Spatio-temporal trajectory representation learning plays a crucial role in various urban applications such as transportation systems, urban planning, and environmental monitoring. Existing methods can be divided into single-view and multi-view approaches, with the latter offering richer representations by integrating multiple sources of spatio-temporal data. However, these methods often struggle to generalize across diverse urban scenes due to multi-city structural heterogeneity, which arises from the disparities in road networks, grid layouts, and traffic regulations across cities, and the amplified seesaw phenomenon, where optimizing for one city, view, or task can degrade performance in others. These challenges hinder the deployment of trajectory learning models across multiple cities, limiting their realworld applicability. In this work, we propose SMARTraj2, a novel stable multi-city adaptive method for multi-view spatio-temporal trajectory representation learning. Specifically, we introduce a feature disentanglement module to separate domaininvariant and domain-specific features, and a personalized gating mechanism to dynamically stabilize the contributions of different views and tasks. Our approach achieves superior generalization across heterogeneous urban scenes while maintaining robust performance across multiple downstream tasks. Extensive experiments on benchmark datasets demonstrate the effectiveness of SMARTraj2 in enhancing cross-city generalization and outperforming state-of-the-art methods.

In cooperative Multi-Agent Reinforcement Learning (MARL), agents that share policy network parameters often learn similar behaviors, which hinders effective exploration and can lead to suboptimal cooperative policies. Recent advances have attempted to promote multi-agent diversity by leveraging the Wasserstein distance to increase policy differences. However, these methods cannot effectively encourage diverse policies due to ineffective Wasserstein distance caused by the policy similarity. To address this limitation, we propose Wasserstein Contrastive Diversity (WCD) exploration, a novel approach that promotes multi-agent diversity by maximizing the Wasserstein distance between the trajectory distributions of different agents in a latent representation space. To make the Wasserstein distance meaningful, we propose a novel next-step prediction method based on Contrastive Predictive Coding (CPC) to learn distinguishable trajectory representations. Additionally, we introduce an optimized kernel-based method to compute the Wasserstein distance more efficiently. Since the Wasserstein distance is inherently defined for two distributions, we extend it to support multiple agents, enabling diverse policy learning. Empirical evaluations across a variety of challenging multi-agent tasks demonstrate that WCD outperforms existing state-of-the-art methods, delivering superior performance and enhanced exploration.

Policy network parameter sharing is a commonly used technique in advanced deep multi-agent reinforcement learning (MARL) algorithms to improve learning efficiency by reducing the number of policy parameters and sharing experiences among agents. Nevertheless, agents that share the policy parameters tend to learn similar behaviors. To encourage multi-agent diversity, prior works typically maximize the mutual information between trajectories and agent identities using variational inference. However, this category of methods easily leads to inefficient exploration due to limited trajectory visitations. To resolve this limitation, inspired by the learning of pre-trained models, in this paper, we propose a novel Contrastive Trajectory Representation (CTR) method based on learning distinguishable trajectory representations to encourage multi-agent diversity.

Recent work has demonstrated the effectiveness of formulating decision making as supervised learning on offline-collected trajectories. Powerful sequence models, such as GPT or BERT, are often employed to encode the trajectories. However, the benefits of performing sequence modeling on trajectory data remain unclear. In this work, we investigate whether sequence modeling has the ability to condense trajectories into useful representations that enhance policy learning. We adopt a two-stage framework that first leverages sequence models to encode trajectory-level representations, and then learns a goal-conditioned policy employing the encoded representations as its input.

Our approach, named ORDER, uses a three-step training process. In the next parts of this section, we'll explain the methods, structures, and settings we use in each of After that, we'll talk about how we set up and carried out our experiments. In this section, we'll break down the design of the state encoder, how we decided on the best We used a grid search strategy to find the optimal hyper-parameters for our experiments. This allowed each observation dimension to match up with a state factor. We summarize the training process in Algorithm 1.

Urban analytics increasingly relies on AI-driven trajectory analysis, yet current approaches suffer from methodological fragmentation: trajectory learning captures movement patterns but ignores spatial context, while spatial embedding methods encode street networks but miss temporal dynamics. Three gaps persist: (1) lack of joint training that integrates spatial and temporal representations, (2) origin-agnostic treatment that ignores directional asymmetries in navigation ($A \to B \ne B \to A$), and (3) over-reliance on auxiliary data (POIs, imagery) rather than fundamental geometric properties of urban space. We introduce a conditional trajectory encoder that jointly learns spatial and movement representations while preserving origin-dependent asymmetries using geometric features. This framework decomposes urban navigation into shared cognitive patterns and origin-specific spatial narratives, enabling quantitative measurement of cognitive asymmetries across starting locations. Our bidirectional LSTM processes visibility ratio and curvature features conditioned on learnable origin embeddings, decomposing representations into shared urban patterns and origin-specific signatures through contrastive learning. Results from six synthetic cities and real-world validation on Beijing's Xicheng District demonstrate that urban morphology creates systematic cognitive inequalities. This provides urban planners quantitative tools for assessing experiential equity, offers architects insights into layout decisions' cognitive impacts, and enables origin-aware analytics for navigation systems.

Foundation models (FMs) have emerged as a powerful paradigm, enabling a diverse range of data analytics and knowledge discovery tasks across scientific fields. Inspired by the success of FMs, particularly large language models, researchers have recently begun to explore spatio-temporal foundation models (STFMs) to improve adaptability and generalization across a wide spectrum of spatio-temporal (ST) tasks. Despite rapid progress, a systematic investigation of trajectory foundation models (TFMs), a crucial subclass of STFMs, is largely lacking. This tutorial addresses this gap by offering a comprehensive overview of recent advances in TFMs, including a taxonomy of existing methodologies and a critical analysis of their strengths and limitations. In addition, the tutorial highlights open challenges and outlines promising research directions to advance spatio-temporal general intelligence through the development of robust, responsible, and transferable TFMs.