Daily Papers

Masked Diffusion Models (MDMs) have emerged as a promising non-autoregressive paradigm for generative tasks, offering parallel decoding and bidirectional context utilization. However, current sampling methods rely on simple confidence-based heuristics that ignore the long-term impact of local decisions, leading to trajectory lock-in where early hallucinations cascade into global incoherence. While search-based methods mitigate this, they incur prohibitive computational costs (O(K) forward passes per step). In this work, we propose Backward-on-Entropy (BoE) Steering, a gradient-guided inference framework that approximates infinite-horizon lookahead via a single backward pass. We formally derive the Token Influence Score (TIS) from a first-order expansion of the trajectory cost functional, proving that the gradient of future entropy with respect to input embeddings serves as an optimal control signal for minimizing uncertainty. To ensure scalability, we introduce ActiveQueryAttention, a sparse adjoint primitive that exploits the structure of the masking objective to reduce backward pass complexity. BoE achieves a superior Pareto frontier for inference-time scaling compared to existing unmasking methods, demonstrating that gradient-guided steering offers a mathematically principled and efficient path to robust non-autoregressive generation. We will release the code.

We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., ell^1 or ell^2, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure.

Multi-objective optimization problems are ubiquitous in robotics, e.g., the optimization of a robot manipulation task requires a joint consideration of grasp pose configurations, collisions and joint limits. While some demands can be easily hand-designed, e.g., the smoothness of a trajectory, several task-specific objectives need to be learned from data. This work introduces a method for learning data-driven SE(3) cost functions as diffusion models. Diffusion models can represent highly-expressive multimodal distributions and exhibit proper gradients over the entire space due to their score-matching training objective. Learning costs as diffusion models allows their seamless integration with other costs into a single differentiable objective function, enabling joint gradient-based motion optimization. In this work, we focus on learning SE(3) diffusion models for 6DoF grasping, giving rise to a novel framework for joint grasp and motion optimization without needing to decouple grasp selection from trajectory generation. We evaluate the representation power of our SE(3) diffusion models w.r.t. classical generative models, and we showcase the superior performance of our proposed optimization framework in a series of simulated and real-world robotic manipulation tasks against representative baselines.

Accurate prediction of Lagrangian trajectories in turbulent flow remains challenging due to limited temporal information in transport functions. This paper shows that surrounding coherent motions sharing the same dynamics carry enough information to provide highly probable trajectories even from sparse temporal observations. The proposed coherent predictor builds on Lagrangian coherent structures (LCSs), the advective transport barriers that govern the cohesive motion of neighbouring particles. Coherent trajectories are quantified using a local segmentation with the finite-time Lyapunov exponents (FTLE). The coherent predictor incorporates information from the particle's position history and neighbouring coherent velocity and acceleration into a novel cost function to predict its trajectory. The proposed cost function follows a physics-informed approach where the position history acts as a data fidelity term and the coherent velocity and acceleration act as physics-based regularisation constraints. We assess our proposed approach using both three-dimensional (3D) synthetic and experimental data of the wake behind a smooth cylinder and two-dimensional (2D) homogeneous isotropic turbulent (HIT) flow. The coherent predictor is deemed generic due to its consistent behaviour regardless of flow dimensions, Reynolds number, and flow topology. Our results show that the optimal cost function parameters can be modelled from the measurement uncertainties, giving lower prediction error and uncertainty than current methods. We see direct signatures of flow topology on the prediction error map, including the cylinder leading edge boundary layer, the sideward shear layers, and the vortex formation structures. These topologies are marked by high Lagrangian gradients and 3D directional motions.

We present MotionDiffuser, a diffusion based representation for the joint distribution of future trajectories over multiple agents. Such representation has several key advantages: first, our model learns a highly multimodal distribution that captures diverse future outcomes. Second, the simple predictor design requires only a single L2 loss training objective, and does not depend on trajectory anchors. Third, our model is capable of learning the joint distribution for the motion of multiple agents in a permutation-invariant manner. Furthermore, we utilize a compressed trajectory representation via PCA, which improves model performance and allows for efficient computation of the exact sample log probability. Subsequently, we propose a general constrained sampling framework that enables controlled trajectory sampling based on differentiable cost functions. This strategy enables a host of applications such as enforcing rules and physical priors, or creating tailored simulation scenarios. MotionDiffuser can be combined with existing backbone architectures to achieve top motion forecasting results. We obtain state-of-the-art results for multi-agent motion prediction on the Waymo Open Motion Dataset.

We present Kinodynamic RRT*, an incremental sampling-based approach for asymptotically optimal motion planning for robots with linear differential constraints. Our approach extends RRT*, which was introduced for holonomic robots (Karaman et al. 2011), by using a fixed-final-state-free-final-time controller that exactly and optimally connects any pair of states, where the cost function is expressed as a trade-off between the duration of a trajectory and the expended control effort. Our approach generalizes earlier work on extending RRT* to kinodynamic systems, as it guarantees asymptotic optimality for any system with controllable linear dynamics, in state spaces of any dimension. Our approach can be applied to non-linear dynamics as well by using their first-order Taylor approximations. In addition, we show that for the rich subclass of systems with a nilpotent dynamics matrix, closed-form solutions for optimal trajectories can be derived, which keeps the computational overhead of our algorithm compared to traditional RRT* at a minimum. We demonstrate the potential of our approach by computing asymptotically optimal trajectories in three challenging motion planning scenarios: (i) a planar robot with a 4-D state space and double integrator dynamics, (ii) an aerial vehicle with a 10-D state space and linearized quadrotor dynamics, and (iii) a car-like robot with a 5-D state space and non-linear dynamics.

One-step generative models construct a static generator through iterative training-time transport. Existing transport objectives primarily assess distributional motion, although a neural generator needs to realize the requested sample displacements jointly through shared parameter updates. The training-time construction raises the question: once training becomes the iterative process that constructs the final one-step map, what to optimize: the next distributional move, or the route by which the finite generator learns the final map? To address the question, we introduce Training Dynamics Action (TDAction), which selects transport targets according to local shared-parameter realization cost while retaining a prescribed level of distributional progress. We formulate the cost as a soft-terminal control problem and derive a closed-form Batch Tangent Action-to-Go value that accounts for parameter effort and terminal mismatch. The criterion captures cross-sample interactions omitted by independent pairwise costs; under isotropic mobility, the criterion agrees with quadratic Euclidean assignment for deterministic balanced couplings. Randomized tangent probes provide a low-rank implementation that constructs shared detached targets without adding an inference-time trajectory. Controlled studies examine the relationship between generator geometry, transport selection, and realized local action. On ImageNet 256times256, TDAction attains an FID below 1.1 without distillation.

We analyze the state constrained inverse Stefan type parabolic free boundary problem as an optimal control problem in the Sobolev-Besov spaces framework. Boundary heat flux, density of heat sources, and free boundary are components of the control vector. Cost functional is the sum of the L_2-norm declinations of the temperature measurement at the final moment, the phase transition temperature, the final position of the free boundary, and the penalty term, taking into account the state constraint on the temperature. We prove the existence of optimal control, Frechet differentiability, and optimality condition in the Besov spaces under minimal regularity assumptions on the data. We pursue space-time discretization through finite differences and prove that the sequence of discrete optimal control problems converges to the original problem both with respect to functional and control.

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

Diffusion models have achieved remarkable success in generative modeling, with their sampling procedures routinely modified to control generation and improve efficiency. These modifications introduce perturbations along the sampling trajectory, raising a central question: how do such perturbations affect generated output? To address this question, we develop a theoretical framework to investigate perturbation propagation, combining dynamical analysis of the sampling process with an information-theoretic characterization of output responses. Within this framework, we quantify perturbation strength using the Kullback--Leibler (KL) divergence between perturbed and reference trajectory distributions, termed as path cost, which is shown to bound, but do not determine, changes in the output distribution. Building on this analysis, we derive a response identity that connects the propagation and accumulation of local perturbations with the information captured by a selected feature mean, explaining why changes in the output distribution can remain undetected by its first-order response. We test our theoretical analysis through controlled interventions at equal path cost in pretrained diffusion models, revealing distinct patterns of output sensitivity across sampling stages and spatial frequencies. To assess whether our framework can diagnose perturbations arising from practical approximations, we apply it to cache-based acceleration and show that our propagation analysis reliably identifies sampling intervals where caching causes larger image errors.

Ensuring safe navigation in complex environments requires accurate real-time traversability assessment and understanding of environmental interactions relative to the robot`s capabilities. Traditional methods, which assume simplified dynamics, often require designing and tuning cost functions to safely guide paths or actions toward the goal. This process is tedious, environment-dependent, and not generalizable. To overcome these issues, we propose a novel learned perceptive Forward Dynamics Model (FDM) that predicts the robot`s future state conditioned on the surrounding geometry and history of proprioceptive measurements, proposing a more scalable, safer, and heuristic-free solution. The FDM is trained on multiple years of simulated navigation experience, including high-risk maneuvers, and real-world interactions to incorporate the full system dynamics beyond rigid body simulation. We integrate our perceptive FDM into a zero-shot Model Predictive Path Integral (MPPI) planning framework, leveraging the learned mapping between actions, future states, and failure probability. This allows for optimizing a simplified cost function, eliminating the need for extensive cost-tuning to ensure safety. On the legged robot ANYmal, the proposed perceptive FDM improves the position estimation by on average 41% over competitive baselines, which translates into a 27% higher navigation success rate in rough simulation environments. Moreover, we demonstrate effective sim-to-real transfer and showcase the benefit of training on synthetic and real data. Code and models are made publicly available under https://github.com/leggedrobotics/fdm.

Recent success in large multimodal models (LMMs) has sparked promising applications of agents capable of autonomously completing complex web tasks. While open-source LMM agents have made significant advances in offline evaluation benchmarks, their performance still falls substantially short of human-level capabilities in more realistic online settings. A key bottleneck is the lack of diverse and large-scale trajectory-level datasets across various domains, which are expensive to collect. In this paper, we address this challenge by developing a scalable recipe to synthesize the largest and most diverse trajectory-level dataset to date, containing over 94K successful multimodal web trajectories, spanning 49K unique URLs, 720K screenshots, and 33M web elements. In particular, we leverage extensive web exploration and refinement to obtain diverse task intents. The average cost is 28 cents per successful trajectory, making it affordable to a wide range of users in the community. Leveraging this dataset, we train Explorer, a multimodal web agent, and demonstrate strong performance on both offline and online web agent benchmarks such as Mind2Web-Live, Multimodal-Mind2Web, and MiniWob++. Additionally, our experiments highlight data scaling as a key driver for improving web agent capabilities. We hope this study makes state-of-the-art LMM-based agent research at a larger scale more accessible.

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models. We characterize an implicit denoising trajectory and discuss its vital role in forming the coupled sampling trajectory with a strong shape regularity, regardless of the generated content. We also describe a dynamic programming-based scheme to make the time schedule in sampling better fit the underlying trajectory structure. This simple strategy requires minimal modification to any given ODE-based numerical solvers and incurs negligible computational cost, while delivering superior performance in image generation, especially in 5sim 10 function evaluations.

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.

While current navigation benchmarks prioritize task success in simplified settings, they neglect the multidimensional economic constraints essential for the real-world commercialization of autonomous delivery systems. We introduce CostNav, an Economic Navigation Benchmark that evaluates physical AI agents through comprehensive economic cost-revenue analysis aligned with real-world business operations. By integrating industry-standard data - such as SEC filings and AIS injury reports - with Isaac Sim's detailed collision and cargo dynamics, CostNav transcends simple task completion to accurately evaluate business value in complex, real-world scenarios. To our knowledge, CostNav is the first work to quantitatively expose the gap between navigation research metrics and commercial viability, revealing that optimizing for task success on a simplified task fundamentally differs from optimizing for real-world economic deployment. Our evaluation of rule-based Nav2 navigation shows that current approaches are not economically viable: the contribution margin is -22.81/run (AMCL) and -12.87/run (GPS), resulting in no break-even point. We challenge the community to develop navigation policies that achieve economic viability on CostNav. We remain method-agnostic, evaluating success solely on the metric of cost rather than the underlying architecture. All resources are available at https://github.com/worv-ai/CostNav.

Safety-critical applications such as autonomous vehicles and social robots require fast computation and accurate probability density estimation on trajectory prediction. To address both requirements, this paper presents a new normalizing flow-based trajectory prediction model named FlowChain. FlowChain is a stack of conditional continuously-indexed flows (CIFs) that are expressive and allow analytical probability density computation. This analytical computation is faster than the generative models that need additional approximations such as kernel density estimation. Moreover, FlowChain is more accurate than the Gaussian mixture-based models due to fewer assumptions on the estimated density. FlowChain also allows a rapid update of estimated probability densities. This update is achieved by adopting the newest observed position and reusing the flow transformations and its log-det-jacobians that represent the motion trend. This update is completed in less than one millisecond because this reuse greatly omits the computational cost. Experimental results showed our FlowChain achieved state-of-the-art trajectory prediction accuracy compared to previous methods. Furthermore, our FlowChain demonstrated superiority in the accuracy and speed of density estimation. Our code is available at https://github.com/meaten/FlowChain-ICCV2023

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

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

We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions pi_0,pi_1 on R^d, of minimizing a transport cost E[c(X_1-X_0)] in the set of couplings (X_0,X_1) whose marginal distributions on X_0,X_1 equals pi_0,pi_1, respectively, where c is a cost function. Our method iteratively constructs a sequence of neural ordinary differentiable equations (ODE), each learned by solving a simple unconstrained regression problem, which monotonically reduce the transport cost while automatically preserving the marginal constraints. This yields a monotonic interior approach that traverses inside the set of valid couplings to decrease the transport cost, which distinguishes itself from most existing approaches that enforce the coupling constraints from the outside. The main idea of the method draws from rectified flow, a recent approach that simultaneously decreases the whole family of transport costs induced by convex functions c (and is hence multi-objective in nature), but is not tailored to minimize a specific transport cost. Our method is a single-object variant of rectified flow that guarantees to solve the OT problem for a fixed, user-specified convex cost function c.

Existing industrial-scale navigation applications contend with massive road networks, typically employing two main categories of approaches for route planning. The first relies on precomputed road costs for optimal routing and heuristic algorithms for generating alternatives, while the second, generative methods, has recently gained significant attention. However, the former struggles with personalization and route diversity, while the latter fails to meet the efficiency requirements of large-scale real-time scenarios. To address these limitations, we propose GenMRP, a generative framework for multi-route planning. To ensure generation efficiency, GenMRP first introduces a skeleton-to-capillary approach that dynamically constructs a relevant sub-network significantly smaller than the full road network. Within this sub-network, routes are generated iteratively. The first iteration identifies the optimal route, while the subsequent ones generate alternatives that balance quality and diversity using the newly proposed correctional boosting approach. Each iteration incorporates road features, user historical sequences, and previously generated routes into a Link Cost Model to update road costs, followed by route generation using the Dijkstra algorithm. Extensive experiments show that GenMRP achieves state-of-the-art performance with high efficiency in both offline and online environments. To facilitate further research, we have publicly released the training and evaluation dataset. GenMRP has been fully deployed in a real-world navigation app, demonstrating its effectiveness and benefits.

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

Drones equipped with cameras are emerging as a powerful tool for large-scale aerial 3D scanning, but existing automatic flight planners do not exploit all available information about the scene, and can therefore produce inaccurate and incomplete 3D models. We present an automatic method to generate drone trajectories, such that the imagery acquired during the flight will later produce a high-fidelity 3D model. Our method uses a coarse estimate of the scene geometry to plan camera trajectories that: (1) cover the scene as thoroughly as possible; (2) encourage observations of scene geometry from a diverse set of viewing angles; (3) avoid obstacles; and (4) respect a user-specified flight time budget. Our method relies on a mathematical model of scene coverage that exhibits an intuitive diminishing returns property known as submodularity. We leverage this property extensively to design a trajectory planning algorithm that reasons globally about the non-additive coverage reward obtained across a trajectory, jointly with the cost of traveling between views. We evaluate our method by using it to scan three large outdoor scenes, and we perform a quantitative evaluation using a photorealistic video game simulator.

Large language models (LLMs) embedded in multi-turn agentic harnesses are reshaping software engineering (SWE), but routing every task to a frontier model is wasteful when many issues admit cheap fixes. Existing LLM routers operate on the task description alone, which inherits an information-theoretic Bayes-error floor in agentic settings: a similar issue can hide either a localized typo or a multi-module refactor, and the prompt does not separate the two. We introduce SWE-Router, a value-based temporal approach that lets a cheap model run for a few exploratory turns and reads the resulting partial trajectory before deciding whether to continue cheaply or to escalate to an expensive model. We provide a Bayes-optimality theorem showing that conditioning on the partial trajectory never harms routing and is strictly better whenever exploration is informative. Across the LLM pairs of weak and strong models spanning the contemporary cost--capability frontier, we show that SWE-Router greatly improves the cost efficiency of SWE tasks, while maintaining the majority of the performances of the stronger model. We additionally release a multi-LLM trajectory dataset which allows reproduction of our trajectory-level routing.

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

Recent advances in reinforcement learning for foundation models, such as Group Relative Policy Optimization (GRPO), have significantly improved the performance of foundation models on reasoning tasks. Notably, the advantage function serves as a central mechanism in GRPO for ranking the trajectory importance. However, existing explorations encounter both advantage reversion and advantage mirror problems, which hinder the reasonable advantage allocation across different query samples. In this work, we propose an easy but effective GRPO strategy, Mixed Advantage Policy Optimization (MAPO). We reveal that the trajectory appears with different certainty and propose the advantage percent deviation for samples with high-certainty trajectories. Furthermore, we dynamically reweight the advantage function for samples with varying trajectory certainty, thereby adaptively configuring the advantage function to account for sample-specific characteristics. Comparison with related state-of-the-art methods, along with ablation studies on different advantage variants, validates the effectiveness of our approach.

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

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

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

To measure the difference between two probability distributions, referred to as the source and target, respectively, we exploit both the chain rule and Bayes' theorem to construct conditional transport (CT), which is constituted by both a forward component and a backward one. The forward CT is the expected cost of moving a source data point to a target one, with their joint distribution defined by the product of the source probability density function (PDF) and a source-dependent conditional distribution, which is related to the target PDF via Bayes' theorem. The backward CT is defined by reversing the direction. The CT cost can be approximated by replacing the source and target PDFs with their discrete empirical distributions supported on mini-batches, making it amenable to implicit distributions and stochastic gradient descent-based optimization. When applied to train a generative model, CT is shown to strike a good balance between mode-covering and mode-seeking behaviors and strongly resist mode collapse. On a wide variety of benchmark datasets for generative modeling, substituting the default statistical distance of an existing generative adversarial network with CT is shown to consistently improve the performance. PyTorch code is provided.

Coding agents perform long-running tasks spanning dozens of model calls, tool uses, and code edits. As these runs unfold, users face a practical cost-quality trade-off: escalating to a stronger model when a cheaper one struggles, or downshifting once the hard reasoning is complete. Each switch requires the receiver to continue a non-native trajectory produced by another model. We study how this handoff affects quality and cost, and how varying the trajectory information inherited by the receiver changes the outcome. Using pairs of low-cost, low-capability (LC) and high-cost, high-capability (HC) models from the Claude and GPT families, we vary handoff direction, timing, and interface, comparing full-trajectory transfer, compaction, and trajectory removal while preserving the repository state. Across both model families, full-trajectory escalation recovers less than half of the LC-to-HC quality gap while incurring a substantial cost premium. We term this cost-quality penalty the handoff tax. By contrast, downshift offers a favorable cost-quality point. Interestingly, the preferred interface also reverses with direction: reducing LC-model trajectory information improves escalation quality, whereas removing the HC-model trajectory reduces downshift quality.

Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each vertex in the graph is a continuous decision variable constrained in a convex set, and the length of an edge is a convex function of the position of its endpoints. Problems of this form arise naturally in many areas, from motion planning of autonomous vehicles to optimal control of hybrid systems. The price for such a wide applicability is the complexity of this problem, which is easily seen to be NP-hard. Our main contribution is a strong and lightweight mixed-integer convex formulation based on perspective operators, that makes it possible to efficiently find globally optimal paths in large graphs and in high-dimensional spaces.

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

Diffusion models offer powerful generative capabilities for robot trajectory planning, yet their practical deployment on robots is hindered by a critical bottleneck: a reliance on imitation learning from expert demonstrations. This paradigm is often impractical for specialized robots where data is scarce and creates an inefficient, theoretically suboptimal training pipeline. To overcome this, we introduce PegasusFlow, a hierarchical rolling-denoising framework that enables direct and parallel sampling of trajectory score gradients from environmental interaction, completely bypassing the need for expert data. Our core innovation is a novel sampling algorithm, Weighted Basis Function Optimization (WBFO), which leverages spline basis representations to achieve superior sample efficiency and faster convergence compared to traditional methods like MPPI. The framework is embedded within a scalable, asynchronous parallel simulation architecture that supports massively parallel rollouts for efficient data collection. Extensive experiments on trajectory optimization and robotic navigation tasks demonstrate that our approach, particularly Action-Value WBFO (AVWBFO) combined with a reinforcement learning warm-start, significantly outperforms baselines. In a challenging barrier-crossing task, our method achieved a 100% success rate and was 18% faster than the next-best method, validating its effectiveness for complex terrain locomotion planning. https://masteryip.github.io/pegasusflow.github.io/

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

Diffusion and flow-matching schedules control the signal and noise coefficients that mix data and noise along affine probability paths. Minimizing a kinetic action defined on coefficient paths, motivated by optimal transport, helps explain strong baselines but remains model-agnostic and ignores prediction error. Here we introduce a model-aware schedule construction based on fiberwise optimal transport. At a fixed time and state on the probability path, compatible signal/noise decompositions form an affine fiber. We define a fiberwise prediction risk by averaging optimal-transport costs between the true and predictor-induced decompositions within these fibers. On a fixed coefficient curve, combining this risk with coefficient-path kinetic action yields a closed-form optimal time allocation. This construction extends to general linear prediction targets, and the risk profile can be estimated from an early baseline checkpoint. We evaluate DDPMs and flow matching across prediction targets, training configurations, risk-estimation checkpoints, datasets, and architectures. Our model-aware schedules consistently outperform strong baselines, including a 38.6% relative FID reduction for flow matching on CIFAR-10 at 16 function evaluations. Each model-agnostic kinetic baseline determines its own kinetic reference coordinate. In these coordinates, fiberwise-risk profiles from independently trained models in different settings align closely after normalization to unit area. The resulting schedule deformations used in training also align, suggesting empirical universality across the evaluated models and settings. Pretrained-checkpoint diagnostics extend this normalized-risk agreement to larger conditional latent diffusion and 2-RF models. A frozen analytic allocation template retains most of the model-aware improvement without further risk estimation or model-specific fitting.

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

Mobility simulation supports logistics, safety, and communications planning in industrial environments such as ports, mines, and airports. Existing trajectory models, however, rely on absolute coordinates, road-network tokens, or semantic zones: representations that are site-specific and not well suited to unstructured industrial terrain. We introduce the Industrial Kinematic Trajectory Model (IKTM), a coordinate-free trajectory generator that represents industrial vehicle motion through kinematic sequences (speed and heading change) with no absolute spatial reference. IKTM uses an autoregressive causal transformer with probabilistic mixture heads and extends our prior coordinate-free Markovian model with deep sequence modelling and an explicit duration-conditioning signal. Trained on one site and evaluated zero-shot on three unseen sites, it matches the small-turn shape of the empirical turn-rate distributions of held-out telematics; across all four sites, the per-site mean Jensen-Shannon divergence over 100 sampling seeds spans approximately 0.035-0.050 bits under an oracle-length duration-target protocol and approximately 0.032-0.042 bits under a fully zero-shot prior-length protocol, with similar ranges whether out-of-distribution (OOD) duration targets are drawn from each held-out site's empirical length distribution or from the Site A prior. Both protocols stay above the metric's sampling-noise floor (<=0.0049 bits). Paired by site, the oracle-length values are 5.3-6.0x lower than those of a re-implementation of our prior Markovian model under the same 1 Hz protocol. Termination is duration-conditioned rather than spatial: rollouts stop on 100% of trials with a length-tracking error of +0.0 +/- 0.0 s against the sampled target (100 of 100 exactly on target; N=100, T=0.2, untouched in-distribution test split).

Latent world models are judged by how well they predict, so when planning fails at long horizons the natural reading is that the predictor degrades. On a reproduction of LeWorldModel on TwoRoom we show the binding constraint is the planner's objective instead. The predictor is not the limit: its imagined state seventy-five environment steps ahead is still only 0.189 as wrong as assuming the world froze, while the planner never imagines beyond twenty-five. The objective is. Cross-entropy-method planning minimises squared latent distance, which tracks true distance at r = 0.426, saturates by about eighty arena units and decreases beyond a hundred and twenty, so moving away from the goal can lower the cost. The information is present throughout: a ridge probe recovers position from the frozen embedding at R^2 0.9922. The pathology is the method's, not one reimplementation's. It is present in the authors' released weights, and across four checkpoints long-horizon success rank-orders exactly with metric quality and inversely with prediction accuracy. Replacing only the objective, with nothing retrained and no GPU, lifts goals reached at offset 100 from 26.0% to 98.0%, equals the 98.0% at offset 25, and reaches 92.0% under a third of the budget: planning stops depending on the horizon. The best cost is not the most accurate. A head learned from frame separation alone predicts spatial distance worse than a position probe (r = 0.819 against 0.9897) yet plans better, charging 24% more to cross the environment's dividing wall where squared latent distance charges 4% less. It has learned reachability, not proximity.

We introduce AgentSynth, a scalable and cost-efficient pipeline for automatically synthesizing high-quality tasks and trajectory datasets for generalist computer-use agents. Leveraging information asymmetry, AgentSynth constructs subtasks that are simple during generation but significantly more challenging when composed into long-horizon tasks, enabling the creation of over 6,000 diverse and realistic tasks. Our pipeline begins with an LLM-based task proposer guided by a persona, followed by an execution agent that completes the task and logs the trajectory. This process is repeated iteratively to form a sequence of subtasks, which are then summarized by a separate agent into a composite task of controllable difficulty. A key strength of AgentSynth is its ability to precisely modulate task complexity by varying the number of subtasks. Empirical evaluations show that state-of-the-art LLM agents suffer a steep performance drop, from 18% success at difficulty level 1 to just 4% at level 6, highlighting the benchmark's difficulty and discriminative power. Moreover, our pipeline achieves a low average cost of \$0.60 per trajectory, orders of magnitude cheaper than human annotations. Our code and data are publicly available at https://github.com/sunblaze-ucb/AgentSynth

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

Effective spatio-temporal representation is fundamental to modeling, understanding, and predicting dynamics in videos. The atomic unit of a video, the pixel, traces a continuous 3D trajectory over time, serving as the primitive element of dynamics. Based on this principle, we propose representing any video as a Trajectory Field: a dense mapping that assigns a continuous 3D trajectory function of time to each pixel in every frame. With this representation, we introduce Trace Anything, a neural network that predicts the entire trajectory field in a single feed-forward pass. Specifically, for each pixel in each frame, our model predicts a set of control points that parameterizes a trajectory (i.e., a B-spline), yielding its 3D position at arbitrary query time instants. We trained the Trace Anything model on large-scale 4D data, including data from our new platform, and our experiments demonstrate that: (i) Trace Anything achieves state-of-the-art performance on our new benchmark for trajectory field estimation and performs competitively on established point-tracking benchmarks; (ii) it offers significant efficiency gains thanks to its one-pass paradigm, without requiring iterative optimization or auxiliary estimators; and (iii) it exhibits emergent abilities, including goal-conditioned manipulation, motion forecasting, and spatio-temporal fusion. Project page: https://trace-anything.github.io/.

Diffusion models have shown strong competitiveness in offline reinforcement learning tasks by formulating decision-making as sequential generation. However, the practicality of these methods is limited due to the lengthy inference processes they require. In this paper, we address this problem by decomposing the sampling process of diffusion models into two decoupled subprocesses: 1) generating a feasible trajectory, which is a time-consuming process, and 2) optimizing the trajectory. With this decomposition approach, we are able to partially separate efficiency and quality factors, enabling us to simultaneously gain efficiency advantages and ensure quality assurance. We propose the Trajectory Diffuser, which utilizes a faster autoregressive model to handle the generation of feasible trajectories while retaining the trajectory optimization process of diffusion models. This allows us to achieve more efficient planning without sacrificing capability. To evaluate the effectiveness and efficiency of the Trajectory Diffuser, we conduct experiments on the D4RL benchmarks. The results demonstrate that our method achieves it 3-it 10 times faster inference speed compared to previous sequence modeling methods, while also outperforming them in terms of overall performance. https://github.com/RenMing-Huang/TrajectoryDiffuser Keywords: Reinforcement Learning and Efficient Planning and Diffusion Model

We study a dynamical optimal transport problem on path-space with kinetic cost and nonlocal interaction. For a Gaussian interaction kernel, cyclical monotonicity and the regularity of the effective endpoint cost yield a conservative vector field associated with the initial momentum of the optimal trajectories. Separately, the Gaussian interaction potential W_{π_0} satisfies a uniform gradient estimate and, under a quantitative condition on the interaction strength, is a classical and hence viscosity subsolution of an eikonal equation. We also derive the Euler--Lagrange dynamics directly from path-space optimality by means of endpoint-preserving perturbations of the optimal path measure. The associated phase-space marginals satisfy a measure-valued Liouville-type, or nonlocal kinetic, equation driven by the smooth Gaussian self-consistent force. Conversely, a superposition principle lifts suitable measure-valued solutions of the phase-space continuity equation to measures on phase-space trajectories. Thus path-space optimal transport provides a variational connection between endpoint geometry, eikonal behavior of the Gaussian interaction potential, and kinetic mean-field dynamics.

Aerial imagery provides essential global context for autonomous navigation, enabling route planning at scales inaccessible to onboard sensing. We address the problem of generating global costmaps for long-range planning directly from satellite imagery when entities and mission-specific traversal rules are expressed in natural language at test time. This setting is challenging since mission requirements vary, terrain entities may be unknown at deployment, and user prompts often encode compositional traversal logic. Existing approaches relying on fixed ontologies and static cost mappings cannot accommodate such flexibility. While foundation models excel at language interpretation and open-vocabulary perception, no single model can simultaneously parse nuanced mission directives, locate arbitrary entities in large-scale imagery, and synthesize them into an executable cost function for planners. We therefore propose OVerSeeC, a zero-shot modular framework that decomposes the problem into Interpret-Locate-Synthesize: (i) an LLM extracts entities and ranked preferences, (ii) an open-vocabulary segmentation pipeline identifies these entities from high-resolution imagery, and (iii) the LLM uses the user's natural language preferences and masks to synthesize executable costmap code. Empirically, OVerSeeC handles novel entities, respects ranked and compositional preferences, and produces routes consistent with human-drawn trajectories across diverse regions, demonstrating robustness to distribution shifts. This shows that modular composition of foundation models enables open-vocabulary, preference-aligned costmap generation for scalable, mission-adaptive global planning.

Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality. To address these limitations, we presents a novel paradigm: modeling dynamics directly in the weight space of a neural network by projecting the evolving probability distribution. We first theoretically establish the connection between dynamic optimal transport in measure space and an equivalent energy functional in weight space. Subsequently, we design WeightFlow, which constructs the neural network weights into a graph and learns its evolution via a graph controlled differential equation. Experiments on interdisciplinary datasets demonstrate that WeightFlow improves performance by an average of 43.02\% over state-of-the-art methods, providing an effective and scalable solution for modeling high-dimensional stochastic dynamics.

Multi-turn, long-horizon tasks are increasingly common for large language models (LLMs), but solving them typically requires many sequential model invocations, accumulating substantial inference costs. Here, we study cost-aware multi-turn LLM routing: selecting which model to invoke at each turn from a model pool, given a fixed cost budget. We propose MTRouter, which encodes the interaction history and candidate models into joint history-model embeddings, and learns an outcome estimator from logged trajectories to predict turn-level model utility. Experiments show that MTRouter improves the performance-cost trade-off: on ScienceWorld, it surpasses GPT-5 while reducing total cost by 58.7%; on Humanity's Last Exam (HLE), it achieves competitive accuracy while reducing total cost by 43.4% relative to GPT-5, and these gains even carry over to held-out tasks. Further analyses reveal several mechanisms underlying its effectiveness: relative to prior multi-turn routers, MTRouter makes fewer model switches, is more tolerant to transient errors, and exhibits emergent specialization across models. Code: https://github.com/ZhangYiqun018/MTRouter

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be seen as an extension of classical diffusion models to an infinite-dimensional domain. Functional diffusion is very versatile as images, videos, audio, 3D shapes, deformations, \etc, can be handled by the same framework with minimal changes. In addition, functional diffusion is especially suited for irregular data or data defined in non-standard domains. In our work, we derive the necessary foundations for functional diffusion and propose a first implementation based on the transformer architecture. We show generative results on complicated signed distance functions and deformation functions defined on 3D surfaces.

Training vision-language web agents with multi-step RL is compute-intensive, with two dominant forms of inefficiency: idle GPUs in synchronous RL, and trajectories that use more steps and tokens than necessary. We present AsyncWebRL, which addresses both. On the system side, an asynchronous design overlaps rollout, gradient update, and policy refresh across iterations, paired with two web-agent-specific adaptations, namely an everlasting rollout pool and lightweight screenshot handling, that together deliver up to a 2.9times end-to-end training-throughput speedup over the previously fastest open synchronous pipeline (WebGym). On the algorithmic side, we identify the per-trajectory normalizer 1/|τ_i| in multi-step GRPO as the root cause of trajectory-level and token-level inefficiency: because failures are systematically longer than successes, it down-weights the negative gradient on failed tokens, so the policy keeps producing verbose memory schemas. Replacing 1/|τ_i| with a constant 1/k breaks this coupling, contracting trajectories while preserving aggregate success. Together, these contributions set a new open-source state of the art on the WebGym out-of-distribution test split (+5.8% relative over the 42.9% prior best), with the largest gains on the harder slices (+42% relative on Medium, +48% relative on Hard).

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.

Given a dataset on actions and resulting long-term rewards, a direct estimation approach fits value functions that minimize prediction error on the training data. Temporal difference learning (TD) methods instead fit value functions by minimizing the degree of temporal inconsistency between estimates made at successive time-steps. Focusing on finite state Markov chains, we provide a crisp asymptotic theory of the statistical advantages of this approach. First, we show that an intuitive inverse trajectory pooling coefficient completely characterizes the percent reduction in mean-squared error of value estimates. Depending on problem structure, the reduction could be enormous or nonexistent. Next, we prove that there can be dramatic improvements in estimates of the difference in value-to-go for two states: TD's errors are bounded in terms of a novel measure - the problem's trajectory crossing time - which can be much smaller than the problem's time horizon.

In this paper, we address the problem of human trajectory forecasting, which aims to predict the inherently multi-modal future movements of humans based on their past trajectories and other contextual cues. We propose a novel motion prediction conditional flow matching model, termed MoFlow, to predict K-shot future trajectories for all agents in a given scene. We design a novel flow matching loss function that not only ensures at least one of the K sets of future trajectories is accurate but also encourages all K sets of future trajectories to be diverse and plausible. Furthermore, by leveraging the implicit maximum likelihood estimation (IMLE), we propose a novel distillation method for flow models that only requires samples from the teacher model. Extensive experiments on the real-world datasets, including SportVU NBA games, ETH-UCY, and SDD, demonstrate that both our teacher flow model and the IMLE-distilled student model achieve state-of-the-art performance. These models can generate diverse trajectories that are physically and socially plausible. Moreover, our one-step student model is 100 times faster than the teacher flow model during sampling. The code, model, and data are available at our project page: https://moflow-imle.github.io

This paper presents a distributed algorithm applicable to a wide range of practical multi-robot applications. In such multi-robot applications, the user-defined objectives of the mission can be cast as a general optimization problem, without explicit guidelines of the subtasks per different robot. Owing to the unknown environment, unknown robot dynamics, sensor nonlinearities, etc., the analytic form of the optimization cost function is not available a priori. Therefore, standard gradient-descent-like algorithms are not applicable to these problems. To tackle this, we introduce a new algorithm that carefully designs each robot's subcost function, the optimization of which can accomplish the overall team objective. Upon this transformation, we propose a distributed methodology based on the cognitive-based adaptive optimization (CAO) algorithm, that is able to approximate the evolution of each robot's cost function and to adequately optimize its decision variables (robot actions). The latter can be achieved by online learning only the problem-specific characteristics that affect the accomplishment of mission objectives. The overall, low-complexity algorithm can straightforwardly incorporate any kind of operational constraint, is fault-tolerant, and can appropriately tackle time-varying cost functions. A cornerstone of this approach is that it shares the same convergence characteristics as those of block coordinate descent algorithms. The proposed algorithm is evaluated in three heterogeneous simulation set-ups under multiple scenarios, against both general-purpose and problem-specific algorithms. Source code is available at https://github.com/athakapo/A-distributed-plug-n-play-algorithm-for-multi-robot-applications.

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

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

Trajectory-based data attribution methods estimate the influence of training samples on model predictions by unrolling the training trajectory. They are widely used in applications such as data selection, data valuation, and model diagnosis, but there is a lack of comprehensive error analysis of these methods, raising concerns about method faithfulness and hindering reliable deployment. In this work, we provide the first systematic analysis of error sources in trajectory-based data attribution, together with concrete remedies to mitigate them and practical guidelines for downstream use. We organize the total error into three categories, config-level, algorithm-level, and system-level. We make three contributions. First, we identify optimizer mismatch as the dominant config-level error: existing methods derive their attribution under the assumption of SGD, even for models trained with the modern de facto optimizer AdamW. We propose AdamW-influence to fully account for AdamW's optimization dynamics, yielding improvements from 10% to over 300% in Spearman correlation between estimated and ground-truth influence across four settings spanning MLP, CNN, GPT-2, and Llama 3.2-1B. Second, we isolate the remaining algorithm-level error arising from the first-order Taylor approximation, identify the learning rate and trajectory length as factors governing the error magnitude, and derive a closed-form error proxy that can be evaluated along the original trajectory without retraining. Third, we translate these insights into practical guidelines for data selection by unifying offline and online strategies under a K-step look-ahead framework. Under this framework, online selection with a short horizon often matches or exceeds offline, and the optimal horizon can be tuned jointly with the learning rate. Together, these results turn the framework into an actionable selection recipe for practitioners.

Reinforcement learning offers the prospect of a reusable sequential decision-making mechanism for spacecraft trajectory design, motivating policy interfaces that connect learned decisions to the underlying maneuver geometry. This paper develops Reachability Analysis-Informed Reinforcement Learning (RARL) for deterministic multi-impulse interplanetary transfers, placing intermediate waypoint selection at the center of the learned decision process. Local first-order reachability maps bounded velocity perturbations into an ellipsoidal set of next-node positions, within which the policy selects its waypoint. Lambert reconstruction then determines the corresponding maneuver to reach this selected waypoint along a dynamically consistent ballistic arc, coupling learned transfer-geometry selection with classical astrodynamics. A terminal two-impulse reconstruction completes the rendezvous, supported by a linear maneuver-demand assessment used for reward shaping. Numerical studies characterize this interface on a two-body Earth-Mars benchmark. Across three independent training runs, RARL achieves a mean maneuver cost of 10.23 km/s, 1.72% above a validated local sequential convex programming reference. Training over dispersed initial states extends policy reuse across a departure family with fixed target state and transfer duration. Each of the three independently trained multi-state policies completes all 10,000 held-out Monte Carlo departures without impulse-cap violations, compared with a mean feasibility rate of 6.49% for single-state policies. This broader sampled feasibility is accompanied by a 0.61% increase in mean nominal maneuver cost, without further training across departures. These results demonstrate that a reachability-informed decision interface supports benchmark-quality trajectory construction and policy reuse across dispersed departure conditions.

A safe action is not necessarily a viable one. A frozen vision-language-action (VLA) policy can favor a locally admissible move that leaves no policy-supported route to safe task completion. We call this the feasibility-likelihood gap: likelihood ranks the next move, while feasibility depends on the futures it leaves open. To bring those futures into the decision, we derive the exact next-block marginal of the history-conditioned policy-environment trajectory law restricted to safe task completion. The derivation reveals a candidate-dependent feasible-future mass: its support records whether safe completion remains possible under the frozen continuation process, while its magnitude measures how much weighted safe-completion mass remains. Since exact evaluation is impractical online, we develop a selective finite-candidate approximation and establish conditions for recovering the best retained viable candidate. Our alarm-triggered, training-free reranker VICS-G lowers mean cumulative safety cost by 1.9%-57.5% across six Safety-CHORES settings while remaining within 2.5 percentage points of policy sampling in success and 0.82 steps in mean episode length. Our approach offers a promising and practical path toward safer task completion, grounded in an exact policy-relative target yet requiring neither policy retraining nor online rollouts.

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

Large language models (LLMs) have demonstrated powerful decision-making and planning capabilities in solving complicated real-world problems. LLM-based autonomous agents can interact with diverse tools (e.g., functional APIs) and generate solution plans that execute a series of API function calls in a step-by-step manner. The multitude of candidate API function calls significantly expands the action space, amplifying the critical need for efficient action space navigation. However, existing methods either struggle with unidirectional exploration in expansive action spaces, trapped into a locally optimal solution, or suffer from exhaustively traversing all potential actions, causing inefficient navigation. To address these issues, we propose ToolChain*, an efficient tree search-based planning algorithm for LLM-based agents. It formulates the entire action space as a decision tree, where each node represents a possible API function call involved in a solution plan. By incorporating the A* search algorithm with task-specific cost function design, it efficiently prunes high-cost branches that may involve incorrect actions, identifying the most low-cost valid path as the solution. Extensive experiments on multiple tool-use and reasoning tasks demonstrate that ToolChain* efficiently balances exploration and exploitation within an expansive action space. It outperforms state-of-the-art baselines on planning and reasoning tasks by 3.1% and 3.5% on average while requiring 7.35x and 2.31x less time, respectively.

User profiling and region analysis are two tasks of significant commercial value. However, in practical applications, modeling different features typically involves four main steps: data preparation, data processing, model establishment, evaluation, and optimization. This process is time-consuming and labor-intensive. Repeating this workflow for each feature results in abundant development time for tasks and a reduced overall volume of task development. Indeed, human mobility data contains a wealth of information. Several successful cases suggest that conducting in-depth analysis of population movement data could potentially yield meaningful profiles about users and areas. Nonetheless, most related works have not thoroughly utilized the semantic information within human mobility data and trained on a fixed number of the regions. To tap into the rich information within population movement, based on the perspective that Regions Are Who walk them, we propose a large spatiotemporal model based on trajectories (RAW). It possesses the following characteristics: 1) Tailored for trajectory data, introducing a GPT-like structure with a parameter count of up to 1B; 2) Introducing a spatiotemporal fine-tuning module, interpreting trajectories as collection of users to derive arbitrary region embedding. This framework allows rapid task development based on the large spatiotemporal model. We conducted extensive experiments to validate the effectiveness of our proposed large spatiotemporal model. It's evident that our proposed method, relying solely on human mobility data without additional features, exhibits a certain level of relevance in user profiling and region analysis. Moreover, our model showcases promising predictive capabilities in trajectory generation tasks based on the current state, offering the potential for further innovative work utilizing this large spatiotemporal model.

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.

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

We present CosFly, a box-structured planning and multimodal simulation pipeline for aerial tracking, together with CosFly-Track, a large-scale UAV dataset for dynamic target tracking across diverse environments including urban centers, highways, rural landscapes, forests, and coastal towns. In our current implementation on CARLA, CosFly provides a modular 7-step construction pipeline that converts complex 3D worlds into structured obstacle representations for planning, then projects the resulting trajectories back into multi-modal sensor data -- including RGB images, high-precision depth maps, and semantic segmentation masks -- paired with natural language navigation instructions. A key feature is the support for configurable fixed-FOV zoom levels (one FOV setting drawn per trajectory and held constant throughout), enabling simulation of various focal lengths through camera-intrinsic adjustments. The pipeline covers the complete workflow from 3D map export through grid simplification, pedestrian and drone trajectory planning, multi-modal rendering with 6-DOF pose annotations, quality inspection, and teacher-student caption generation. We analyze two trajectory-planning paradigms for aerial target tracking: a conventional two-stage pipeline with front-end candidate generation and backend refinement, and a direct gradient-based formulation that optimizes multiple tracking constraints in a single objective. The public CosFly-Track release contains 250 validated trajectories and approximately 100,000 rendered images with complete 6-DOF drone pose annotations (position x, y, z and orientation yaw, pitch, roll). Together, the pipeline and dataset establish a scalable foundation for aerial-ground collaborative research, supporting dynamic target tracking, UAV navigation, and multi-modal perception across diverse environments.

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

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

In collection operations, accumulating payload progressively slows the vehicle, imposing a cumulative penalty on routing efficiency. An onboard drone can offset this penalty by retrieving outlying items, thereby shortening the makespan and increasing operational profit. However, travel time remains load-dependent, and each item collected by the ground vehicle shifts the arrival times that govern the drone's launch and rendezvous points. This paper introduces the Travelling Thief Problem with Drone (TTP-D), which maximises the collected profit, net of a time-based rental cost, by jointly optimising item selection, vehicle routing, and flight synchronisation. We formulate a mixed-integer linear program that solves small instances to optimality, and develop both metaheuristics and an attention-based Deep Reinforcement Learning (DRL) policy for larger instances. We further propose a learner-initialised hybrid solver, in which the DRL policy constructs an initial solution that a short annealing run subsequently refines. On two benchmark sets, this hybrid recovers most of the metaheuristic baseline's quality at a fraction of its computational budget, although the largest instances still require the baseline at its full budget. Finally, a sensitivity analysis reveals that the rental ratio is the primary driver of profitability, whereas the fleet parameters affect profit only at the margin.

Aiming at promoting the safe real-world deployment of Reinforcement Learning (RL), research on safe RL has made significant progress in recent years. However, most existing works in the literature still focus on the online setting where risky violations of the safety budget are likely to be incurred during training. Besides, in many real-world applications, the learned policy is required to respond to dynamically determined safety budgets (i.e., constraint threshold) in real time. In this paper, we target at the above real-time budget constraint problem under the offline setting, and propose Trajectory-based REal-time Budget Inference (TREBI) as a novel solution that approaches this problem from the perspective of trajectory distribution. Theoretically, we prove an error bound of the estimation on the episodic reward and cost under the offline setting and thus provide a performance guarantee for TREBI. Empirical results on a wide range of simulation tasks and a real-world large-scale advertising application demonstrate the capability of TREBI in solving real-time budget constraint problems under offline settings.

MeanFlow has recently emerged as a powerful framework for few-step generative modeling trained from scratch, but its success is not yet fully understood. In this work, we show that the MeanFlow objective naturally decomposes into two parts: trajectory flow matching and trajectory consistency. Through gradient analysis, we find that these terms are strongly negatively correlated, causing optimization conflict and slow convergence. Motivated by these insights, we introduce alpha-Flow, a broad family of objectives that unifies trajectory flow matching, Shortcut Model, and MeanFlow under one formulation. By adopting a curriculum strategy that smoothly anneals from trajectory flow matching to MeanFlow, alpha-Flow disentangles the conflicting objectives, and achieves better convergence. When trained from scratch on class-conditional ImageNet-1K 256x256 with vanilla DiT backbones, alpha-Flow consistently outperforms MeanFlow across scales and settings. Our largest alpha-Flow-XL/2+ model achieves new state-of-the-art results using vanilla DiT backbones, with FID scores of 2.58 (1-NFE) and 2.15 (2-NFE).

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.

Recent successful generative models are trained by fitting a neural network to an a-priori defined tractable probability density path taking noise to training examples. In this paper we investigate the space of Gaussian probability paths, which includes diffusion paths as an instance, and look for an optimal member in some useful sense. In particular, minimizing the Kinetic Energy (KE) of a path is known to make particles' trajectories simple, hence easier to sample, and empirically improve performance in terms of likelihood of unseen data and sample generation quality. We investigate Kinetic Optimal (KO) Gaussian paths and offer the following observations: (i) We show the KE takes a simplified form on the space of Gaussian paths, where the data is incorporated only through a single, one dimensional scalar function, called the data separation function. (ii) We characterize the KO solutions with a one dimensional ODE. (iii) We approximate data-dependent KO paths by approximating the data separation function and minimizing the KE. (iv) We prove that the data separation function converges to 1 in the general case of arbitrary normalized dataset consisting of n samples in d dimension as n/drightarrow 0. A consequence of this result is that the Conditional Optimal Transport (Cond-OT) path becomes kinetic optimal as n/drightarrow 0. We further support this theory with empirical experiments on ImageNet.

Autoregressive generation underlies real-time, causal video synthesis and is the backbone of video world models. Today's dominant approach distills a bidirectional diffusion model into a causal few-step student, but existing pipelines make this conversion prohibitively expensive, requiring offline Probability Flow ODE} (PF-ODE) trajectories that cost tens of thousands of GPU-hours and terabytes of storage. We show it can be made dramatically more efficient. Pushing this efficiency to its extreme, we reduce trajectory supervision to a single sample, the strictest setting possible, and find that it causes severe quality collapse. We trace this to the teacher's trajectory geometry: the high-noise regime, governing semantic layout and motion, and the low-noise regime, governing fine texture exhibit fundamentally different curvature and optimization behavior, so a single monolithic student cannot jointly fit both, causing severe representation interference. Motivated by this, we propose Glance Forcing, a lightweight distillation framework that decouples the denoising trajectory into two complementary slow and fast experts, each guided by a tailored, stage-specific objective, while keeping the pretrained teacher entirely frozen. This decoupling further reveals a general mechanism underlying few-step distillation: PF-ODE distillation mainly straightens the few-step trajectory geometry, while the subsequent distribution-matching stage independently governs distributional quality. Using only one PF-ODE trajectory, Glance Forcing already surpasses the fully-trained state-of-the-art baseline, raising the VBench Total score from 84.04 to 84.22 while cutting trajectory-collection cost from thousands of GPU-hours to about one A100-GPU-hour, with markedly larger gains in dynamic degree, VisionReward, and instruction-following, and consistent preference from human raters over strong baselines.

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

We develop policy gradients methods for stochastic control with exit time in a model-free setting. We propose two types of algorithms for learning either directly the optimal policy or by learning alternately the value function (critic) and the optimal control (actor). The use of randomized policies is crucial for overcoming notably the issue related to the exit time in the gradient computation. We demonstrate the effectiveness of our approach by implementing our numerical schemes in the application to the problem of share repurchase pricing. Our results show that the proposed policy gradient methods outperform PDE or other neural networks techniques in a model-based setting. Furthermore, our algorithms are flexible enough to incorporate realistic market conditions like e.g. price impact or transaction costs.

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

Visual navigation ability is strongly tied to its underlying representation of the world. Unlike classical 3D maps that require globally-consistent geometry, image- or object-relative topological graphs almost entirely do away with geometric understanding. But, this comes at the cost of navigation capability, often limiting it to merely teach-and-repeat. In this work, we propose a novel map representation in the form of pixel-relative connectivity, which is geometrically accurate but does not require global geometric consistency. Inspired by recent progress in 3D grounded image matching, we construct a map from an image sequence through inter-image connectivity based on pixel correspondences in the relative 3D coordinate systems of individual image pairs. We then use this pixel-level graph to perform global path planning by approximating and sparsifying intra-image pixel connectivity. Through this, we derive a ''WayPixel Costmap'' representation and train a controller conditioned on it to predict a trajectory rollout. We show that this dense pixel-level costmap based on relative geometry is a more accurate conditioning variable for control prediction than its image- and object-level counterparts. This enables a highly capable navigation system, as validated on four types of navigation tasks in the simulator and through real world demonstrations.

A robot's flash endurance is a non-renewable stock: every persisted write spends one of a few thousand program/erase cycles and never refills, yet no fielded robot memory system prices which memories are worth an erase cycle. We treat embodied memory as depreciating capital and price that stock with a single endurance shadow price η, which makes cost-minimizing placement across a RAM / on-board NVM / cloud hierarchy a threshold in a wear-augmented per-byte index. The index is cost-optimal whatever the sign of the value-write association χ; only when χ> 0 does the optimum turn non-monotone, sending a robot's most valuable memories off its flash. The pivot is thus empirical, and we measure χ on real robot logs at a pre-specified gate: its sign is a property of the deployment regime -- positive on recurrent long-horizon manipulation (hatχ approx +1.0 times 10^{-3}, replicated at full power), null on a shorter-horizon suite, and negative on non-recurrent teleoperation. Two boundaries scope the result. The endurance budget is dormant on premium 3,000-P/E TLC at datasheet prices and binding on the commodity QLC/eMMC (sim1,000 P/E) that cheaper edge robots run. And where it binds, a learned wear-aware controller only ties price-based routing on task value, because realized value is tier-invariant across RAM, NVM, and cloud: the rent governs device lifetime and cost, not task performance. Whether wear-aware placement improves task value remains open -- χ is measured against a value proxy, and the non-monotone optimum, while proven, is not yet observed in data.

Generating high-fidelity synthetic GPS trajectories is increasingly important for applications in transportation, urban planning, and what-if scenario simulation, especially as privacy concerns limit access to real-world mobility data. Existing trajectory generation models face a trade-off between efficiency and faithfulness to road network topology: continuous-space methods enable fast generation but ignore the road network, while topology-aware approaches rely on search-based autoregressive decoding that limits generation speed. We propose TrajDLM, a topology-aware trajectory generation framework based on block diffusion language models that bridges this gap. TrajDLM models trajectories as sequences of discrete road segments, combining a block diffusion backbone for efficient denoising, topology-aware embeddings from a road network encoder, and topology-constrained sampling to ensure coherent and realistic trajectories. Across three city-scale datasets, TrajDLM achieves strong performance on fine-grained local similarity metrics while being up to 2.8times faster than prior work, and demonstrates strong zero-shot transfer across domains, including unseen transportation modes. These results highlight the effectiveness of block-wise discrete diffusion as a scalable approach to accurate and efficient trajectory generation. Our code is available at https://github.com/cruiseresearchgroup/TrajDLM/

Personalized Query prediction maps implicit behavioral signals---clicks, favorites, purchases, and post-purchase exploration---to explicit retrieval intent. On-device deployment makes this task particularly challenging: behavioral trajectories are noisy and multi-scale, multiple Queries may be valid for a single trajectory, and a uniform reasoning policy either expends unnecessary computation on simple instances or allocates insufficient capacity to complex ones. We introduce RecGPT-Mobile-V2, an end-to-end framework that treats intent quality and execution efficiency as coupled objectives within a staged design. The framework transforms heterogeneous interactions into an evidence-preserving trajectory, establishes a recommendation-native foundation through domain adaptation and supervised alignment, and applies reasoning-cost optimization only after grouped rollouts meet grounding and utility criteria. The resulting teacher is distilled into a compact student deployed with low-bit execution, structured compression, and budget-aware device--cloud routing. In an aligned CoT ablation, an evidence-focused short rationale increases ROUGE-L from 0.228 to 0.315 and Jaccard from 0.174 to 0.248, while slightly outperforming the full five-stage rationale. In the controlled RL comparison, the complete reward formulation improves Query quality from 73.2% under quality-only RL to 78.6%, lowers the hard-failure rate from 3.6% to 1.6%, and reduces the median CoT length from 62 to 14 tokens. Online retrieval analysis further indicates that the Query recall channel retrieves inventory complementary to that surfaced by established recall channels. Collectively, these findings support sufficiency-oriented rather than uniformly short reasoning: retain decision-relevant evidence and allocate additional computation only when it is likely to improve the predicted Query.

Risk-aware planners score paths on uncertain elevation maps using the path cost's mean and standard deviation. Modeling rigid contact, however, requires computing a maximum over several uncertain cells. First-order propagation loses accuracy here by differentiating at only a single cell, while Monte Carlo sampling requires a full path evaluation per draw. We compute the moments of that contact maximum in closed form using Clark's pairwise recursion. By tracking each contact's covariance against the shared map cells, we propagate the smooth remainder using exact Gaussian quadratic-form identities. A contest-depth calibration, fitted once on two design traverses, closes the aggregate standard-deviation shortfall that remains. On 317 held-out rover path segments, scored against a Monte Carlo reference from the same belief, every pre-registered criterion was met. The corrected Clark fold cuts the median error of the mean from linearization's 2.3% to 0.19% and attains the lowest error in the conditional value at risk (CVaR) at the 90% level of every method tested. A benchmark plan costs just 5.5 microseconds on a GPU. These accuracy gains concentrate at contested contacts. While they seldom change which path is chosen on this terrain, the fold still selects the reference-best path in 98% of decisions against linearization's 93 to 96%. On a second dataset the mean transfers, though the risk number does not.

In this work, we propose a training-free, trajectory-based controllable T2I approach, termed TraDiffusion. This novel method allows users to effortlessly guide image generation via mouse trajectories. To achieve precise control, we design a distance awareness energy function to effectively guide latent variables, ensuring that the focus of generation is within the areas defined by the trajectory. The energy function encompasses a control function to draw the generation closer to the specified trajectory and a movement function to diminish activity in areas distant from the trajectory. Through extensive experiments and qualitative assessments on the COCO dataset, the results reveal that TraDiffusion facilitates simpler, more natural image control. Moreover, it showcases the ability to manipulate salient regions, attributes, and relationships within the generated images, alongside visual input based on arbitrary or enhanced trajectories.

Large language model agents can often make reasonable local decisions on short tasks, yet their performance degrades when success requires long sequences of dependent actions and tool calls. During execution, task requirements, historical evidence, and the current execution state may gradually become disconnected, so later decisions can drift from the original objective. We study this problem by introducing the Adaptive Consistency Graph (ACG) for long-horizon execution. ACG incrementally organizes execution evidence and its provenance in a persistent graph, then constructs a temporary requirement-centered view for each decision under a bounded context budget. Rather than replacing the base agent's planner or tool executor, ACG provides a structured and traceable context view for each decision. In the matched evaluation, ACG improves GPT-5.6-luna's average success from 44.5\% with ReAct to 50.2\%, with the largest gain on BrowseComp-Plus (73.5\% versus 62.4\%). We further analyze trajectory structure and inference cost to characterize this improvement.

Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple, this combination has a number of empirical shortcomings, suggesting that learned models may not be well-suited to standard trajectory optimization. In this paper, we consider what it would look like to fold as much of the trajectory optimization pipeline as possible into the modeling problem, such that sampling from the model and planning with it become nearly identical. The core of our technical approach lies in a diffusion probabilistic model that plans by iteratively denoising trajectories. We show how classifier-guided sampling and image inpainting can be reinterpreted as coherent planning strategies, explore the unusual and useful properties of diffusion-based planning methods, and demonstrate the effectiveness of our framework in control settings that emphasize long-horizon decision-making and test-time flexibility.

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition.

Operating effectively in complex environments while complying with specified constraints is crucial for the safe and successful deployment of robots that interact with and operate around people. In this work, we focus on generating long-horizon trajectories that adhere to novel static and temporally-extended constraints/instructions at test time. We propose a data-driven diffusion-based framework, LTLDoG, that modifies the inference steps of the reverse process given an instruction specified using finite linear temporal logic (LTL_f). LTLDoG leverages a satisfaction value function on LTL_f and guides the sampling steps using its gradient field. This value function can also be trained to generalize to new instructions not observed during training, enabling flexible test-time adaptability. Experiments in robot navigation and manipulation illustrate that the method is able to generate trajectories that satisfy formulae that specify obstacle avoidance and visitation sequences. Code and supplementary material are available online at https://github.com/clear-nus/ltldog.

Recent advances in diffusion/flow-matching policies have enabled imitation learning of complex, multi-modal action trajectories. However, they are computationally expensive because they sample a trajectory of trajectories: a diffusion/flow trajectory of action trajectories. They discard intermediate action trajectories, and must wait for the sampling process to complete before any actions can be executed on the robot. We simplify diffusion/flow policies by treating action trajectories as flow trajectories. Instead of starting from pure noise, our algorithm samples from a narrow Gaussian around the last action. Then, it incrementally integrates a velocity field learned via flow matching to produce a sequence of actions that constitute a single trajectory. This enables actions to be streamed to the robot on-the-fly during the flow sampling process, and is well-suited for receding horizon policy execution. Despite streaming, our method retains the ability to model multi-modal behavior. We train flows that stabilize around demonstration trajectories to reduce distribution shift and improve imitation learning performance. Streaming flow policy outperforms prior methods while enabling faster policy execution and tighter sensorimotor loops for learning-based robot control. Project website: https://streaming-flow-policy.github.io/

Recent work has demonstrated the effectiveness of formulating decision making as a supervised learning problem on offline-collected trajectories. However, the benefits of performing sequence modeling on trajectory data is not yet clear. In this work we investigate if sequence modeling has the capability to condense trajectories into useful representations that can contribute to policy learning. To achieve this, we adopt a two-stage framework that first summarizes trajectories with sequence modeling techniques, and then employs these representations to learn a policy along with a desired goal. This design allows many existing supervised offline RL methods to be considered as specific instances of our framework. Within this framework, we introduce Goal-Conditioned Predicitve Coding (GCPC), an approach that brings powerful trajectory representations and leads to performant policies. We conduct extensive empirical evaluations on AntMaze, FrankaKitchen and Locomotion environments, and observe that sequence modeling has a significant impact on some decision making tasks. In addition, we demonstrate that GCPC learns a goal-conditioned latent representation about the future, which serves as an "implicit planner", and enables competitive performance on all three benchmarks.

Offline reinforcement learning is typically analyzed under process-level reward supervision, yet many sequential decision datasets record only trajectory-level outcomes. We develop a statistical theory for offline policy optimization from such outcome-level supervision. We first study the canonical setting where the target remains the expected cumulative reward, but each offline trajectory provides only a scalar label whose conditional mean is the cumulative return. We propose OPAC, a pessimistic actor-critic algorithm that learns a latent reward model and optimizes a policy from trajectory-level labels. We prove a high-probability guarantee of order widetilde O(H^2C_{sa(π^star)/n}) and a matching lower bound, characterizing the sharp statistical cost of replacing process-level rewards with one trajectory-level label. We then extend the principle to preference-based feedback, preserving the leading horizon and concentrability dependence up to preference-model constants. Finally, we study generalized outcome-based offline RL, where both the supervision and the objective are trajectory-level quantities induced by a nonlinear aggregation of latent per-step rewards. This problem is not learnable in general: for all-success objectives, any offline learner may require Ω(2^H) trajectories even with deterministic transitions and constant concentrability. We then identify a tractable regime through two structural coefficients, κ_μ(σ) and χ_μ(σ), capturing information loss in outcome aggregation and generalized Bellman updates, under which generalized OPAC achieves polynomial sample complexity. Together, our results delineate when outcome-level supervision enables sample-efficient offline control and when missing process-level rewards create fundamental statistical barriers.

Due to the stochasticity of human behaviors, predicting the future trajectories of road agents is challenging for autonomous driving. Recently, goal-based multi-trajectory prediction methods are proved to be effective, where they first score over-sampled goal candidates and then select a final set from them. However, these methods usually involve goal predictions based on sparse pre-defined anchors and heuristic goal selection algorithms. In this work, we propose an anchor-free and end-to-end trajectory prediction model, named DenseTNT, that directly outputs a set of trajectories from dense goal candidates. In addition, we introduce an offline optimization-based technique to provide multi-future pseudo-labels for our final online model. Experiments show that DenseTNT achieves state-of-the-art performance, ranking 1st on the Argoverse motion forecasting benchmark and being the 1st place winner of the 2021 Waymo Open Dataset Motion Prediction Challenge.

How can we rely on an end-to-end autonomous vehicle's complex decision-making system during deployment? One common solution is to have a ``fallback layer'' that checks the planned trajectory for rule violations and replaces it with a pre-defined safe action if necessary. Another approach involves adjusting the planner's decisions to minimize a pre-defined ``cost function'' using additional system predictions such as road layouts and detected obstacles. However, these pre-programmed rules or cost functions cannot learn and improve with new training data, often resulting in overly conservative behaviors. In this work, we propose Centaur (Cluster Entropy for Test-time trAining using Uncertainty) which updates a planner's behavior via test-time training, without relying on hand-engineered rules or cost functions. Instead, we measure and minimize the uncertainty in the planner's decisions. For this, we develop a novel uncertainty measure, called Cluster Entropy, which is simple, interpretable, and compatible with state-of-the-art planning algorithms. Using data collected at prior test-time time-steps, we perform an update to the model's parameters using a gradient that minimizes the Cluster Entropy. With only this sole gradient update prior to inference, Centaur exhibits significant improvements, ranking first on the navtest leaderboard with notable gains in safety-critical metrics such as time to collision. To provide detailed insights on a per-scenario basis, we also introduce navsafe, a challenging new benchmark, which highlights previously undiscovered failure modes of driving models.

Online decision-making faces a tension between efficient inference and long-horizon reasoning. Value-based methods rely on short-horizon bootstrapping that limits the propagation of long-term information, while trajectory optimization methods plan explicitly but must solve a high-dimensional optimization problem at every decision step. We propose Generative Trajectory Planning (GTP), a model-based framework that addresses this tension by learning a generative model as a proposal distribution over action sequences. Instead of optimizing sequences from scratch, GTP samples candidate sequences from a diffusion prior and refines them using learned dynamics, reward, and value models, enabling efficient trajectory-level reasoning. Across continuous control and long-horizon manipulation tasks, GTP matches or exceeds state-of-the-art model-free, diffusion-policy, and model-based baselines, and remains stable in regimes where strong baselines degrade. Our results suggest that generative models are best understood not as policies, but as structured proposal distributions for planning, offering a new perspective on how to integrate generative modeling with model-based decision-making.

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

Group-relative reinforcement learning waits for sibling rollouts of the same prompt, which is costly for long and variable tool-use trajectories. Single-stream Policy Optimization (SPO) removes this dependency with a persistent prompt-level value estimate, but its recipe whitens one advantage per trajectory before optimizing a token-mean actor loss. We show that trajectory centering generally does not center the token-weighted quantity consumed by the actor, and fix the mismatch by standardizing terminal-outcome advantages under the action-token measure. We additionally organize prompt evidence by the policy event that generated it rather than learner receipt order. Across matched runs on ALFWorld at two model scales and on Math-TIR, SPO++ improves online learning efficiency over SPO. A paired ablation identifies action-token-measure normalization as the strongest tested component.

Effective trajectory stitching for long-horizon planning is a significant challenge in robotic decision-making. While diffusion models have shown promise in planning, they are limited to solving tasks similar to those seen in their training data. We propose CompDiffuser, a novel generative approach that can solve new tasks by learning to compositionally stitch together shorter trajectory chunks from previously seen tasks. Our key insight is modeling the trajectory distribution by subdividing it into overlapping chunks and learning their conditional relationships through a single bidirectional diffusion model. This allows information to propagate between segments during generation, ensuring physically consistent connections. We conduct experiments on benchmark tasks of various difficulties, covering different environment sizes, agent state dimension, trajectory types, training data quality, and show that CompDiffuser significantly outperforms existing methods.

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

We investigate the exploration of an unknown environment when no reward function is provided. Building on the incremental exploration setting introduced by Lim and Auer [1], we define the objective of learning the set of ε-optimal goal-conditioned policies attaining all states that are incrementally reachable within L steps (in expectation) from a reference state s_0. In this paper, we introduce a novel model-based approach that interleaves discovering new states from s_0 and improving the accuracy of a model estimate that is used to compute goal-conditioned policies to reach newly discovered states. The resulting algorithm, DisCo, achieves a sample complexity scaling as O(L^5 S_{L+ε} Γ_{L+ε} A ε^{-2}), where A is the number of actions, S_{L+ε} is the number of states that are incrementally reachable from s_0 in L+ε steps, and Γ_{L+ε} is the branching factor of the dynamics over such states. This improves over the algorithm proposed in [1] in both ε and L at the cost of an extra Γ_{L+ε} factor, which is small in most environments of interest. Furthermore, DisCo is the first algorithm that can return an ε/c_{min}-optimal policy for any cost-sensitive shortest-path problem defined on the L-reachable states with minimum cost c_{min}. Finally, we report preliminary empirical results confirming our theoretical findings.

MeanFlow (MF) has recently been established as a framework for one-step generative modeling. However, its ``fastforward'' nature introduces key challenges in both the training objective and the guidance mechanism. First, the original MF's training target depends not only on the underlying ground-truth fields but also on the network itself. To address this issue, we recast the objective as a loss on the instantaneous velocity v, re-parameterized by a network that predicts the average velocity u. Our reformulation yields a more standard regression problem and improves the training stability. Second, the original MF fixes the classifier-free guidance scale during training, which sacrifices flexibility. We tackle this issue by formulating guidance as explicit conditioning variables, thereby retaining flexibility at test time. The diverse conditions are processed through in-context conditioning, which reduces model size and benefits performance. Overall, our improved MeanFlow (iMF) method, trained entirely from scratch, achieves 1.72 FID with a single function evaluation (1-NFE) on ImageNet 256times256. iMF substantially outperforms prior methods of this kind and closes the gap with multi-step methods while using no distillation. We hope our work will further advance fastforward generative modeling as a stand-alone paradigm.

In robot manipulation, robot learning has become a prevailing approach. However, generative models within this field face a fundamental trade-off between the slow, iterative sampling of diffusion models and the architectural constraints of faster Flow-based methods, which often rely on explicit consistency losses. To address these limitations, we introduce MP1, which pairs 3D point-cloud inputs with the MeanFlow paradigm to generate action trajectories in one network function evaluation (1-NFE). By directly learning the interval-averaged velocity via the "MeanFlow Identity", our policy avoids any additional consistency constraints. This formulation eliminates numerical ODE-solver errors during inference, yielding more precise trajectories. MP1 further incorporates CFG for improved trajectory controllability while retaining 1-NFE inference without reintroducing structural constraints. Because subtle scene-context variations are critical for robot learning, especially in few-shot learning, we introduce a lightweight Dispersive Loss that repels state embeddings during training, boosting generalization without slowing inference. We validate our method on the Adroit and Meta-World benchmarks, as well as in real-world scenarios. Experimental results show MP1 achieves superior average task success rates, outperforming DP3 by 10.2% and FlowPolicy by 7.3%. Its average inference time is only 6.8 ms-19x faster than DP3 and nearly 2x faster than FlowPolicy. Our code is available at https://github.com/LogSSim/MP1.git.

Assigning one of K options to each of N groups under a total cost budget is a recurring problem in efficient AI, including mixed-precision quantization, non-uniform pruning, and expert selection. The objective, typically model loss, depends jointly on all assignments and does not decompose across groups, preventing combinatorial solvers from directly optimizing the true objective and forcing reliance on proxy formulations. Methods such as evolutionary search evaluate the actual loss but lack gradient information, while penalty-based approaches enforce the budget only approximately and often require extensive hyperparameter tuning. We present a new approach by showing that, under softmax relaxation, the budget constraint defines a smooth Riemannian manifold in logit space with unusually simple geometry. The normal vector admits a closed-form expression, shifting logits along the cost vector changes expected cost monotonically, and vector transport reduces to a single inner product. Building on these properties, we propose Riemannian Constrained Optimization (RCO), which augments a standard Adam step with tangent projection, binary-search retraction, and momentum transport. Combined with Gumbel straight-through estimation and budget-constrained dynamic programming for discrete feasibility, RCO enables first-order optimization of the actual loss under exact budget enforcement without introducing constraint-specific hyperparameters. Across both synthetic benchmarks and realistic LLM compression settings, RCO matches or exceeds state-of-the-art methods while often requiring substantially less wall-clock time. Source code is available at https://github.com/IST-DASLab/RCO.

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

We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. Furthermore, we derive an accelerated proximal algorithm with a closed-form projection and proximal operator scheme, thereby affording a more scalable algorithm for computing optimal transport plans. We provide a novel argument for the uniqueness of the optimum even in the absence of strong convexity. Our experiments show that the new regularizer not only results in a better preservation of the class structure in the data but also yields additional robustness to the data geometry, compared to previous regularizers.

Multi-turn agent systems based on Large Language Models (LLMs) have been increasingly popular for software engineering tasks. While LLM agents show decent effectiveness, the high computational cost of input tokens due to the ever-growing trajectory remains an efficiency concern for their applications. Efficiency is largely neglected in existing studies and agent products, and this paper fills the gap by introducing an inference-time trajectory reduction approach to reduce the cost of agents. Through analyzing existing agent trajectories, we demonstrate that useless, redundant, and expired information is widespread in all trajectories, which can be identified and reduced without harming the agent's performance. We then design a simple yet effective trajectory reduction approach, AgentDiet, which automatically removes such waste information. We implement AgentDiet on a top-performing coding agent, and the evaluation on two LLMs and two benchmarks shows that AgentDiet can reduce input tokens by 39.9% ~ 59.7%, or the final computational cost by 21.1% ~ 35.9%, while maintaining the same agent performance. This indicates that trajectory reduction is a promising direction for agent systems.

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

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

Temporal credit assignment in reinforcement learning is often approached by introducing value estimates at multiple discount factors. A natural next step is to let the actor dynamically route among these temporal heads, using either differentiable attention or heuristic uncertainty weights. This paper argues that such routing can create a numerical shortcut rather than a reliable temporal abstraction. We study this issue in a controlled PPO setting on LunarLander-v2, using the environment as a visual sandbox for diagnosing failure modes. First, we formalize Surrogate Objective Hacking: a differentiable softmax router exposed to the PPO surrogate receives a direct gradient toward advantage heads that are numerically favorable for the current update, even when this routing change does not correspond to improved physical control. Because unnormalized advantages at different discount factors have different effective scales, this creates a scale-discrepancy vulnerability. Second, we identify the Paradox of Temporal Uncertainty in gradient-free error-based routing: short-horizon heads can receive the largest routing share because their prediction targets are easier, even when they are less aligned with delayed task success. As a structural response, we study Target Decoupling: the critic may retain multi-timescale auxiliary heads, but the actor is updated only with the long-horizon advantage. Target Decoupling is not presented as a broad performance booster; in this run set it removes the exploitable actor-side routing pathway and improves the observed worst-seed return. Code is available at https://github.com/ben-dlwlrma/Representation-Over-Routing.

Current evaluations of Large Language Model (LLM) agents primarily emphasize task completion, often overlooking resource efficiency and adaptability. This neglects a crucial capability: agents' ability to devise and adjust cost-optimal plans in response to changing environments. To bridge this gap, we introduce CostBench, a scalable, cost-centric benchmark designed to evaluate agents' economic reasoning and replanning abilities. Situated in the travel-planning domain, CostBench comprises tasks solvable via multiple sequences of atomic and composite tools with diverse, customizable costs. It also supports four types of dynamic blocking events, such as tool failures and cost changes, to simulate real-world unpredictability and necessitate agents to adapt in real time. Evaluating leading open-sourced and proprietary models on CostBench reveals a substantial gap in cost-aware planning: agents frequently fail to identify cost-optimal solutions in static settings, with even GPT-5 achieving less than 75% exact match rate on the hardest tasks, and performance further dropping by around 40% under dynamic conditions. By diagnosing these weaknesses, CostBench lays the groundwork for developing future agents that are both economically rational and robust.

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

Proximal Policy Optimization (PPO) is widely used in reinforcement learning with verifiable rewards for language-model reasoning. While value evolution along trajectory characterizes relative token-level credit, yet standard critics often fail to track it under sparse terminal rewards. To model this evolution, we analyze the relation between successive prefix values and show that they admit a Bayesian decomposition with additive updates in log-odds space. We use this additive structure to construct Tracking-Value PPO (\method), a cumulative value parameterization that sums position-wise scalar outputs into value logits. These outputs are learned through terminal-outcome supervision on the reconstructed values. \method improves aggregate mathematical reasoning scores over PPO by 7.0 and 8.4 points on Qwen3-4B-Base and Qwen3-8B-Base, respectively, while improving out-of-distribution generalization. Gains extend to Qwen3-4B, Qwen2.5-Math-1.5B, Qwen3.5-9B and to countdown, and scientific coding tasks. Further analysis shows more accurate tracking of value evolution and more reliable advantage estimates. Our code is publicly available in https://github.com/LINs-lab/TPPO.

We present a novel reasoning approach called Flow-of-Options (FoO), designed to address intrinsic biases in Large Language Models (LLMs). FoO enables LLMs to systematically explore a diverse range of possibilities in their reasoning, as demonstrated by an FoO-based agentic system for autonomously solving Machine Learning tasks (AutoML). Our framework outperforms state-of-the-art baselines, achieving improvements of 38.2% - 69.2% on standard data science tasks, and 37.4% - 47.9% on therapeutic chemistry tasks. With an overall operation cost under $1 per task, our framework is well-suited for cost-sensitive applications. Beyond classification and regression, we illustrate the broader applicability of our FoO-based agentic system to tasks such as reinforcement learning and image generation. Our framework presents significant advancements compared to current state-of-the-art agentic systems for AutoML, due to the benefits of FoO in enforcing diversity in LLM solutions through compressed, explainable representations that also support long-term memory when combined with case-based reasoning.

Aligning generative flow models on continuous spaces via online reinforcement learning is constrained by intractable trajectory likelihoods. Existing density-approximated policy gradient methods rely on stochastic SDE samplers to construct tractable transition kernels, which introduce training-inference inconsistencies and necessitates Classifier-Free Guidance (CFG). While implicit frameworks such as DiffusionNFT directly optimize forward-process velocity fields, its heuristic fixed-magnitude corrections prevent optimization strength from relative intra-group quality. We propose Flow Advantage-Weighted Rectification (FlowAWR), a paradigm that recasts continuous generative policy optimization as supervised regression toward a theoretically optimal velocity field. Starting from the optimal policy of a KL-constrained reward maximization, FlowAWR derives the optimal velocity field that admits a magnitude-aware, advantage-weighted rectification form, yielding SDE-free optimization and CFG-free generation. In comparative evaluations on SD3.5-Medium, FlowAWR achieves improved alignment performance alongside a 2times to 5times convergence acceleration over DiffusionNFT (e.g., reaching a 24.12 PickScore in 1.2k steps, versus 23.82 in 2.0k steps for DiffusionNFT and 23.50 in >4k steps for FlowGRPO). Under multi-reward constraints, FlowAWR sustains generation quality, satisfying structural rules while maintaining stable out-of-domain performance.

We study the parameter dependence and transversality properties of trajectories of the controlled ODE $ U_x = P, qquad P_x = - f(U) - βP + tilde α(x)U, arising from traveling-wave solutions of a bistable reaction-diffusion equation with control. Optimal profiles minimizing the L^1-norm of the control \tilde α are determined by the unstable and stable manifolds Γ_u, Γ_s, the critical curve P^*(U) = Uf(U), and the associated function F(U) = dP^*{dU} + f(U){P^*(U)}. We establish generic transversality properties for these objects with respect to perturbations of the speed β and the nonlinear source f, together with quantitative estimates on the first- and second-order dependence of the invariant manifolds on these parameters. We also analyze the loss of regularity at the critical speed β^{**}, where the unstable manifold approaches the strongly stable manifold of the equilibrium (U^*,0)$. These results provide the ODE ingredients used in the analysis of the structure and regularity of optimal profiles in paper [S. Bianchini and C. Trifone. Traveling profiles and control cost for a PDE describing the evolution of invasive species. 2026. arXiv: 2606.23979 [math.OC]].

Among on-policy reinforcement learning algorithms, Proximal Policy Optimization (PPO) demonstrates is widely favored for its simplicity, numerical stability, and strong empirical performance. Standard PPO relies on surrogate objectives defined via importance ratios, which require evaluating policy likelihood that is typically straightforward when the policy is modeled as a Gaussian distribution. However, extending PPO to more expressive, high-capacity policy models such as continuous normalizing flows (CNFs), also known as flow-matching models, is challenging because likelihood evaluation along the full flow trajectory is computationally expensive and often numerically unstable. To resolve this issue, we propose PolicyFlow, a novel on-policy CNF-based reinforcement learning algorithm that integrates expressive CNF policies with PPO-style objectives without requiring likelihood evaluation along the full flow path. PolicyFlow approximates importance ratios using velocity field variations along a simple interpolation path, reducing computational overhead without compromising training stability. To further prevent mode collapse and further encourage diverse behaviors, we propose the Brownian Regularizer, an implicit policy entropy regularizer inspired by Brownian motion, which is conceptually elegant and computationally lightweight. Experiments on diverse tasks across various environments including MultiGoal, PointMaze, IsaacLab and MuJoCo Playground show that PolicyFlow achieves competitive or superior performance compared to PPO using Gaussian policies and flow-based baselines including FPO and DPPO. Notably, results on MultiGoal highlight PolicyFlow's ability to capture richer multimodal action distributions.

The recent emergence of new algorithms for permuting models into functionally equivalent regions of the solution space has shed some light on the complexity of error surfaces, and some promising properties like mode connectivity. However, finding the right permutation is challenging, and current optimization techniques are not differentiable, which makes it difficult to integrate into a gradient-based optimization, and often leads to sub-optimal solutions. In this paper, we propose a Sinkhorn re-basin network with the ability to obtain the transportation plan that better suits a given objective. Unlike the current state-of-art, our method is differentiable and, therefore, easy to adapt to any task within the deep learning domain. Furthermore, we show the advantage of our re-basin method by proposing a new cost function that allows performing incremental learning by exploiting the linear mode connectivity property. The benefit of our method is compared against similar approaches from the literature, under several conditions for both optimal transport finding and linear mode connectivity. The effectiveness of our continual learning method based on re-basin is also shown for several common benchmark datasets, providing experimental results that are competitive with state-of-art results from the literature.

Agentic applications based on large language models increasingly rely on multi-step interaction loops involving planning, action execution, and environment feedback. While such systems are now deployed at scale, improving them post-deployment remains challenging. Agent trajectories are voluminous and non-deterministic, and reviewing each one, whether through human review or auxiliary LLMs, is slow and cost-prohibitive. We propose a lightweight, signal-based framework for triaging agentic interaction trajectories. Our approach computes cheap, broadly applicable signals from live interactions and attaches them as structured attributes for trajectory triage, identifying interactions likely to be informative without affecting online agent behavior. We organize signals into a coarse-grained taxonomy spanning interaction (misalignment, stagnation, disengagement, satisfaction), execution (failure, loop), and environment (exhaustion), designed for computation without model calls. In a controlled annotation study on τ-bench, a widely used benchmark for tool-augmented agent evaluation, we show that signal-based sampling achieves an 82\% informativeness rate compared to 74\% for heuristic filtering and 54\% for random sampling, with a 1.52x efficiency gain per informative trajectory. The advantage is robust across reward strata and task domains, confirming that signals provide genuine per-trajectory informativeness gains rather than merely oversampling obvious failures. These results show that lightweight signals can serve as practical sampling infrastructure for agentic systems, and suggest a path toward preference data construction and post-deployment optimization.

Diffusion models sample effectively from high-dimensional, multimodal distributions, but their outputs may violate deployment constraints. For task-space robot policies, generated grasps, waypoints, or trajectories can be distributionally valid yet infeasible, violating reachability, collision-avoidance, or closed-loop executability requirements. This embodiment gap limits zero-shot deployment across robots, even when the task-space behavior itself is transferable. We propose an inference-time optimization framework that couples the behavior generation to physical feasibility by formulating diffusion guidance as a constrained optimization problem. Our key insight is to replace the sampling perturbation in the backward process with an optimized correction, allowing hard constraints or soft penalties to be imposed during sampling without the need to retrain the diffusion model, while keeping samples close to the learned prior. We evaluate the method on dexterous grasp synthesis with reachability and collision-avoidance constraints, and dynamic manipulation with controller-level trackability constraints. Across settings and robot embodiments, optimization-guided denoising matches the feasibility of projection- and gradient-guidance baselines while better preserving grasp quality, and improving controller-level executability and task success, with task success improving by up to 20pp. on dexterous grasping and 23pp. on visuomotor manipulation over the best baseline.

Real-time path planning in outdoor environments still challenges modern robotic systems due to differences in terrain traversability, diverse obstacles, and the necessity for fast decision-making. Established approaches have primarily focused on geometric navigation solutions, which work well for structured geometric obstacles but have limitations regarding the semantic interpretation of different terrain types and their affordances. Moreover, these methods fail to identify traversable geometric occurrences, such as stairs. To overcome these issues, we introduce ViPlanner, a learned local path planning approach that generates local plans based on geometric and semantic information. The system is trained using the Imperative Learning paradigm, for which the network weights are optimized end-to-end based on the planning task objective. This optimization uses a differentiable formulation of a semantic costmap, which enables the planner to distinguish between the traversability of different terrains and accurately identify obstacles. The semantic information is represented in 30 classes using an RGB colorspace that can effectively encode the multiple levels of traversability. We show that the planner can adapt to diverse real-world environments without requiring any real-world training. In fact, the planner is trained purely in simulation, enabling a highly scalable training data generation. Experimental results demonstrate resistance to noise, zero-shot sim-to-real transfer, and a decrease of 38.02% in terms of traversability cost compared to purely geometric-based approaches. Code and models are made publicly available: https://github.com/leggedrobotics/viplanner.

Modern LLM deployments confront a widening cost-performance spectrum: premium models deliver strong reasoning but are expensive, while lightweight models are economical yet brittle on complex tasks. Static escalation rules and keyword heuristics under-utilize this spectrum and fail to adapt across task types. We present xRouter, a tool-calling-based routing system in which a learned router can either answer directly or invoke one or more external models. The router is trained end-to-end with reinforcement learning using an explicit, cost-aware reward that encodes cost-performance trade-offs, eliminating the need for hand-engineered routing rules. Our implementation encompasses the full reinforcement learning framework, including reward and cost accounting, as well as the deployment and evaluation pipelines. Across diverse benchmarks, xRouter achieves strong cost-performance trade-offs (e.g., substantial cost reductions at comparable task completion rates), and provides empirical insights into what reliably helps learned routing and what does not, ranging from model trainability to the difficulty of eliciting sophisticated orchestration behaviors in small open models. We hope these findings and our open implementation will serve as a practical substrate for advancing learned, cost-aware LLM orchestration.

Generative Flow Networks or GFlowNets are related to Monte-Carlo Markov chain methods (as they sample from a distribution specified by an energy function), reinforcement learning (as they learn a policy to sample composed objects through a sequence of steps), generative models (as they learn to represent and sample from a distribution) and amortized variational methods (as they can be used to learn to approximate and sample from an otherwise intractable posterior, given a prior and a likelihood). They are trained to generate an object x through a sequence of steps with probability proportional to some reward function R(x) (or exp(-E(x)) with E(x) denoting the energy function), given at the end of the generative trajectory. Like for other RL settings where the reward is only given at the end, the efficiency of training and credit assignment may suffer when those trajectories are longer. With previous GFlowNet work, no learning was possible from incomplete trajectories (lacking a terminal state and the computation of the associated reward). In this paper, we consider the case where the energy function can be applied not just to terminal states but also to intermediate states. This is for example achieved when the energy function is additive, with terms available along the trajectory. We show how to reparameterize the GFlowNet state flow function to take advantage of the partial reward already accrued at each state. This enables a training objective that can be applied to update parameters even with incomplete trajectories. Even when complete trajectories are available, being able to obtain more localized credit and gradients is found to speed up training convergence, as demonstrated across many simulations.

Robot motion can have many goals. Depending on the task, we might optimize for pose error, speed, collision, or similarity to a human demonstration. Motivated by this, we present PyRoki: a modular, extensible, and cross-platform toolkit for solving kinematic optimization problems. PyRoki couples an interface for specifying kinematic variables and costs with an efficient nonlinear least squares optimizer. Unlike existing tools, it is also cross-platform: optimization runs natively on CPU, GPU, and TPU. In this paper, we present (i) the design and implementation of PyRoki, (ii) motion retargeting and planning case studies that highlight the advantages of PyRoki's modularity, and (iii) optimization benchmarking, where PyRoki can be 1.4-1.7x faster and converges to lower errors than cuRobo, an existing GPU-accelerated inverse kinematics library.

A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed, as user-specified rewards are usually only well defined on the data distribution at the end of generation. While common workarounds to this problem are to use a denoiser to estimate what a sample would have been at the end of generation, we propose a simple solution to this problem by working directly with a flow map. By exploiting a relationship between the flow map and velocity field governing the instantaneous transport, we construct an algorithm, Flow Map Trajectory Tilting (FMTT), which provably performs better ascent on the reward than standard test-time methods involving the gradient of the reward. The approach can be used to either perform exact sampling via importance weighting or principled search that identifies local maximizers of the reward-tilted distribution. We demonstrate the efficacy of our approach against other look-ahead techniques, and show how the flow map enables engagement with complicated reward functions that make possible new forms of image editing, e.g. by interfacing with vision language models.

Predicting single-cell perturbation responses requires mapping between two unpaired populations of cells measured before and after the perturbation. Optimal transport (OT) provides a principled framework for constructing such mappings by minimizing the transport cost, and neural OT methods (e.g., CellOT) have been employed for this prediction task. However, these methods rely on a fixed transport cost, typically the squared Euclidean distance. This cost may connect cells with the wrong responses. Lineage tracing provides the information needed to learn the cost, as heritable barcodes link the cells of the same clone before and after the perturbation. Here, we propose \CloneOT, a neural inverse OT method that learns both the transport cost and the transport map from partially lineage-traced single-cell datasets. \CloneOT\ represents the cost as a neural network. It learns the cost by minimizing the extra cost that the lineage adds to the optimal transport, so that the cheapest transport keeps the cells of each clone together. Our experiments demonstrate that \CloneOT\ recovers the correct transport on 2D datasets, while the squared Euclidean cost fails. Moreover, \CloneOT\ outperforms five baselines on 14 lineage-tracing perturbation scenarios of cancer cells, for both seen and unseen clones. Furthermore, we show that \CloneOT\ reveals the clone-specific transcriptional programs of drug-tolerant persister cells and forecasts the fate of each clone from its cells before treatment. Our implementation is available at https://github.com/poseidonchan/CloneOT.