficiency of our method in reducing token consumption.

Knowledge distillation is central to LLM post-training, yet its design space remains poorly understood, especially alongside reinforcement learning (RL). We show that the prevailing paradigms, off-policy distillation and on-policy distillation (OPD), implicitly couple two orthogonal choices: prefix source and token-level KL direction. This follows from decomposing sequence-level KL over autoregressive response distributions: forward KL pairs teacher prefixes with token-level forward KL, and reverse KL pairs student prefixes with token-level reverse KL. We argue this coupling is not intrinsic: decoupling the two axes yields four valid objectives. We establish gradient-level identities showing forward KL gives SFT-style cross-entropy matching with teacher soft targets, whereas reverse KL gives an RL-style policy-gradient objective with a dense teacher-student log-ratio reward, connecting them to off-policy SFT, DAgger-style on-policy SFT, offline-RL-style distillation, and OPD. We conduct an extensive controlled study on math reasoning, evaluating the four objectives both as standalone methods and as initializations for subsequent RL. The results reveal three tradeoffs: KL direction induces an accuracy-entropy tradeoff, prefix source a quality-compute tradeoff, and training length an accuracy-stability tradeoff. Motivated by these findings, we propose KL mixing and an entropy-gated length curriculum. KL mixing shows long-sequence distillation requires substantial forward-KL weight to prevent entropy collapse and length inflation without sacrificing accuracy. The entropy-gated length curriculum improves Avg@k and Pass@k by 3.6 and up to 5.8 points, and cuts average response length by roughly 3x versus fixed long-horizon training. Our results provide a framework and practical methods for designing reasoning distillation objectives that balance accuracy, diversity, compute, and RL behavior.

Accurate multi-step port-of-call sequence prediction is vital for tactical resource orchestration and logistical efficiency. However, existing methods struggle with unreliable voyage schedules and the inability of AIS data to provide visibility beyond the immediate next port. To address this, this study proposes a Connectivity-Constrained and Retrieval-Enhanced (CCRE) deep learning framework. Inspired by Retrieval-Augmented Generation, CCRE introduces a retrieval-enhanced historical encoder that queries a global maritime database for contextually similar navigational precedents. Transforming these scenarios into candidate-level semantic representations compensates for data sparsity in long-tail routes and resolves routing ambiguities. Integrating this with a Transformer-based trajectory encoder, the architecture executes adaptive "middle fusion" via cross-attention. This dynamically shifts predictive reliance from real-time kinematics for short-term accuracy to historical context for long-term strategic stability. To ensure sequence-level coherence, forecasting is formulated as a joint sequence generation problem using an autoregressive Transformer decoder enriched with Scheduled Sampling and Gumbel-Softmax relaxation. This mitigates error accumulation, while topology masks strictly enforce maritime network reachability to eliminate operationally infeasible routes. Evaluated on a global dataset, CCRE achieves a 72.3% first-destination accuracy and a 61.4% average three-step accuracy, outperforming baselines like CatBoost and LSTM by average margins of 12.6% and 11.3%, respectively. Case studies further corroborate the model's scalability and ability to capture complex routing patterns across diverse international trade lanes.

Harness engineering has emerged as an important inference-time technique for large language model (LLM) agents, aiming to improve long-term performance through task decomposition and guided execution. However, more elaborate harnesses are not uniformly better: increasing decomposition or guidance can sometimes improve execution, but can also reduce final task success. We study harness design through the lens of inference-time trajectory alignment. This perspective separates harness into two mechanisms: task decomposition, which structures a task into sub-goals, and guided execution, which reshapes local action distributions during execution. This decomposition allows us to quantify how workflow granularity, retry budgets, and guidance-induced action reweighting shape the performance limits of harness design. It further reveals concrete failure modes, including over-decomposition, over-pruning, and hallucinated execution. We validate these predictions through controlled synthetic experiments and real terminal agent benchmarks. Inspired by the theory, we further show that effective harnesses can be partial: specifying only the initial steps and leaving the remaining execution to agent can achieve higher pass rate than fully structured workflows.

The integration of Unmanned Aerial Vehicles(UAVs) into Intelligent Transportation Systems (ITS) offers synoptic visibility for traffic monitoring, yet scalable deployment is hindered by trajectory fragmentation, where vehicle identity persistence is lost across multi-UAV Fields of View (FOV). While state-of-the-art frameworks excel in optimizing local trajectory extraction and stability for single-drone imagery, they often function as isolated data silos that generate disjointed trajectories, thereby precluding network-level analysis such as Origin-Destination estimation. This paper presents a real-time Multi-Camera Multi-Vehicle Tracking (MCMT) system designed to handle global identity persistence. Addressing the visual ambiguity and computational cost of appearance-based Re-Identification (Re-ID) in nadir views, we introduce a lightweight Topology-Based Spatiotemporal Handover mechanism. We implement a high-throughput parallel pipeline leveraging YOLO11 and ByteTrack to process concurrent 4K streams. Our core contribution is a deterministic queue-based matching algorithm that utilizes geometric overlaps and virtual lane discretization to predictively manage identity handover via FIFO queues. Experimental results on complex urban environments, including intersections and merging traffic, demonstrate a Handover Success Rate (HOSR) of 99.8% in continuous traffic flows, significantly outperforming Re-ID baselines (74.1%) while validating edge deployment feasibility. The source code is available at https://github.com/JYe9/multi-camera-multi-vehicle-tracking-system.

Human trajectory forecasting is crucial for safe navigation in crowded environments, requiring models that balance accuracy with computational efficiency. Efficiently modeling social interactions is key to performance in dense crowds. Yet, most recent methods rely on attention mechanisms, which are effective at capturing complex dependencies, but incur quadratic computational costs that scale poorly with the growing number of neighbors. Recently, Selective State-Space Models have provided a linear-time alternative; however, their inherently sequential design is misaligned with the unstructured and dynamic nature of social interactions. To address this challenge, we propose Social-Mamba, a forecasting architecture that reformulates social interactions as structured sequential processes. At its core is the Cycle Mamba block, a novel module that enables continuous bidirectional information flow. Social-Mamba organizes agents on an egocentric grid and introduces social triplet factorization, which decomposes interactions into temporal, egocentric, and goal-centric scans. These are dynamically integrated through a learnable social gate and global scan to generate accurate and efficient trajectory predictions. Extensive experiments on five trajectory forecasting benchmarks show that Social-Mamba achieves state-of-the-art accuracy while offering superior parameter efficiency and computational scalability. Furthermore, embedding Social-Mamba into a flow-matching framework further enhances both accuracy and efficiency, establishing it as a flexible and robust foundation for future trajectory forecasting research. The code is publicly available: https://github.com/vita-epfl/Social-Mamba

LLMs are increasingly deployed in autonomous laboratories, under the assumption that their domain priors and reasoning over iterative feedback let them converge on good designs in fewer iterations than feedback-only baselines. Current iterative scientific design benchmarks, however, score only outcome snapshots at fixed horizons. This leaves the learning trajectory unmeasured, even though the trajectory is what captures learning efficiency, where each iteration saved is a real saving in cost and time. Motivated by this, we examine three evaluation choices that change the conclusions one draws about LLM learning efficiency in iterative scientific design: what to measure, what baseline to compare against, and what to ground against. We introduce LEAPBench, Learning Efficiency in Adaptive Processes, a 55-task framework that pairs a best-so-far area under the curve (AUC) trajectory metric with a classical Bayesian-optimization reference and an audit grounded in published literature. Applied to eight contemporary LLMs, switching from final-outcome to trajectory scoring changes the best-model decision on 53% of tasks at matched horizons, and exposes efficiency gains overlooked by outcome-based scoring. LLMs do not outperform a classical Bayesian baseline. On 16 biology tasks where the oracle's reward signal is aligned with configurations from the published-best design, domain-aware prompting leads to LLM choices that match the published-best's approximately 10 percentage points less often than domain-agnostic prompting at iteration 30. The pattern is sharpest on 6 tasks where the literature-typical and published-best configurations diverge, and domain-agnostic prompting matches the published-best more often on all 6. The trajectory metric also doubles as a tractable training target. Offline reinforcement learning with the metric as a reward improves performance on 14 of 21 held-out tasks.

This paper addresses the problem of reconstructing missing or dropped frames in top-down drone video of autonomous surface vehicles performing structured maritime manoeuvres. We propose a pipeline that converts raw GPS telemetry and a single reference frame into a trajectory-guided video sequence using a pre-trained image-to-video diffusion model, requiring no domain-specific fine-tuning. GPS coordinates from onboard telemetry logs are projected into image space via an equirectangular mapping, producing per-vessel motion cues that condition the SG-I2V diffusion model. The generated frames are evaluated against ground-truth video using perceptual, temporal and trajectory-based metrics, and benchmarked against optical flow extrapolation and RIFE interpolation baselines. SG-I2V produces the most naturally appearing frames among all methods (BRISQUE 25.52, closest to ground-truth 23.64), the most realistic motion magnitude (temporal smoothness 1.14 vs. ground truth 1.42), and the strongest GPS trajectory adherence (9.31px vs. 28.70px for ground-truth, the latter reflecting approximate temporal alignment between footage and GPS logs rather than generation error), demonstrating that trajectory-guided diffusion synthesis is a viable approach to maritime video reconstruction under challenging low-texture, small-object conditions.

This work reformulates language generation as a stochastic optimal control problem, providing a unified theoretical perspective to analyze autoregressive and diffusion models and explain their limitations (Efficiency-Fidelity Paradox, Irreversibility Error Propagation, Optimization Tractability and Fidelity) in terms of combination of trajectory singularity, adjoint state vanishing, and gradient absence. To address these issues, we approximate the solution to the Hamilton-Jacobi-Bellman (HJB) equation, yielding an optimal policy that acts as a closed-loop controller. To bypass the intractability of directly solving the HJB PDE, we employ Flow Matching as the optimal trajectory solver within the rectified latent control space. This allows our Manta-LM with Global Integral Operator to approximate the global vector field, effectively realizing a model that simultaneously achieves high-fidelity text generation and efficient, low-cost parallel sampling. Empirically, our method achieves strong performance on language modeling and conditional generation tasks, while exhibiting improved stability, efficiency, and controllability.

We study analogical trajectory transfer, where the goal is to translate motion trajectories in one 3D environment to a semantically analogous location in another. Such a capacity would enable machines to perform analogical spatial reasoning, with applications in AR/VR co-presence, content creation, and robotics. However, even semantically similar scenes can still differ substantially in object placement, scale, and layout, so naively matching semantics leads to collisions or geometric distortions. Furthermore, finding where each trajectory point should transfer to has a large search space, as the mapping must preserve semantics and functionality without tearing the trajectory apart or causing collisions. Our key insight is to decompose the problem into spatially segregated subproblems and merge their solutions to produce semantically consistent and spatially coherent transfers. Specifically, we partition scenes into object-centric clusters and estimate cross-scene mappings via hierarchical smooth map prediction, using 3D foundation model features that encode contextual information from object and open-space arrangements. We then combinatorially assemble the per-cluster maps into an initial transfer and refine the result to remove collisions and distortions, yielding a spatially coherent trajectory. Our method does not require training, attains a fast runtime around 0.6 seconds, and outperforms baselines based on LLMs, VLMs, and scene graph matching. We further showcase applications in virtual co-presence, multi-trajectory transfer, camera transfer, and human-to-robot motion transfer, which indicates the broad applicability of our work to AR/VR and robotics.

While generative models have shown promise in pediatric sleep analysis, the latent structure of their multimodal embeddings remains poorly understood. This work investigates session-wide diagnostic information contained in the sequences of 30-second pediatric PSG epochs embedded by a multimodal masked autoencoder. We test whether augmenting embeddings with PHATE-derived per-epoch coordinates and whole-night movement descriptors, persistent homology summaries of the embedding cloud, and EHR yields task-relevant signals. Simple linear and MLP models, chosen for interpretability rather than state-of-the-art performance, show that geometric, topological, and clinical features each provide complementary gains. For binary predictions, feature importance is task-dependent, and more expressive late-fusion models generally perform better, with AUPRC improving from 0.26 to 0.34 for desaturation, 0.31 to 0.48 for EEG arousal, 0.09 to 0.22 for hypopnea, and 0.05 to 0.14 for apnea. We also report Brier score and Expected Calibration Error, where the full fusion model yields the best calibration across all four binary tasks. Our study reveals that latent geometry/topology and EHR offer complementary, interpretable signals beyond embeddings, improving calibration and robustness under extreme imbalance.

In robotics, a common challenge in imitation learning is the mismatch between training and deployment conditions, caused, for example, by environmental changes or imperfect observation and control. When a robot follows a nominal trajectory under such mismatch, it may become stuck and fail to complete the task. This calls for adaptive online exploration strategies that remain grounded in demonstrations. To this end, we propose an adaptive ergodic imitation approach that constructs a target distribution from the geometry of the retrieved demonstrations and uses it to generate trajectories that adaptively interpolate between tracking and exploration. Our method extends ergodic control beyond its traditional role in area-coverage and search by incorporating demonstrations into a retrieval-based receding-horizon framework for adaptive imitation.

Diffusion language models are a promising alternative to autoregressive models, yet post-training methods for them largely adapt reward-maximizing objectives. We identify a central failure mode in this setting we call trajectory locking: sampled reward-driven updates over-concentrate probability mass onto a narrow set of denoising paths, reducing coverage of alternative correct solutions under repeated sampling. To address this, we propose TraFL (Trajectory Flow baLancing), a trajectory-balance objective that trains the policy toward a reward-tilted target distribution anchored to a frozen reference model. We make this practical for diffusion language models with a diffusion-compatible sequence-level surrogate and a learned prompt-dependent normalization. Across mathematical reasoning and code generation benchmarks, TraFL is the only evaluated post-training method that improves over the base model in every benchmark-length setting, with gains that persist as the sampling budget increases. The improvements transfer to held-out evaluations: TraFL stays above the base model on Minerva Math and is the strongest method on every LiveCodeBench difficulty split.

Designing continuous trajectories whose time-averaged occupancy provably matches a prescribed spatial density (the \emph{ergodic coverage} problem) is central to UAV-assisted data collection and sensing, robotic exploration, and mobile monitoring. For flying agents in particular, this challenge is acute: trajectories must balance coverage fidelity against tight energy budgets, no-fly zones, and acceleration limits. Existing methods either re-optimize each trajectory online (with cost growing in the horizon and re-running for every target, agent, and realization) or rely on bespoke analytical constructions that must be re-derived for each new constraint. We propose a \emph{epushforward} framework that decouples ergodicity from density matching: an analytic latent trajectory provides exact uniform ergodicity on a simple annular domain, and a single map, learned offline by optimal-transport conditional flow matching, transports this latent occupancy onto the prescribed target density. The composed trajectory is then asymptotically ergodic with respect to the learned pushforward distribution, with deviation from the target controlled by the flow-matching training loss. Once trained for a given target density and constraint set, the map serves an unbounded number of trajectories and a multi-agent fleet without per-agent retraining, and many differentiable operational constraints (no-fly zones, acceleration ceilings, or fairness penalties) enter as additive soft penalties in the training loss without re-deriving the design. We prove three results (an acceleration-energy bound, an $O(1/\sqrt{K})$ ergodic convergence rate in the number of trajectory cycles $K$, and an approximation-error bound) that combine into an end-to-end coverage bound estimable from CFM training diagnostics (certified given an architectural Lipschitz bound on $v_θ$).

Learning and representing the subjectivities of agents has become a challenging but crucial problem in the trajectory prediction task. Such subjectivities not only present specific spatial or temporal structures, but also are anisotropic for all interaction participants. Despite great efforts, it remains difficult to explicitly learn and forecast these subjectivities, let alone further modulate models' predictions through a specific ego's subjectivity. Inspired by prefactual thoughts in psychology and relevant theatrical concepts, we interpret such subjectivities in future trajectories as the continuous process from rehearsal to encore. In the rehearsal phase, the proposed ego predictor focuses on how each ego agent learns to derive and direct a set of explicitly biased rehearsal trajectories for all participants in the scene from the short-term observations. Then, these rehearsal trajectories serve as immediate controls to condition final predictions, providing direct yet distinct ego biases for the prediction network to simulate agents' various subjectivities. Experiments across datasets not only demonstrate a consistent improvement in the performance of the proposed \emph{Encore} trajectory prediction model but also provide clear interpretability regarding subjectivities as biased ego rehearsals.

Local interaction laws governing multi-agent systems can be difficult to recover from trajectory data, even when the dynamics are observed faithfully. In systems governed by a nonlinear sheaf Laplacian -- a generalization of the graph Laplacian accommodating heterogeneous state spaces and asymmetric communication channels -- the coordination law is encoded by edge potential functions whose gradients produce the inter-agent forces. Because trajectory observations record node-state evolution, they expose only the aggregate effect of the edge forces at each node: distinct interaction laws that agree at the node level are indistinguishable from trajectory data alone. We show that the fundamental obstruction to recovery is topological, measured by sheaf cohomology, and that unique recovery from an unconstrained function class is possible if and only if this cohomology vanishes. When the obstruction is nontrivial, we show that recovery within a finite-dimensional parameterized class is possible precisely when a data-dependent information matrix is positive definite. Experiments validate the theory and illustrate that accurate trajectory reproduction need not certify recovery of the underlying interaction law.

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

Multi-agent trajectory modeling traditionally focuses on forecasting, often neglecting more general tasks like trajectory completion, which is essential for real-world applications such as correcting tracking data. Existing methods also generally predict agents' states without offering any state-wise measure of heteroscedastic uncertainty. Moreover, popular multi-modal sampling methods lack error probability estimates for each generated scene under the same prior observations, which makes it difficult to rank the predictions at inference time. We introduce U2Diffine, a unified diffusion model built to perform trajectory completion while simultaneously offering state-wise heteroscedastic uncertainty estimates. This is achieved by augmenting the standard denoising loss with the negative log-likelihood of the predicted noise, and then propagating the latent space uncertainty to the real state space using a first-order Taylor approximation. We also propose U2Diff, a faster baseline that avoids gradient computation during sampling. This approach significantly increases inference speed, making it as efficient as a standard generative-only diffusion model. For post-processing, we integrate a Rank Neural Network (RankNN) that enables error probability estimation for each generated mode, demonstrating strong correlation with ground truth errors. Our method outperforms state-of-the-art solutions in both trajectory completion and forecasting across four challenging sports datasets (NBA, Basketball-U, Football-U, Soccer-U), underscoring the effectiveness of our uncertainty and error probability estimation.

Trajectories are nowadays valuable information for a wide range of applications. However they are also inherently sensitive, as they contain highly personal information about individuals. Facing this challenge, synthesizing mobility trajectories has emerged as a promising solution to leverage mobility information while preserving privacy. State-of-the-art models, often rely on the false assumptions of generative models implicit privacy and fails to provide privacy guarantees while preserving trajectories utility. Here, we introduce diffGHOST, a conditional diffusion model based on latent space segmentation, designed to answer this challenge. Thus, this paper propose a methodology that identify and mitigate memorization of critical samples using condition segments of a learn latent space.

End to end (E2E) autonomous driving trajectory prediction is often trained with camera frames sampled at the highest available temporal frequency, assuming that denser sampling improves performance. We question this assumption by treating temporal sampling frequency as an explicit training set design variable. Starting from high frequency E2E driving datasets, we construct frequency sweep training sets by temporally subsampling camera frames along each trajectory. For each model dataset pair, we train and evaluate the same model under a fixed protocol, so the frequency response reflects how prediction performance changes with sampling frequency. We analyze this response from a capacity aware perspective. Sparse sampling may miss driving relevant cues, while dense sampling may add redundant visual content and off manifold noise. For finite capacity models, this can create a driving irrelevant capacity burden. We evaluate three smaller E2E models and a larger VLA style AutoVLA model on Waymo, nuScenes, and PAVE. Results show model and dataset dependent frequency responses. Smaller E2E models often show non monotonic or near plateau trends and achieve their best 3 second ADE at lower or intermediate frequencies. In contrast, AutoVLA achieves its best 3 second ADE and FDE at the highest evaluated frequency on all three datasets. Iteration matched controls suggest that the advantage of lower or intermediate frequencies for smaller models is not explained only by unequal training update counts. These findings show that temporal sampling frequency should be reported and tuned, rather than fixed to the highest available value.

Neural Flows efficiently model irregular multivariate time series by directly learning ODE solution trajectories with neural networks, bypassing step-by-step numerical solvers. Despite their efficiency, many existing approaches treat variables independently, leaving inter-variable interactions underexplored. Moreover, their one-step mapping makes interaction modeling inherently challenging, as it removes the iterative refinement of interactions during learning. To address this challenge, we propose one-step Graph-Structured Neural Flows (GSNF), which introduce two auxiliary-trajectory self-supervision strategies to strengthen interaction learning: (i) interaction-aware trajectory generation via re-initialization, which induces trajectory divergence to expose graph-induced interactions, with a theoretically derived lower bound on divergence; and (ii) reverse-time trajectory generation, which enforces forward-backward consistency to regularize graph learning, enabled by flow invertibility. Experiments on five real-world datasets show that GSNF achieves state-of-the-art classification performance with highly competitive training time and memory usage.