Trajectory Prediction

Diffusion-based trajectory planners can synthesize rich, multimodal robot motions, but their iterative denoising makes online planning and control prohibitively slow. Existing accelerations either modify the sampler or compress the network--sacrificing plan quality or requiring retraining without accounting for downstream control risk. We address the problem of making diffusion-based trajectory planners fast enough for real-time robot use without retraining the model or sacrificing trajectory quality, and in a way that works across diverse state-space diffusion architectures. Our key insight is that diffusion trajectory planners expose two signals we can exploit: a cheap probe of how their internal trajectory representation changes across steps, and analytic coefficients that describe how denoiser errors affect the sampler's state update. By calibrating the first signal against the second on offline runs, we obtain a per-step score that upper-bounds how far the final trajectory can deviate when we reuse a cached denoiser output, and we treat this bound as an uncertainty budget that we can spend over the denoising process. Building on this insight, we present Muninn, a training-free caching wrapper that tracks this uncertainty budget during sampling and, at each diffusion step, chooses between reusing a cached denoiser output when the predicted deviation is small and recomputing the denoiser when it is not. Across standard benchmarks Muninn delivers up to 4.6x wall-clock speedups across several trajectory diffusion models by reducing denoiser evaluations, while preserving task performance and safety metrics. Muninn further certifies that cached rollouts remain within a specified distance of their full-compute counterparts, and we validate these gains in real-time closed-loop navigation and manipulation hardware deployments. Project page: https://github.com/gokulp01/Muninn.

Most language-model training data shows final artifacts, not the process that produced them. We study a tractable version of this question in tool use: when a model learns a stream of new API domains, does keeping tool-use trajectories help compared with stripping the intermediate API trace? We fine-tune Llama 3.1 8B Instruct with QLoRA on API-Bank using four sequential domain blocks. Condition A strips previous API request/response lines from the prompt and trains the model to predict the next API call. Condition B keeps the trajectory context. In a single-seed pilot, full held-out generation evaluation shows that Condition B reaches 56.9% final exact full-call accuracy compared with 39.2% for Condition A. B also improves final API-name accuracy by 7.7 points. However, B uses 25.1% more training tokens, the run uses one seed, and the task is next-call prediction rather than full dialogue success.

Multi-object tracking (MOT) is a fundamental task in computer vision that requires continuously tracking multiple targets while maintaining consistent identities across frames. However, most existing approaches primarily rely on instance-level object features for trajectory association, which often leads to degraded performance under challenging conditions such as object deformation, nonlinear motion, and occlusion. In this work, we propose SAMOFT, a robust tracker that leverages pixel-level cues to improve robustness under complex motion scenarios. Specifically, we introduce a Pixel Motion Matching (PMM) module that integrates the Segment Anything Model (SAM) with dense optical flow to refine Kalman filter-based motion prediction using instantaneous foreground pixel motion. To further enhance robustness under unreliable detections, we design a Centroid Distance Matching (CDM) module that performs flexible mask-based centroid matching for low-confidence or partially occluded observations. Moreover, a Distribution-Based Correction (DBC) module models long-tailed motion patterns in a training-free manner using historical optical flow statistics and dynamically corrects trajectory states online. We also incorporate a Cluster-Aware ReID (CA-ReID) strategy to improve the stability and discriminative power of trajectory appearance features. Extensive experiments on the DanceTrack and MOTChallenge benchmarks demonstrate that SAMOFT consistently improves baseline trackers and achieves competitive performance compared with recent state-of-the-art methods, validating the effectiveness of leveraging pixel-level cues for robust multi-object tracking.

Agentic memory enables LLMs to persist information beyond a single context window and reuse it in later decisions, but it also introduces a new vulnerability: spurious correlations, where retrieved memory carries miscorrelated evidence and propagates erroneous reasoning into downstream decisions. Despite the widespread use of agentic memory, this risk remains largely underexplored. We address it from two aspects. First, we benchmark several canonical types of spurious patterns identified through causal structure and record them across trajectory-level memory. Diagnosing agentic memory systems on this benchmark reveals that memory improves reasoning on clean inputs but amplifies reliance on spurious patterns when they are present. Second, we propose CAMEL, a plug-and-play calibration method that operates across diverse memory architectures at both write and retrieval time. CAMEL consistently reduces reliance on spurious patterns across all three types while preserving or improving performance on clean inputs and staying robust under adaptive attacks targeting the calibration. Overall, CAMEL offers a principled and lightweight solution toward more reliable agentic memory deployment.

Deep generative models provide flexible frameworks for modeling complex, structured data such as images, videos, 3D objects, and texts. However, when applied to sequences of human skeletons, standard variational autoencoders (VAEs) often allocate substantial capacity to nuisance factors-such as camera orientation, subject scale, viewpoint, and execution speed-rather than the intrinsic geometry of shapes and their motion. We propose the Elastic Shape - Variational Autoencoder (ES-VAE), a geometry-aware generative model for skeletal trajectories that leverages the transported square-root velocity field (TSRVF) representation on Kendall's shape manifold. This representation inherently removes rigid translations, rotations, and global scaling of shapes, and temporal rate variability of sequences, isolating the underlying shape dynamics. The ES-VAE encoder maps skeletal sequences to a low-dimensional latent space incorporating the Riemannian logarithm map, while the decoder reconstructs sequences using the corresponding exponential map. We demonstrate the effectiveness of ES-VAE on two datasets. First, we analyze skeletal gait cycles to predict clinical mobility scores and classify subjects into healthy and post-stroke groups. Second, we evaluate action recognition on the NTU RGB+D dataset. Across both settings, ES-VAE consistently outperforms standard VAEs and a range of sequence modeling baselines, including temporal convolutional networks, transformers, and graph convolutional networks. More broadly, ES-VAE provides a principled framework for learning generative models of longitudinal data on pose shape manifolds, offering improved latent representation and downstream performance compared to existing deep learning approaches.

Reasoning-based end-to-end (E2E) autonomous driving has recently emerged as a promising approach to improving the interpretability of driving decisions as it can generate human-readable reasoning together with predicted trajectories. Such approaches commonly generate multiple trajectories to capture diverse future behaviors, and they fall into two categories: (1) multi-reasoning, where one reasoning sequence is generated per trajectory, and (2) single-reasoning, where a single reasoning is shared across all trajectories. The former offers richer diversity at the cost of redundant computation, while the latter is more efficient but is often assumed to sacrifice diversity. Alpamayo 1, a representative system, adopts the multi-reasoning approach and achieves competitive trajectory prediction performance. However, the efficiency of this design remains largely unexplored, making it a well-motivated subject for investigation. In this paper, we systematically analyze and improve Alpamayo 1 in two ways. First, we reduce inference latency while preserving trajectory diversity by redesigning Alpamayo 1 into a single-reasoning system. Through extensive experiments, we find that replacing multi-reasoning with single-reasoning does not meaningfully degrade trajectory diversity. Second, we accelerate diffusion-based action generation by eliminating inter-block overhead arising from unnecessary copy operations and inefficient kernel execution. Through closed-loop and open-loop experiments, we validate both optimizations, demonstrating a 69.23% reduction in inference latency while maintaining trajectory diversity and prediction quality. These results highlight the importance of jointly analyzing system architecture and runtime execution to improve the efficiency of reasoning-based E2E AD systems.

End-to-end autonomous driving requires models to understand traffic scenes, infer driving intent, and generate executable motion plans. Recent vision-language-action (VLA) models inherit semantic priors from large-scale vision-language pretraining, yet still face a coupling trade-off: fully shared backbones preserve multimodal interaction but may entangle language reasoning and trajectory prediction, whereas decou pled reasoning-action pipelines reduce task conflict but weaken semantic-motion coupling. We propose VECTOR-DRIVE, a tightly coupled VLA framework built on Qwen2.5-VL-3B. VECTOR-DRIVE keeps all tokens coupled through shared self attention and routes feed-forward computation according to token semantics. Vision and language tokens are processed by a Vision-Language Expert to preserve semantic priors, while target-point, ego-state, and noisy action tokens are routed to a Trajectory Expert for motion-specific computation. On the action-token pathway, a flow-matching planner refines noisy action tokens into future waypoints and speed profiles. This design couples semantic reasoning and motion planning within a single multimodal Transformer while separating task-specific FFN computation. On Bench2Drive, VECTOR-DRIVE achieves 88.91 Driving Score and outperforms representative end-to end and VLA-based baselines. Qualitative results and ablations further validate the benefits of shared attention, semantic-aware expert routing, progressive training, and flow-based action de coding.

Diffusion models for multi-agent trajectory prediction are limited by iterative denoising, which causes inference latency that hinders their use in time-critical settings like autonomous driving. Fast-sampling variants using DDIM and informed initial noise distributions partially alleviate this issue, but they either fail to achieve true single-step generation or are constrained by the chosen noise distribution. Consistency Models (CMs) offer high-quality one-step generation by mapping noise directly to data, but are difficult to train from scratch. We propose ECTraj, an enhanced CM pipeline with improved training and conditional generation for trajectory prediction. Our framework extends the student-teacher consistency training scheme: the student produces standard outputs, while the teacher explicitly fuses its predictions with parts of the ground truth to give stronger supervision. We also exploit CMs' direct denoising for top-K multi-shot generation during training. Combining conditional generation with this enhanced consistency objective yields faster inference and improved prediction accuracy, establishing competitive new benchmarks on the large-scale Argoverse 2 dataset.

Diffusion-based models decompose sampling into many small Gaussian denoising steps -- an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation, consistency training, or adversarial objectives, but sacrifice the likelihood framework in the process. We introduce Normalizing Trajectory Models (NTM), which models each reverse step as an expressive conditional normalizing flow with exact likelihood training. Architecturally, NTM combines shallow invertible blocks within each step with a deep parallel predictor across the trajectory, forming an end-to-end network trainable from scratch or initializable from pretrained flow-matching models. Its exact trajectory likelihood further enables self-distillation: a lightweight denoiser trained on the model's own score produces high-quality samples in four steps. On text-to-image benchmarks, NTM matches or outperforms strong image generation baselines in just four sampling steps while uniquely retaining exact likelihood over the generative trajectory.

Discrete flow matching generates text by iteratively transforming noise tokens into coherent language, but may require hundreds of forward passes. Distillation uses the multi-step trajectory to train a student to reproduce the process in a few steps. When the student underperforms, the usual explanation is insufficient capacity. We argue the opposite: the trajectory is the bottleneck, not the student. Each training trajectory is built through a chain of blind stochastic jumps with no evaluation of sequence quality; a single bad decision at an early midpoint propagates through subsequent steps, yet the student must imitate the result. Trajectory-Shaped Discrete Flow Matching (TS-DFM) replaces these blind jumps with guided navigation: a lightweight energy compass evaluates candidate continuations at each midpoint, selecting the most coherent. All shaping is training-only; inference cost is unchanged. On 170M-parameter language modeling, the shaped student at 8 steps achieves 32% lower perplexity than the 1,024-step teacher while being 128x faster, with gains consistent across source distributions and three evaluators of increasing scale. TS-DFM achieves the best perplexity of any discrete-generation baseline we compare against, including methods trained on 6x more data or using 5x larger models.

Alignment of large language models (LLMs) via SFT and RLHF/DPO typically ignores the global geometry of the representation space, relying instead on local token likelihoods or scalar scores. We view generation as tracing a semantic trajectory in hidden space and propose a topology-enhanced alignment framework that regularizes these trajectories using 0-dimensional persistent homology. First, for SFT, we introduce Trajectory Topology Loss (TTL). Treating prompt and gold-answer embeddings as a mixed point cloud, we use a 0D persistent homology algorithm to extract "prompt-answer bridges." TTL aligns the model's actual update direction with these topological bridges rather than arbitrary directions. Second, for DPO, we propose Topological Preference Optimization (TPO). TPO constructs topic-specific semantic preference vectors and aligns the improvement direction between rejected and chosen responses with these vectors in an intermediate hidden layer. We also introduce a dynamic weighting scheme to balance DPO and TPO losses. Evaluating on Qwen2.5-7B-Instruct using UltraChat and Anthropic HH-RLHF, our topology-enhanced objectives consistently outperform strong non-topological baselines (e.g., per-example, nearest-neighbor, random regularizers) on automatic preference metrics and LLM-judge evaluations, while maintaining or improving toxicity. Results show persistent homology and trajectory geometry offer a promising direction for controllable alignment.

The interaction of robots with bendable objects in midair presents significant challenges in control, often resulting in performance degradation and potential crashes, especially for aerial robots due to their limited actuation capabilities and constant need to remain airborne. This paper presents an adaptive controller that enables two aerial vehicles to collaboratively follow a trajectory while transporting a bendable object without relying on explicit elasticity models. Our method allows on-the-fly adaptation to the object's unknown deformable properties, ensuring stability and performance in trajectory-tracking tasks. We use Lyapunov analysis to demonstrate that our adaptive controller is asymptotically stable. Our method is evaluated through hardware experiments in various scenarios, demonstrating the capabilities of using multirotor aerial vehicles to handle bendable objects.

Gradient-based attribution methods are model-faithful and scalable, but Integrated Gradients (IG) can be brittle because explanations depend on heuristic baselines, straight-line paths, discretization, and saturation. We propose Fisher--Rao Integrated Gradients (FRInGe), which defines both the reference and interpolation schedule in predictive distribution space. FRInGe replaces input baselines with a maximum-entropy predictive reference and follows a Fisher-Rao geodesic on the probability simplex. The corresponding input-space trajectory is realized through the pullback Fisher metric and stabilized by KL and Euclidean trust regions; attributions are obtained by integrating input gradients along this trajectory. Across six ImageNet architectures, FRInGe most clearly improves calibration-oriented attribution metrics, especially MAS scores, while remaining competitive on perturbation AUC and infidelity.

The goal of this paper is certifying safety of dynamical systems subject to uncertainty. Existing approaches use trajectory data to estimate transition probabilities, and compute safety probabilities recursively via dynamic programming (DP). This recursion may lead to compounding errors in the certified safety probability, thus collapsing to a vacuous lower bound for growing horizons $T$. We propose a kernel embedding framework that treats safety certification as a classification problem on trajectory data, directly estimating the $T$-step safety probability without recursion. We show that the framework subsumes well-established approaches from the literature (e.g., barrier certificates, robust Markov models) as special cases, and allows us to go beyond their limitations. As the main consequence, it bypasses compounding error across the horizon and enables certification for systems with non-Markovian dynamics. We demonstrate that direct estimators remain stable independent of the certification horizon and in the non-Markovian setting, whilst DP-based certificates silently go unsound -- confirmed in simulation on a neural-controlled quadrotor.

Gap-closing rate and visual looming swap discriminative dominance depending on deceleration intensity - a finding that reconciles a long-standing conflict in the car-following literature and challenges spacing-centered assumptions in traditional driver behavior models. This study presents a two-stage analytical framework that distinguishes between information availability (kinematic variables measurable in the environment) and information utilization (variables that demonstrably separate driver behavioral patterns), applied to 1,060,119 valid car-following observations from the NGSIM trajectory dataset (2,932 vehicles). Six kinematic features are extracted, and deceleration events are detected under two threshold conditions (-0.5 m/s^2 and -0.3 m/s^2). K-means clustering identifies behavioral modes, and one-way ANOVA with eta-squared effect sizes ranks each feature's discriminative power. Three key findings emerge: (1) threshold selection fundamentally shapes behavioral inference - the stricter threshold yields three interpretable modes while the permissive threshold collapses these to two; (2) hard braking prioritizes gap-closing rate (eta^2 = 0.715) while moderate braking emphasizes visual looming (eta^2 = 0.574); and (3) spacing headway is negligible (eta^2 <= 0.014) across both thresholds. These findings provide empirically grounded candidates for perceptual cue prioritization and have direct implications for ADAS warning system design and autonomous vehicle control.

A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a Euclidean space and relates these trajectories to node embeddings. In multilayer and unfolded spectral constructions, however, node embeddings and their underlying latent positions are identifiable only up to general linear transformations. Although this ambiguity preserves edge probabilities, it can distort geometry and invalidate distance based temporal comparisons at both the trajectory and node-levels. We develop Multiscale Euclidean Network Trajectories (MENT), a framework for multiscale temporal trajectories based on second-moment geometry. By imposing an isotropic normalization on the anchor latent positions, we reduce the relevant ambiguity to orthogonal transformations and prevent distortion of the second-moment geometry. In this canonical representation, we define a trace variation distance and mode-wise variation distances along orthogonal directions, and use multidimensional scaling to obtain low-dimensional trajectories of time points at both global and mode-wise levels. The resulting trajectories support interpretation and inference. They admit mode-wise decompositions, support attribution of global and mode-wise temporal changes to nodes, and enable change point detection through 1D trajectories. We prove consistency of the proposed unfolded spectral embedding and of the induced temporal trajectories. Experiments on two synthetic and two real dynamic networks illustrate stable and interpretable recovery of temporal structure and show strong performance against existing change point detection baselines.

Representation Engineering analyses often characterize refusal using static directions extracted from terminal or pooled representations. We ask whether this view misses how refusal is constructed across layer-token positions. Using causal tracing, we identify a \textit{Refusal Trajectory}: a sparse upstream activation pattern that often persists even when attacks such as GCG suppress terminal refusal signals. Based on this observation, we propose SALO (Sparse Activation Localization Operator), a lightweight white-box detector that operates on raw hidden-state volumes from a selected layer window. Across Qwen, Llama, and Mistral models, SALO improves jailbreak detection on several attack families under a fixed XSTest-calibrated operating point. We further analyze static RepE-style baselines, ROI sensitivity, adaptive GCG attacks, and encoded-input boundary cases, clarifying both the promise and limitations of refusal-trajectory monitoring.

Distributed blackbox consensus optimization is a fundamental problem in multi-agent systems, where agents must improve a global objective using only local objective queries and limited neighbor communication. Existing methods largely rely on handcrafted update rules and static cooperation patterns, which often struggle to balance local adaptation, global coordination, and communication efficiency in heterogeneous nonconvex environments. In this paper, we take an initial step toward trajectory-driven self-design for distributed black-box consensus optimization. We first redesign the agent-level swarm dynamics with an adaptive internal mechanism tailored to decentralized consensus settings, improving the balance between exploration, convergence, and local escape. Built on top of this adaptive execution layer, we propose Learning to Act and Cooperate (LACMAS), a trajectorydriven framework in which large language models provide sparse highlevel guidance for shaping both agentinternal action behaviors and agentexternal cooperation patterns from historical optimization trajectories. We further introduce a phased cognitive scheduling strategy to activate different forms of adaptation in a resource-aware manner. Experiments on standard distributed black-box benchmarks and real-world distributed tasks show that LAC-MAS consistently improves solution quality, convergence efficiency, and communication efficiency over strong baselines, suggesting a practical route from handcrafted distributed coordination toward self-designing multi-agent optimization systems.

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

Large language model (LLM) agents deployed in clinical settings often exhibit abrupt, threshold-driven behavior, offering little visibility into accumulating risk prior to escalation. In real-world care, however, clinicians act on gradually rising concern rather than instantaneous triggers. We study whether explicit state dynamics can expose such pre-escalation signals without delegating clinical authority to the agent. We introduce a lightweight agent architecture in which a memoryless clinical risk encoder is integrated over time using first- and second-order dynamics to produce a continuous escalation pressure signal. Across synthetic ward scenarios, stateless agents exhibit sharp escalation cliffs, while second-order dynamics produce smooth, anticipatory concern trajectories despite similar escalation timing. These trajectories surface sustained unease prior to escalation, enabling human-in-the-loop monitoring and more informed intervention. Our results suggest that explicit state dynamics can make LLM agents more clinically legible by revealing how long concern has been rising, not just when thresholds are crossed.

Deep reinforcement learning (DRL) finds extensive application in autonomous drone navigation within complex, high-risk environments. However, its practical deployment faces a safety-exploration dilemma: soft penalty mechanisms encourage risky trial-and-error, while most constraint-based methods suffer degraded performance under sensor noise and intent uncertainty. We propose Dynamic-TD3, a physically enhanced framework that enforces strict safety constraints while maintaining maneuverability by modeling navigation as a Constrained Markov Decision Process (CMDP). This framework integrates an Adaptive Trajectory Relational Evolution Mechanism (ATREM) to capture long-range intentions and employs a Physically Aware Gated Kalman Filter (PAG-KF) to mitigate non-stationary observation noise. The resulting state representation drives a dual-criterion policy that balances mission efficiency against hard safety constraints via Lagrangian relaxation. In experiments with aggressive dynamic threats, this approach demonstrates superior collision avoidance performance, reduced energy consumption, and smoother flight trajectories.

We show that replacing the rolling SVD of AdamW updates with a rolling SVD of loss gradients changes the diagnostic by 1-2 orders of magnitude. Performing SVD on the loss gradient instead of the AdamW update increases the measured perturbative coupling between SED directions and Linear Centroid Hypothesis (LCH) features from $\bar{R}_k \approx 3$--$9\times$ to $100$--$330\times$ across four single-task modular arithmetic operations, eliminating the apparent operation dependence in the original measurement. On a multitask transformer with a shared encoder, update-based SED gives $\bar{R}_k \leq 1$ -- an apparent failure of the diagnostic -- while per-operation gradient-based SED recovers $\bar{R}_k = 20$--$45\times$ across all four operations. Gradient aggregation across competing tasks is the main obstruction; performing SVD on per-task gradients resolves it. A causal intervention shows that constraining attention updates to any rank-3 subspace (whether SED-derived or random) accelerates grokking by approximately $2.3\times$ across random seeds and operations, while removing the rank-3 component has negligible effect under proper gradient-projection methodology. The SED-LCH coupling is therefore a strong diagnostic of where feature formation concentrates in parameter space, but it is not a unique causal pathway: the natural full-rank AdamW attention update is highly rank-redundant under our hyperparameters.

We solve the time-dependent Schrödinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under the classical potential supplemented by a quantum potential depending on the score function of the evolving density. These non-crossing Bohmian trajectories form a continuous normalizing flow governed by the score. We parametrize the score with a neural network and minimize a self-consistent Fisher divergence between the network and the score of the resulting density. We prove that the zero-loss minimizer of this self-consistent objective recovers Schrödinger dynamics for nodeless wave functions, a condition naturally met in quantum vibrations of atoms. We demonstrate the approach on wavepacket splitting in a double-well potential and anharmonic vibrations of a Morse chain. By recasting real-time quantum dynamics as a self-consistent score-driven normalizing flow, this framework opens the time-dependent Schrödinger equation to the rapidly advancing toolkit of modern generative modeling.

Diffusion models have achieved unprecedented success in text-aligned generation, largely driven by Classifier-Free Guidance (CFG). However, standard CFG operates strictly on instantaneous gradients, omitting the intrinsic curvature of the data manifold. Recent methods like Zigzag-sampling (Z-Sampling) explicitly traverse multi-step forward-backward trajectories to probe this curvature, significantly improving semantic alignment. Yet, these explicit traversals triple the Neural Function Evaluation (NFE) cost and introduce unconstrained truncation errors from off-manifold evaluations, causing cumulative drift from the true marginal distribution. In this paper, we theoretically demonstrate that the explicit zigzag sequence is topologically reducible. We propose Implicit Z-Sampling, rigorously proving that intermediate states can be algebraically annihilated via operator dualities, physically eliminating off-manifold approximation errors. To push sampling efficiency to its theoretical lower bound, we introduce $Z^2$-Sampling (Zero-cost Zigzag Sampling). Exploiting the Probability Flow ODE's temporal coherence, $Z^2$-Sampling couples implicit algebraic collapse with a dynamically cached Temporal Semantic Surrogate. This restores the standard 2-NFE baseline without sacrificing semantic exploration. We formally prove via Backward Error Analysis that this discrete collapse inherently synthesizes a directional derivative curvature penalty. Finally, extensive evaluations demonstrate that $Z^2$-Sampling structurally shatters the performance-efficiency Pareto frontier. We validate its universal applicability across diverse architectures (U-Nets, DiTs) and modalities (image/video), establishing seamless orthogonality with advanced alignment frameworks (AYS, Diffusion-DPO).

Reward hacking in code generation, where models exploit evaluation loopholes to obtain high reward without correctly solving the intended task, poses a critical challenge for Reinforcement Learning (RL) and the deployment of reasoning models. Existing studies often rely on explicitly prompted hacking trajectories, but it remains unclear whether monitors trained on such data can detect reward hacks that arise without direct hacking instructions during RL training. In this work, we introduce Trace-and-Amplify, a framework for scalable curation of reward-hacking trajectories that arise during RL training without explicit hacking instructions. The framework uses unit-test tracers to identify hacking solutions when they occur and retains such trajectories for monitor training and evaluation. Through controlled comparisons between monitors trained on prompt-elicited hacking trajectories and training-time reward-hacking trajectories collected by Trace-and-Amplify, we find that \textbf{(1) prompt-elicited-data-trained monitors often fail to generalize to trajectories curated by our framework}, and \textbf{(2) monitors trained on our Trace-and-Amplify trajectories demonstrate stronger generalizability to unseen hacking types}. Our results indicate that prompted reward hacking data may not fully reflect training-time reward-hacking behaviors, and that relying solely on these data can lead to misleading conclusions. Codebase is available at https://github.com/LichenLillc/CoTMonitoring.git

Predicting future trajectories of surrounding traffic agents is critical for safe autonomous navigation and collision avoidance. Despite all advances in the trajectory forecasting realm, the prediction models remains vulnerable to uncertainty caused by occlusions, limited sensing range, and perception errors. Collaborative vehicle-to-vehicle (V2V) approaches help reduce this uncertainty by sharing complementary information. Existing collaborative trajectory prediction methods typically fuse feature maps at the perception stage to construct a holistic scene view. Further this holistic representation is decoded into the future trajectories. Such design incurs substantial communication overhead due to the exchange of high-dimensional feature representations and often assumes idealized bandwidth and synchronization, limiting practical deployment. We address these limitations by shifting collaboration from perception to the prediction module and introducing a late-fusion framework for shared forecasts. The framework is model-agnostic and treats collaborating vehicles as independent asynchronous agents. We evaluate the approach on the OPV2V, V2V4Real, and DeepAccident datasets, comparing individual and collaborative forecasting. Across all datasets, late fusion consistently reduces miss rate and improves trajectory success rate ($\mathrm{TSR}_{0.5}$), defined as the fraction of ground-truth agents with final displacement error below 0.5 m. On the real-world V2V4Real dataset, collaborative prediction improves the success rate by $1.69\%$ and $1.22\%$ for both intelligent vehicles, respectively, compared with individual forecasting.

Parallel trajectory optimization via the Alternating Direction Method of Multipliers (ADMM) has emerged as a scalable approach to long-horizon motion planning. However, existing frameworks typically decompose the problem into parallel subproblems based on a predefined fixed structure. Such structural rigidity often causes optimization stagnation in highly constrained regions, where a few lagging subproblems delay global convergence. A natural remedy is to adaptively re-split these stagnating segments online. Yet, deciding when, where, and how to split exceeds the capability of rule-based heuristics. To this end, we propose ATRS, a novel framework that embeds a shared Deep Reinforcement Learning policy into the parallel ADMM loop. We formulate this adaptive adjustment as a Multi-Agent Shared-Policy Markov Decision Process, where all trajectory segments act as homogeneous agents and share a unified neural policy network. This parameter-sharing architecture endows the system with size invariance, enabling it to handle dynamically changing segment counts during re-splitting and generalize to arbitrary trajectory lengths. Furthermore, our formulation inherently supports zero-shot generalization to unseen environments, as our network relies solely on the internal states of the numerical solver rather than on the geometric features of the environment. To ensure solver stability, a Confidence-Based Election mechanism selects only the most stagnating segment for re-splitting at each step. Extensive simulations demonstrate that ATRS accelerates convergence, reducing the number of iterations by up to 26.0% and the computation time by up to 19.1%. Real-world experiments further confirm its applicability to both large-scale offline global planning and real-time onboard replanning within 35 ms per cycle, with no sim-to-real degradation.

Coordinating the motions of multiple autonomous vehicles (AVs) requires planning frameworks that ensure safety while making efficient use of space and time. This paper presents a new approach, termed variable-time-step spatio-temporal corridor (V-STC), that enhances the temporal efficiency of multi-vehicle coordination. An optimization model is formulated to construct a V-STC for each AV, in which both the spatial configuration of the corridor cubes and their time durations are treated as decision variables. By allowing the corridor's spatial position and time step to vary, the constructed V-STC reduces the overall temporal occupancy of each AV while maintaining collision-free separation in the spatio-temporal domain. Based on the generated V-STC, a dynamically feasible trajectory is then planned independently for each AV. Simulation studies demonstrate that the proposed method achieves safe multi-vehicle coordination and yields more time-efficient motion compared with existing STC approaches.

Large language models (LLMs) have recently demonstrated strong reasoning capabilities and attracted increasing research attention in the field of autonomous driving (AD). However, safe application of LLMs on AD perception and prediction still requires a thorough understanding of both the dynamic traffic agents and the static road infrastructure. To this end, this study introduces a framework to evaluate the capability of LLMs in understanding the behaviors of dynamic traffic agents and the topology of road networks. The framework leverages frozen LLMs as the reasoning engine, employing a traffic encoder to extract spatial-level scene features from observed trajectories of agents, while a lightweight Convolutional Neural Network (CNN) encodes the local high-definition (HD) maps. To assess the intrinsic reasoning ability of LLMs, the extracted scene features are then transformed into LLM-compatible tokens via a reprogramming adapter. By residing the prediction burden with the LLMs, a simpler linear decoder is applied to output future trajectories. The framework enables a quantitative analysis of the influence of multi-modal information, especially the impact of map semantics on trajectory prediction accuracy, and allows seamless integration of frozen LLMs with minimal adaptation, thereby demonstrating strong generalizability across diverse LLM architectures and providing a unified platform for model evaluation.

We propose a sampling-based framework for finite-horizon trajectory and policy optimization under differentiable dynamics by casting controller design as inference. Specifically, we minimize a KL-regularized expected trajectory cost, which yields an optimal "Boltzmann-tilted" distribution over controller parameters that concentrates on low-cost solutions as temperature decreases. To sample efficiently from this sharp, potentially multimodal target, we introduce tempered sequential Monte Carlo (TSMC): an annealing scheme that adaptively reweights and resamples particles along a tempering path from a prior to the target distribution, while using Hamiltonian Monte Carlo rejuvenation to maintain diversity and exploit exact gradients obtained by differentiating through trajectory rollouts. For policy optimization, we extend TSMC via (i) a deterministic empirical approximation of the initial-state distribution and (ii) an extended-space construction that treats rollout randomness as auxiliary variables. Experiments across trajectory- and policy-optimization benchmarks show that TSMC is broadly applicable and compares favorably to state-of-the-art baselines.

Trajectory Inference (TI) seeks to recover latent dynamical processes from snapshot data, where only independent samples from time-indexed marginals are observed. In applications such as single-cell genomics, destructive measurements make path-space laws non-identifiable from finitely many marginals, leaving held-out marginal prediction as the dominant but limited evaluation protocol. We introduce a general framework for estimating the Kullback-Leibler divergence (KL) divergence between probability measures on function space, yielding a tractable, data-driven estimator that is scalable to realistic snapshot datasets. We validate the accuracy of our estimator on a benchmark suite, where the estimated functional KL closely matches the analytic KL. Applying this framework to synthetic and real scRNA-seq datasets, we show that current evaluation metrics often give inconsistent assessments, whereas path-space KL enables a coherent comparison of trajectory inference methods and exposes discrepancies in inferred dynamics, especially in regions with sparse or missing data. These results support functional KL as a principled criterion for evaluating trajectory inference under partial observability.

We introduce DialToM, an annotated Theory of Mind (ToM) benchmark built from naturalistic human-human dialogues using a multiple-choice evaluation framework. Concurrent with recent work showing a gap between explicit mental-state inference and applied ToM in synthetic settings~\cite{gu2024simpletom}, we establish a stricter \emph{State-Driven Diagnostic Probe} in which models must forecast state-consistent dialogue trajectories solely from isolated mental-state profiles without dialogue context. Our evaluation reveals a systematic reasoning asymmetry -- LLMs excel at inferring mental states (Literal ToM) but struggle to leverage them for social forecasting (Functional ToM). Crucially, a domain expert achieves 100% accuracy on this task, proving its validity and establishing a stark human-AI capability gap. Further, a teacher-student reasoning injection probe shows that Gemini 3 Pro -- which establishes the leading baseline -- possesses robust Functional ToM capabilities for context-free forecasting that are transferable to weaker models. DialToM, its evaluation code, and dataset are publicly available at https://github.com/Stealth-py/DialToM.

Recent agentic frameworks for 3D scene synthesis have advanced realism and diversity by integrating heterogeneous generation and editing tools. These tools are organized into workflows orchestrated by an off-the-shelf LLM. Current approaches typically adopt an execute-review-reflect loop: at each step, the orchestrator executes a tool, renders intermediate results for review, and then decides on the tool and its parameters for the next step. However, this design has two key limitations. First, next-step tool selection and parameter configuration are driven by heuristic rules, which can lead to suboptimal execution flows, unnecessary tool invocations, degraded output quality, and increased runtime. Second, rendering and reviewing intermediate results after each step introduces additional latency. To address these issues, we propose SceneOrchestra, a trainable orchestration framework that optimizes the tool-call execution flow and eliminates the step-by-step review loop, improving both efficiency and output quality. SceneOrchestra consists of an orchestrator and a discriminator, which we fine-tune with a two-phase training strategy. In the first phase, the orchestrator learns context-aware tool selection and complete tool-call trajectory generation, while the discriminator is trained to assess the quality of full trajectories, enabling it to select the best trajectory from multiple candidates. In the second phase, we perform interleaved training, where the discriminator adapts to the orchestrator's evolving trajectory distribution and distills its discriminative capability back into the orchestrator. At inference, we only use the orchestrator to generate and execute full tool-call trajectories from instructions, without requiring the discriminator. Extensive experiments show that our method achieves state-of-the-art scene quality while reducing runtime compared to previous work.

Human mobility data are used in numerous applications, ranging from public health to urban planning. Human mobility is inherently sensitive, as it can contain information such as religious beliefs and political affiliations. Historically, it has been proposed to modify the information using techniques such as aggregation, obfuscation, or noise addition, to adequately protect privacy and eliminate concerns. As these methods come at a great cost in utility, new methods leveraging development in generative models, were introduced. The extent to which such methods answer the privacy-utility trade-off remains an open problem. In this paper, we introduced a first step towards solving it, by the introduction and application of a new framework for utility evaluation. Furthermore, we provide evidence that privacy evaluation remains a great challenge to consider and that it should be tackled through adversarial evaluation in accordance with the current EU regulation. We propose a new membership inference attack against a subcategory of generative models, even though this subcategory was deemed private due to its resistance over the trajectory user-linking problem.

Current 3D mapping pipelines generally assume static environments, which limits their ability to accurately capture and reconstruct moving objects. To address this limitation, we introduce the novel task of active mapping of moving objects, in which a mapping agent must plan its trajectory while compensating for the object's motion. Our approach, Paparazzo, provides a learning-free solution that robustly predicts the target's trajectory and identifies the most informative viewpoints from which to observe it, to plan its own path. We also contribute a comprehensive benchmark designed for this new task. Through extensive experiments, we show that Paparazzo significantly improves 3D reconstruction completeness and accuracy compared to several strong baselines, marking an important step toward dynamic scene understanding. Project page: https://davidea97.github.io/paparazzo-page/

Recent work has demonstrated the promise of orchestrating large language models (LLMs) within evolutionary and agentic optimization systems. However, the mechanisms driving these optimization gains remain poorly understood. In this work, we present a large-scale study of LLM-guided evolutionary search, collecting optimization trajectories for 15 LLMs across 8 tasks. Although zero-shot problem-solving ability correlates with final optimization outcomes, it explains only part of the variance: models with similar initial capability often induce dramatically different search trajectories and outcomes. By analyzing these trajectories, we find that strong LLM optimizers behave as local refiners, producing frequent incremental improvements while progressively localizing the search in semantic space. Conversely, weaker optimizers exhibit large semantic drift, with sporadic breakthroughs followed by stagnation. Notably, various measures of solution novelty do not predict final performance; novelty is beneficial only when the search remains sufficiently localized around high-performing regions of the solution space. Our results highlight the importance of trajectory analysis for understanding and improving LLM-based optimization systems and provide actionable insights for their design and training.

Real-world image super-resolution (Real-SR) has been revolutionized by leveraging the powerful generative priors from Diffusion Models (DMs) and Flow Matching (FM). However, existing one-step methods typically replace Gaussian noise with degraded low-resolution (LR) latents at initialization, introducing a substantial distribution shift that further leads to trajectory deviation and prior collapse under extreme acceleration. To overcome these limitations, we propose Allo{SR}$^2$, a novel FM-based framework that rectifies one-step SR flows via allomorphic generative flows to maintain high-fidelity generative realism. Specifically, we utilize SNR-Guided Trajectory Initialization to identify a statistically aligned intermediate state along the pre-trained path to integrate LR representations into the generative flow. To ensure a stable, low-curvature path for one-step inference, we propose Flow-Anchored Trajectory Consistency (FATC), which explicitly regularizes the velocity field of the underlying probability flow. Furthermore, we develop Allomorphic Trajectory Matching (ATM), a self-adversarial distillation strategy that jointly models the SR flow and the generative flow within a unified velocity field, enabling one-step Real-SR while preserving the generative prior. Extensive experiments on both synthetic and real-world benchmarks demonstrate that Allo{SR}$^2$ achieves state-of-the-art performance in one-step Real-SR, offering a superior balance between fidelity and realism while maintaining extreme efficiency.

Trajectory Optimization (TO) solvers exploit known system dynamics to compute locally optimal trajectories through iterative improvements. A downside is that each new problem instance is solved independently; therefore, convergence speed and quality of the solution found depend on the initial trajectory proposed. To improve efficiency, a natural approach is to warm-start TO with initial guesses produced by a learned policy trained on trajectories previously generated by the solver. Diffusion-based policies have recently emerged as expressive imitation learning models, making them promising candidates for this role. Yet, a counterintuitive challenge comes from the local optimality of TO demonstrations: when a policy is rolled out, small non-optimal deviations may push it into situations not represented in the training data, triggering compounding errors over long horizons. In this work, we focus on learning-based warm-starting for gradient-based TO solvers that also provide feedback gains. Exploiting this specificity, we derive a first-order loss for Sobolev learning of diffusion-based policies using both trajectories and feedback gains. Through comprehensive experiments, we demonstrate that the resulting policy avoids compounding errors, and so can learn from very few trajectories to provide initial guesses reducing solving time by $2\times$ to $20 \times$. Incorporating first-order information enables predictions with fewer diffusion steps, reducing inference latency.

Precision-critical manipulation requires both global trajectory organization and local execution correction, yet most vision-language-action (VLA) policies generate actions within a single unified space. This monolithic formulation forces macro-level transport and micro-level refinement to be optimized under the same objective, causing large motions to dominate learning while suppressing small but failure-critical corrective signals. In contrast, human manipulation is structured by global movement planning together with continuous local adjustment during execution. Motivated by this principle, we propose AnchorRefine, a hierarchical framework that factorizes VLA action modeling into trajectory anchor and residual refinement. The anchor planner predicts a coarse motion scaffold, while the refinement module corrects execution-level deviations to improve geometric and contact precision. We further introduce a decision-aware gripper refinement mechanism to better capture the discrete and boundary-sensitive nature of gripper control. Experiments on LIBERO, CALVIN, and real-robot tasks demonstrate that AnchorRefine consistently improves both regression-based and diffusion-based VLA backbones, yielding gains of up to 7.8% in simulation success rate and 18% in real-world success rate.

Safe and agile trajectory planning is essential for autonomous systems, especially during complex aerobatic maneuvers. Motivated by the recent success of diffusion models in generative tasks, this paper introduces AeroTrajGen, a novel framework for diffusion-based trajectory generation that incorporates control barrier function (CBF)-guided sampling during inference, specifically designed for unmanned aerial vehicles (UAVs). The proposed CBF-guided sampling addresses two critical challenges: (1) mitigating the inherent unpredictability and potential safety violations of diffusion models, and (2) reducing reliance on extensively safety-verified training data. During the reverse diffusion process, CBF-based guidance ensures collision-free trajectories by seamlessly integrating safety constraint gradients with the diffusion model's score function. The model features an obstacle-aware diffusion transformer architecture with multi-modal conditioning, including trajectory history, obstacles, maneuver styles, and goal, enabling the generation of smooth, highly agile trajectories across 14 distinct aerobatic maneuvers. Trained on a dataset of 2,000 expert demonstrations, AeroTrajGen is rigorously evaluated in simulation under multi-obstacle environments. Simulation results demonstrate that CBF-guided sampling reduces collision rates by 94.7% compared to unguided diffusion baselines, while preserving trajectory agility and diversity. Our code is open-sourced at https://github.com/RoboticsPolyu/CBF-DMP.

Motivated by the challenge presented by non-Markovian objectives in reinforcement learning (RL), we present a novel framework to track and represent the progress of autonomous agents through complex, multi-stage tasks. Given a specification in finite linear temporal logic (LTL), the framework establishes a 'tracking vector' which updates at each time step in a trajectory rollout. The values of the vector represent the status of the specification as the trajectory develops, assigning true, false, or 'open' labels (where 'open' is used for indeterminate cases). Applied to an LTL formula tree, the tracking vector can be used to encode detailed information about how a task is executed over a trajectory, providing a potential tool for new performance metrics, diverse exploration, and reward shaping. In this paper, we formally present the framework and algorithm, collectively named Live LTL Progress Tracking, give a simple working example, and demonstrate avenues for its integration into RL models. Future work will apply the framework to problems such as task-space exploration and diverse solution-finding in RL.

Accurate assessment of lithium-ion battery ageing is challenged by cell-to-cell variability, heterogeneous cycling protocols, and limited transferability of data-driven models across datasets. In particular, robust identification of degradation transitions, such as the knee point, and reliable early-life prediction of remaining useful life (RUL) remain open problems. This study proposes a unified framework for battery ageing analysis based on continuous representations of voltage-capacity and capacity-cycle trajectories learned from heterogeneous public datasets (NASA, CALCE, ISU-ILCC). The continuous formulation enables consistent extraction of degradation descriptors, including curvature, plateau length and knee-related metrics, while reducing sensitivity to dataset-specific discretisation. Across more than 250 cells, statistically significant correlations between knee onset and end-of-life (Pearson 0.75-0.84) are observed. Additional early-life analysis confirms that knee-related features retain predictive value when estimated from partial trajectories. Early-life models provide increasingly stable RUL predictions as the number of observed cycles increases, with meaningful predictive performance emerging within the first 5-20 cycles and remain robust under cross-dataset domain shift. The framework integrates continuous modelling, feature extraction and uncertainty-aware prediction, providing an interpretable and dataset-consistent approach demonstrating robustness across heterogeneous dataset types. Compared with conventional discrete or feature-based methods, the proposed representation reduces sensitivity to sampling resolution and improves cross-dataset consistency. The study is limited to laboratory-scale datasets and capacity-based end-of-life definitions.

This paper focuses on the alignment of flow matching models with human preferences. A promising way is fine-tuning by directly backpropagating reward gradients through the differentiable generation process of flow matching. However, backpropagating through long trajectories results in prohibitive memory costs and gradient explosion. Therefore, direct-gradient methods struggle to update early generation steps, which are crucial for determining the global structure of the final image. To address this issue, we introduce LeapAlign, a fine-tuning method that reduces computational cost and enables direct gradient propagation from reward to early generation steps. Specifically, we shorten the long trajectory into only two steps by designing two consecutive leaps, each skipping multiple ODE sampling steps and predicting future latents in a single step. By randomizing the start and end timesteps of the leaps, LeapAlign leads to efficient and stable model updates at any generation step. To better use such shortened trajectories, we assign higher training weights to those that are more consistent with the long generation path. To further enhance gradient stability, we reduce the weights of gradient terms with large magnitude, instead of completely removing them as done in previous works. When fine-tuning the Flux model, LeapAlign consistently outperforms state-of-the-art GRPO-based and direct-gradient methods across various metrics, achieving superior image quality and image-text alignment.

Mobile agents powered by vision-language models have demonstrated impressive capabilities in automating mobile tasks, with recent leading models achieving a marked performance leap, e.g., nearly 70% success on AndroidWorld. However, these systems keep their training data closed and remain opaque about their task and trajectory synthesis recipes. We present OpenMobile, an open-source framework that synthesizes high-quality task instructions and agent trajectories, with two key components: (1) The first is a scalable task synthesis pipeline that constructs a global environment memory from exploration, then leverages it to generate diverse and grounded instructions. and (2) a policy-switching strategy for trajectory rollout. By alternating between learner and expert models, it captures essential error-recovery data often missing in standard imitation learning. Agents trained on our data achieve competitive results across three dynamic mobile agent benchmarks: notably, our fine-tuned Qwen2.5-VL and Qwen3-VL reach 51.7% and 64.7% on AndroidWorld, far surpassing existing open-data approaches. Furthermore, we conduct transparent analyses on the overlap between our synthetic instructions and benchmark test sets, and verify that performance gains stem from broad functionality coverage rather than benchmark overfitting. We release data and code at https://njucckevin.github.io/openmobile/ to bridge the data gap and facilitate broader mobile agent research.

As power systems transition toward renewable-rich and inverter-dominated operations, accurate time-domain dynamic analysis becomes increasingly critical. Such analysis supports key operational tasks, including transient stability assessment, dynamic security analysis, contingency screening, and post-fault trajectory evaluation. In practice, these tasks may operate under several challenges, including unknown and time-varying system parameters, privacy constraints on data sharing, and the need for fast online inference. Existing learning-based approaches are typically trained for individual systems and therefore lack generalization across operating conditions and physical parameters. Hence, this paper proposes LArge Scale Small ODE (LASS)-ODE-Power, a learning framework for general-purpose time-domain prediction. The proposed approach leverages large-scale pretraining on more than 40 GB of DAE or ordinary differential-equation (ODE) trajectories to learn transferable representations. The resulting model supports trajectory prediction from short measurement prefixes across diverse dynamic regimes, including electromechanical and inverter-driven systems. Hence, the model can be directly used without data sharing in a zero-shot setting. In addition, the proposed architecture incorporates parallel and linearized computation to achieve fast inference. Moreover, to enhance task-specific performance in power systems, a specialized fine-tuning strategy is developed based on approximately 1 GB of heterogeneous power-system dynamic data. Extensive experiments over diverse power-system simulation scenarios demonstrate that LASS-ODE-Power consistently outperforms existing learning-based models in trajectory prediction accuracy with efficient inference.

Safe and efficient assistive planning for visually impaired scenarios remains challenging, since existing methods struggle with multi-objective optimization, generalization, and interpretability. In response, this paper proposes a Momentum-Constrained Hybrid Heuristic Trajectory Optimization Framework (MHHTOF). To balance multiple objectives of comfort and safety, the framework designs a Heuristic Trajectory Sampling Cluster (HTSC) with a Momentum-Constrained Trajectory Optimization (MTO), which suppresses abrupt velocity and acceleration changes. In addition, a novel residual-enhanced deep reinforcement learning (DRL) module refines candidate trajectories, advancing temporal modeling and policy generalization. Finally, a dual-stage cost modeling mechanism (DCMM) is introduced to regulate optimization, where costs in the Frenet space ensure consistency, and reward-driven adaptive weights in the Cartesian space integrate user preferences for interpretability and user-centric decision-making. Experimental results show that the proposed framework converges in nearly half the iterations of baselines and achieves lower and more stable costs. In complex dynamic scenarios, MHHTOF further demonstrates stable velocity and acceleration curves with reduced risk, confirming its advantages in robustness, safety, and efficiency.

We present causal evidence that hallucination in autoregressive language models is an early trajectory commitment governed by asymmetric attractor dynamics. Using same-prompt bifurcation, in which we repeatedly sample identical inputs to observe spontaneous divergence, we isolate trajectory dynamics from prompt-level confounds. On Qwen2.5-1.5B across 61 prompts spanning six categories, 27 prompts (44.3%) bifurcate with factual and hallucinated trajectories diverging at the first generated token (KL = 0 at step 0, KL > 1.0 at step 1). Activation patching across 28 layers reveals a pronounced causal asymmetry: injecting a hallucinated activation into a correct trajectory corrupts output in 87.5% of trials (layer 20), while the reverse recovers only 33.3% (layer 24); both exceed the 10.4% baseline (p = 0.025) and 12.5% random-patch control. Window patching shows correction requires sustained multi-step intervention, whereas corruption needs only a single perturbation. Probing the prompt encoding itself, step-0 residual states predict per-prompt hallucination rate at Pearson r = 0.776 at layer 15 (p < 0.001 against a 1000-permutation null); unsupervised clustering identifies five regime-like groups (eta^2 = 0.55) whose saddle-adjacent cluster concentrates 12 of the 13 bifurcating false-premise prompts, indicating that the basin structure is organized around regime commitments fixed at prompt encoding. These findings characterize hallucination as a locally stable attractor basin: entry is probabilistic and rapid, exit demands coordinated intervention across layers and steps, and the relevant basins are selected by clusterable regimes already discernible at step 0.

Achieving high-fidelity generation in extremely few sampling steps has long been a central goal of generative modeling. Existing approaches largely rely on distillation-based frameworks to compress the original multi-step denoising process into a few-step generator. However, such methods inherently constrain the student to imitate a stronger multi-step teacher, imposing the teacher as an upper bound on student performance. We argue that introducing \textbf{preference alignment awareness} enables the student to optimize toward reward-preferred generation quality, potentially surpassing the teacher instead of being restricted to rigid teacher imitation. To this end, we propose \textbf{Reward-Aware Trajectory Shaping (RATS)}, a lightweight framework for preference-aligned few-step generation. Specifically, teacher and student latent trajectories are aligned at key denoising stages through horizon matching, while a \textbf{reward-aware gate} is introduced to adaptively regulate teacher guidance based on their relative reward performance. Trajectory shaping is strengthened when the teacher achieves higher rewards, and relaxed when the student matches or surpasses the teacher, thereby enabling continued reward-driven improvement. By seamlessly integrating trajectory distillation, reward-aware gating, and preference alignment, RATS effectively transfers preference-relevant knowledge from high-step generators without incurring additional test-time computational overhead. Experimental results demonstrate that RATS substantially improves the efficiency--quality trade-off in few-step visual generation, significantly narrowing the gap between few-step students and stronger multi-step generators.

As agent systems move into increasingly diverse execution settings, trajectory-level safety evaluation and diagnosis require benchmarks that evolve with them. ATBench is a diverse and realistic agent trajectory benchmark for safety evaluation and diagnosis. This report presents ATBench-Claw and ATBench-Codex, two domain-customized extensions that carry ATBench into the OpenClaw and OpenAI Codex / Codex-runtime settings. The key adaptation mechanism is to analyze each new setting, customize the three-dimensional Safety Taxonomy over risk source, failure mode, and real-world harm, and then use that customized taxonomy to define the benchmark specification consumed by the shared ATBench construction pipeline. This extensibility matters because agent frameworks remain relatively stable at the architectural level even as their concrete execution settings, tool ecosystems, and product capabilities evolve quickly. Concretely, ATBench-Claw targets OpenClaw-sensitive execution chains over tools, skills, sessions, and external actions, while ATBench-Codex targets trajectories in the OpenAI Codex / Codex-runtime setting over repositories, shells, patches, dependencies, approvals, and runtime policy boundaries. Our emphasis therefore falls on taxonomy customization, domain-specific risk coverage, and benchmark design under a shared ATBench generation framework.

Current single-cell foundation model benchmarks universally extract final layer embeddings, assuming these represent optimal feature spaces. We systematically evaluate layer-wise representations from scFoundation (100M parameters) and Tahoe-X1 (1.3B parameters) across trajectory inference and perturbation response prediction. Our analysis reveals that optimal layers are task-dependent (trajectory peaks at 60% depth, 31% above final layers) and context-dependent (perturbation optima shift 0-96% across T cell activation states). Notably, first-layer embeddings outperform all deeper layers in quiescent cells, challenging assumptions about hierarchical feature abstraction. These findings demonstrate that "where" to extract features matters as much as "what" the model learns, necessitating systematic layer evaluation tailored to biological task and cellular context rather than defaulting to final-layer embeddings.

Existing agent-safety evaluation has focused mainly on externally induced risks. Yet agents may still enter unsafe trajectories under benign conditions. We study this complementary but underexplored setting through the lens of \emph{intrinsic} risk, where intrinsic failures remain latent, propagate across long-horizon execution, and eventually lead to high-consequence outcomes. To evaluate this setting, we introduce \emph{non-attack intrinsic risk auditing}, a guard-oriented safety evaluation task, and present \textbf{HINTBench}, a benchmark of 596 agent trajectories, comprising 400 synthetic risky trajectories, 136 synthetic safe trajectories, 30 reconstructed real-world risky trajectories, and 30 reconstructed real-world safe trajectories, with an average length of 24.0 steps. HINTBench supports three tasks: risk detection, risk-step localization, and intrinsic failure-type identification, with annotations organized under a unified five-constraint taxonomy. Experiments reveal a substantial capability gap: strong LLMs perform well on trajectory-level risk detection, but the best model remains below 37 on fine-grained Strict-F1 for risk-step localization. Existing off-the-shelf guard models evaluated under their native prompts transfer poorly to this setting. These findings establish intrinsic risk auditing as an open challenge for agent safety.

Deep learning models may converge to suboptimal solutions despite strong validation accuracy, masking an optimization failure we term Trajectory Deviation. This is because as training proceeds, models can abandon high generalization states for specific data sub-populations, thus discarding previously learned latent features without triggering classical overfitting signals. To address this problem we introduce VISTA, an online self-distillation framework that enforces consistency along the optimization trajectory. Using a validation-informed Marginal Coverage score, VISTA identifies expert anchors, which are earlier model states that retain specialized competence over distinct data regions. A coverage-weighted ensemble of these anchors is integrated online during training, regularizing the loss landscape and preserving mastered knowledge. When evaluated across multiple benchmarks, VISTA demonstrates improved robustness and generalization over standard training and prior self-distillation methods, while a lightweight implementation reduces storage overhead by 90% without performance loss.

Trajectory prediction is a key component of autonomous driving systems because future motions directly affect collision checking, behavior planning, and control. The task remains challenging under dense interactions, heterogeneous behaviors, multimodal futures, and limited on-board computation. Existing graph, attention, and generative predictors improve interaction reasoning or uncertainty modeling, but their high-capacity designs are often costly for real-time deployment. Lightweight predictors and conventional distillation reduce inference cost, yet usually rely on static imitation and do not explicitly correct safety-relevant teacher bias. This paper proposes \textbf{MAVEN-T}, a reinforced heterogeneous distillation framework for real-time multi-agent trajectory prediction. A high-capacity teacher models directed local interactions with a surround-aware graph encoder, combines efficient temporal filtering with shifted-window spatial attention, and decodes maneuver-specific futures through a sparse Mixture-of-Experts head. A compact GRU--Squeeze-and-Excitation student with a Low-Rank Adapted policy head is trained by feature-, attention-, and semantic-level distillation. To align prediction with downstream behavior, the student is further refined by Proximal Policy Optimization rewards for collision avoidance, comfort, and progress, while a complexity-aware curriculum and Elastic Weight Consolidation stabilize stage-wise training. Experiments on NGSIM, HighD, MoCAD, Argoverse~2, and the Waymo Open Motion Dataset evaluate accuracy, efficiency, generalization, robustness, and closed-loop safety. The student achieves 6.2$\times$ parameter compression, 3.7$\times$ inference acceleration, and 14.6,ms latency on an NVIDIA Jetson AGX Orin while maintaining competitive accuracy.

Remote sensing segmentation in real deployment is inherently continual: new semantic categories emerge, and acquisition conditions shift across seasons, cities, and sensors. Despite recent progress, many incremental approaches still treat training steps as isolated updates, which leaves representation drift and forgetting insufficiently controlled. We present ProtoFlow, a time-aware prototype dynamics framework that models class prototypes as trajectories and learns their evolution with an explicit temporal vector field. By jointly enforcing low-curvature motion and inter-class separation, ProtoFlow stabilizes prototype geometry throughout incremental learning. Experiments on standard class- and domain-incremental remote sensing benchmarks show consistent gains over strong baselines, including up to 1.5-2.0 points improvement in mIoUall, together with reduced forgetting. These results suggest that explicitly modeling temporal prototype evolution is a practical and interpretable strategy for robust continual remote sensing segmentation. Open-source code:https://github.com/dudududke/protoflow.

Generative video editing has enabled creative control over an object's position in a video by prescribing an object's 3D or 2D motion trajectory, while preserving both video plausibility and identity. However, manually specifying a plausible full motion trajectory, like the arcs of a bouncing ball, requires time and expertise, and may therefore not be a suitable editing task for non-experts or quick edits. In contrast, in the image domain, generative object translation has been established as a simple editing task that requires only a single drag to move an object to a new location; yet an equivalent method is still missing for videos. We propose an analogous new editing task for videos that translates an object's 3D motion trajectory in a video while preserving identity and plausibility of appearance and motion, for example, translating the trajectory of a bouncing ball while preserving its relative motion. The main challenge in training this task lies in obtaining paired video data for this scenario. We introduce TrajectorySynth, a new data generation strategy for large-scale synthetic paired video data and a video generator TrajectoryMover fine-tuned with this data. We show that this enables generative movement of object trajectories. Project Page: https://chhatrekiran.github.io/trajectorymover

Predicting surgical needle trajectories from endoscopic video is critical for robot-assisted suturing, enabling anticipatory planning, real-time guidance, and safer motion execution. Existing methods that directly learn motion distributions from visual observations tend to overlook the sequential dependency among adjacent motion steps. Moreover, sparse waypoint annotations often fail to provide sufficient supervision, further increasing the difficulty of supervised or imitation learning methods. To address these challenges, we formulate image-based needle trajectory prediction as a sequential decision-making problem, in which the needle tip is treated as an agent that moves step by step in pixel space. This formulation naturally captures the continuity of needle motion and enables the explicit modeling of physically plausible pixel-wise state transitions over time. From this perspective, we propose SutureFormer, a goal-conditioned offline reinforcement learning framework that leverages sparse annotations to dense reward signals via cubic spline interpolation, encouraging the policy to exploit limited expert guidance while exploring plausible future motion paths. SutureFormer encodes variable-length clips using an observation encoder to capture both local spatial cues and long-range temporal dynamics, and autoregressively predicts future waypoints through actions composed of discrete directions and continuous magnitudes. To enable stable offline policy optimization from expert demonstrations, we adopt Conservative Q-Learning with Behavioral Cloning regularization. Experiments on a new kidney wound suturing dataset containing 1,158 trajectories from 50 patients show that SutureFormer reduces Average Displacement Error by 58.6% compared with the strongest baseline, demonstrating the effectiveness of modeling needle trajectory prediction as pixel-level sequential action learning.

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

Battery-powered multirotor unmanned aerial vehicles (UAVs) can rapidly map unknown environments, but mission performance is often limited by energy rather than geometry alone. Standard exploration policies that optimise for coverage or time can therefore waste energy through manoeuvre-heavy trajectories. In this paper, we address energy-aware autonomous 3D exploration for multirotor UAVs in initially unknown environments. We propose Energy-Aware Autonomous Exploration (EAAE), a modular frontier-based framework that makes energy an explicit decision variable during frontier selection. EAAE clusters frontiers into view-consistent regions, plans dynamically feasible candidate trajectories to the most informative clusters, and predicts their execution energy using an offline power estimation loop. The next target is then selected by minimising predicted trajectory energy while preserving exploration progress through a dual-layer planning architecture for safe execution. We evaluate EAAE in a full exploration pipeline with a rotor-speed-based power model across simulated 3D environments of increasing complexity. Compared to representative distance-based and information gain-based frontier baselines, EAAE consistently reduces total energy consumption while maintaining competitive exploration time and comparable map quality, providing a practical drop-in energy-aware layer for frontier exploration.

Accurate trajectory prediction is critical for safe autonomous navigation in crowded environments. While many trajectory predictors output Gaussian distributions to represent the multi-modal distribution over future pedestrian positions, the reliability of their confidence levels often remains unaddressed. This limitation can lead to unsafe or overly conservative motion planning when the predictor is integrated with an uncertainty-aware planner. Existing Gaussian trajectory predictors primarily rely on the Negative Log-Likelihood loss, which is prone to predict over- or under-confident distributions, and may compromise downstream planner safety. This paper introduces a novel loss function for calibrating prediction uncertainty which leverages Kernel Density Estimation to estimate the empirical distribution of confidence levels. The proposed formulation enforces consistency with the properties of a Gaussian assumption by explicitly matching the estimated empirical distribution to the Chi-squared distribution. To ensure accurate mean prediction, a Mean Squared Error term is also incorporated in the final loss formulation. Experimental results on real-world trajectory datasets show that our method significantly improves the reliability of confidence levels predicted by different State-Of-The-Art Gaussian trajectory predictors. We also demonstrate the importance of providing planners with reliable probabilistic insights (i.e. calibrated confidence levels) for collision-free navigation in complex scenarios. For this purpose, we integrate Gaussian trajectory predictors trained with our loss function with an uncertainty-aware Model Predictive Control on scenarios extracted from real-world datasets, achieving improved planning performance through calibrated confidence levels.

Ordinary decentralized multi-agent reinforcement learning presents each focal agent with a continual learning problem: peer updates change its induced rewards and dynamics even when the joint Markov game is stationary. We connect the lifetime of success-conditioned reusable structure to peer learning and policy reuse. An invariant core represents maximal abstract patterns shared by a high fraction of successful trajectories; survival refers to a fixed pattern's coverage, not an unchanged maximal frontier. An established sharp conditioning bound limits coverage loss to $\frac{\varepsilon}{p_0}$, where $\varepsilon$ is trajectory-law drift, $p_0$ is reference success mass, and drift is smaller than the initial compatible-success mass. Combining this bound with peer-policy movement certifies $Ω(\frac{1}η)$ survival under bounded peer updates of size $η$ and positive coverage margin. An effective-conflict condition yields a matching $Θ(\frac{1}η)$ first-exit law and holds in an analytic exact-policy-gradient class. With success-mass and performance calibration, structural survival also yields policy-value and finite-library transfer guarantees. An exactly solvable corridor tests the structural predictions. Two registered 64-stream studies in continual control and cue-MNIST show that coverage erosion predicts impending failure and enables near-oracle intervention. An exploratory reanalysis of eight learned-partner Level-Based Foraging pairings suggests the same erosion--failure link under peer learning.