In this work, we introduce the Geometric Diffusion Bridge (GDB), a novel generative modeling framework that accurately bridges initial and target geometric states.

We consider offline reinforcement learning (RL) in $H$-horizon Markov decision processes (MDPs) under the linear $q^\pi$-realizability assumption, where the action-value function of every policy is linear with respect to a given $d$-dimensional feature function. The hope in this setting is that learning a good policy will be possible without requiring a sample size that scales with the number of states in the MDP. Foster et al. [2021] have shown this to be impossible even under $\text{\textit{concentrability}}$, a data coverage assumption where a coefficient $C_\text{conc}$ bounds the extent to which the state-action distribution of any policy can veer off the data distribution. However, the data in this previous work was in the form of a sequence of individual transitions. This leaves open the question of whether the negative result mentioned could be overcome if the data was composed of sequences of full trajectories.

Given a probability distribution $μ$ in $\mathbb{R}^d$ represented by data, we study in this paper the generative modeling of its conditional probability distributions on the level-sets of a collective variable $ξ: \mathbb{R}^d \rightarrow \mathbb{R}^k$, where $1 \le k

Traffic State Estimation and Prediction (TSEP) has been extensively studied to reconstruct traffic state variables (e.g., flow, density, speed, travel time, etc.) using (partial) observed traffic data (Antoniou et al., 2013; Ban et al., 2011; Shi et al., 2021; Li et al., 2020). In recent years, advancements in data collection technologies have enabled TSEP methods to integrate traffic data from diverse sources for more accurate and robust estimation and prediction (Wang et al., 2016; Makridis and Kouvelas, 2023). These data sources can be broadly categorized into infrastructure-collected data and user-contributed data. Infrastructure-collected data typically includes information collected from loop detectors, traffic cameras, and radars installed on roadways or at intersections. In contrast, user-contributed data is derived from individuals, often through vehicles or personal devices, such as GPS traces, vehicle trajectories, and probe data collected via mobile apps or in-vehicle systems.

As more autonomous vehicles operate on public roads, understanding real-world behavior of autonomous vehicles is critical to analyzing traffic safety, making policies, and public acceptance. This paper proposes SVBRD-LLM, a framework that automatically discovers, verifies, and applies interpretable behavioral rules from real traffic videos through zero-shot prompt engineering. The framework extracts vehicle trajectories using YOLOv8 and ByteTrack, computes kinematic features, and employs GPT-5 zero-shot prompting to compare autonomous and human-driven vehicles, generating 35 structured behavioral rule hypotheses. These rules are tested on a validation set, iteratively refined based on failure cases to filter spurious correlations, and compiled into a high-confidence rule library. The framework is evaluated on an independent test set for speed change prediction, lane change prediction, and autonomous vehicle identification tasks. Experiments on over 1500 hours of real traffic videos show that the framework achieves 90.0% accuracy and 93.3% F1-score in autonomous vehicle identification. The discovered rules clearly reveal distinctive characteristics of autonomous vehicles in speed control smoothness, lane change conservativeness, and acceleration stability, with each rule accompanied by semantic description, applicable context, and validation confidence.

Travel mode identification (TMI) from GPS trajectories is critical for urban intelligence, but is hampered by the high cost of annotation, leading to severe label scarcity. Prevailing semi-supervised learning (SSL) methods are ill-suited for this task, as they suffer from catastrophic confirmation bias and ignore the intrinsic data manifold. We propose ST-ProC, a novel graph-prototypical multi-objective SSL framework to address these limitations. Our framework synergizes a graph-prototypical core with foundational SSL Support. The core exploits the data manifold via graph regularization, prototypical anchoring, and a novel, margin-aware pseudo-labeling strategy to actively reject noise. This core is supported and stabilized by foundational contrastive and teacher-student consistency losses, ensuring high-quality representations and robust optimization. ST-ProC outperforms all baselines by a significant margin, demonstrating its efficacy in real-world sparse-label settings, with a performance boost of 21.5% over state-of-the-art methods like FixMatch.

The work was conducted during the internship of Kerong Wang and Hanye Zhao at Microsoft Research.

Urban mobility analysis has been extensively studied in the past decade using a vast amount of GPS trajectory data, which reveals hidden patterns in movement and human activity within urban landscapes. Despite its significant value, the availability of such datasets often faces limitations due to privacy concerns, proprietary barriers, and quality inconsistencies. To address these challenges, this paper presents a synthetic trajectory dataset with high fidelity, offering a general solution to these data accessibility issues.