conservative trajectory refinement

This work addresses the challenge in offline reinforcement learning of improving trajectory performance without exceeding the support of historical data. The authors propose a counterfactual transport flow framework that, for the first time, integrates counterfactual reasoning with optimal transport to retrieve high-return neighboring trajectories in latent trajectory space, forming local preference pairs that serve as weak supervision signals for conservative policy optimization. By introducing an adjustable intensity parameter, the method enables trajectory-level and instance-level policy improvements that are both interpretable and restrained from excessive extrapolation, thereby preserving the original behavioral characteristics. Empirical evaluations demonstrate that the approach significantly enhances trajectory performance on the D4RL benchmark, particularly in AntMaze and MuJoCo tasks, while generating interpretable optimization pathways.

This work addresses the time-parametrization optimization problem for continuous-time transport trajectories in flow-based generative modeling: specifically, how to schedule the time axis to minimize the spatial Lipschitz constant of the velocity field induced by a given transport map—thereby reducing learning error and enhancing model stability. We propose a smooth variational approximation framework grounded in Γ-convergence, unifying optimal transport and dynamical systems theory, and derive, for the first time, a closed-form solution for the optimal time schedule. Theoretically, this solution reduces the Lipschitz constant exponentially compared to conventional constant-speed parametrizations (e.g., Wasserstein geodesics), thereby overcoming the fundamental limitation of zero-acceleration paradigms. Our method yields analytic solutions across broad classes of distribution pairs and transport maps, significantly improving generalization capability and training robustness of flow-based generative models.

Existing counterfactual fairness evaluation methods lack causal interpretability and structured modeling, hindering rigorous individual-level assessment. Method: We propose a sequence-conditioned transport framework integrating causal graphical models with optimal transport theory. Specifically, we extend Knothe–Rearrangement and triangular transport to probabilistic graphical models, enabling causal-constrained, stepwise conditional optimal transport guided by the causal graph structure. This preserves variable dependencies while generating individual-level counterfactuals. Contribution/Results: Our approach yields counterfactuals with enhanced causal plausibility and structural fidelity, as validated on both synthetic and real-world datasets. It establishes a novel, rigorous, traceable, and structure-aware paradigm for individual-level algorithmic fairness evaluation—grounded in causal semantics and geometric transport principles.

This work investigates whether flow matching in temporal generation learns a universal dynamical structure or merely reproduces historical trajectories. By analyzing the empirical flow matching objective under Gaussian conditional paths, we derive—for the first time—a closed-form expression for its optimal velocity field, revealing it to be a similarity-weighted mixture of historical instantaneous velocities. This formulation constitutes a nonparametric, memory-augmented continuous-time dynamical system. Building on this insight, we propose a training-free closed-form sampler that directly generates high-quality probabilistic forecasts from historical transitions. Evaluated on nonlinear dynamical system benchmarks, our method substantially improves sampling efficiency and numerical stability while offering an explicit, interpretable mechanism for data-dependent dynamics.

This work addresses the challenge of generating constrained, interpretable, and domain-compliant trajectory patterns for moving objects in real-world dynamic environments. It proposes a hybrid qualitative-quantitative approach based on Answer Set Programming (ASP), which traverses the environmental graph structure and integrates geometric constraint reasoning with stable model semantics to enumerate geometrically feasible motion behaviors. To the best of our knowledge, this is the first application of ASP to generate diverse trajectory patterns that are verifiable, traceable, and seamlessly incorporate domain knowledge with environmental topology. Experiments on the large-scale Argoverse 2 autonomous driving benchmark demonstrate that the generated trajectories exhibit high interpretability and practical applicability, effectively overcoming the limited explainability inherent in purely data-driven methods.

This study investigates whether introducing a learned command adapter onto a frozen locomotion policy yields observable and recoverable performance gains. To this end, the authors propose an adapter necessity auditing framework that integrates closed-loop system identification, counterfactual reasoning, cluster refitting, and constraint violation analysis to disentangle deployment gain, state allocation gain, and global operational gain, thereby supporting GO/NO-GO/ABSTAIN deployment decisions. Experiments on the Go2 platform reveal only 0.55% recoverable allocation gain; direct querying yields a NO-GO verdict, while VGCC and MPC-based queries result in ABSTAIN, indicating that the value of an adapter must be grounded in observable evidence rather than prior assumptions.

This work addresses the challenge of evaluating model outputs in scenarios where ground-truth outcomes are delayed, censored, or private, rendering conventional code-based deterministic evaluation methods ineffective for immediate validation. The authors propose RouteCast, a novel framework that enables autonomous generation of auditable provisional prediction scores through typed, staged route modeling, reference-based analogy, and deterministic transformations, thereby supporting traceable and decomposable assessment of strategic pathways. Evaluated on 21 retrospective cases, RouteCast achieves an AUC of 0.756—significantly outperforming blind-evaluated large language models (AUC = 0.678) and performing comparably to identity-revealed LLMs (AUC = 0.761)—demonstrating its effectiveness and feasibility in settings with delayed ground truth.

This work addresses the challenge of efficient and accurate ensemble forecasting in chaotic, turbulent, and stochastic systems by proposing a trajectory-aware surrogate modeling approach. The method uniquely learns the probability flow velocity directly from trajectory data, enabling modeling of trajectory-dependent dynamical quantities—such as fluxes and circulations—through first-order trajectory matching (FTM), without requiring estimation of conventional drift or diffusion coefficients, score functions, or explicit simulation. By integrating a simulation-free one-step training loss with stability analysis, the approach achieves high-fidelity ensemble predictions at low computational cost across diverse stochastic dynamical systems and partial differential equation benchmarks, significantly enhancing both trajectory resolution and predictive efficiency.