Trajectory Representation Learning

Latent actions supervise robot policies with action-like codes inferred from visual transitions, and their usefulness hinges on two questions: what a code keeps from a transition, and whether it still means the same thing when reused in a different initial state. The first is a tension in time: an endpoint difference discards how motion unfolds, while the full sequence admits nuisance variation. The second is left open by reconstruction, which only ever observes a latent together with the state it came from. We argue that both questions can be answered in the same place. TERRA (Temporal Effect Representation and Relational Alignment) describes a transition by a compact temporal effect, its net feature change together with a low-order within-window dynamics component, and learns a continuous latent from this effect. The same effect space then serves as the reference for reuse: Effect-Anchored Transport (EAT) decodes a latent in other initial states and anchors the resulting effect to the one observed at its source, so that the latent is shaped by what it does across contexts rather than only by the transition it came from. With frozen linear readers, TERRA predicts actions more accurately than UniVLA and a LAPA-style baseline, degrades more slowly under visual distractors, and keeps transported transitions faithful to the donor action as the recipient context moves farther away; a same-budget control shows that these gains come largely from EAT. At matched pretraining scale, the complete system reaches 93.4% average success on LIBERO, compared with 91.8% for UniVLA.

Predictive world models provide compact visual representations for control. Control requires a latent geometry aligned with temporal reachability rather than predictive similarity alone. We introduce Directed Temporal Representations for Control (DTRC), which learns such a geometry from offline visual trajectories on top of frozen LeWorldModel (LeWM) features. DTRC constructs a directed temporal quasimetric over the learned control representation. Short-range temporal offsets calibrate the distance scale. Bootstrapped targets extend temporal reachability across longer horizons. Action-conditioned consistency aligns the representation with local transition dynamics. The resulting distance estimates temporal reaching cost, and its change across a transition defines goal-relative temporal progress. We use this progress signal as a temporal critic for direct goal-conditioned policy learning. Model-assisted targets provide an additional training-time refinement under behavior-support and dynamics-agreement constraints. Across ten visual control tasks, DTRC achieves strong goal-conditioned control performance relative to planning and direct-policy baselines. Held-out diagnostics on the four LeWM tasks show consistent short-range temporal calibration, task-dependent long-range and directional structure, and positive transition-level progress. Temporal supervision improves the same flow-policy parameterization across all four LeWM tasks, while the resulting policy acts directly without iterative trajectory search at test time.

Autoregressive generation is natural for language, where predicted tokens can be directly reused as the next prediction state, but trajectory forecasting lacks such a clean token: motion is continuous, multimodal, and expressed in local coordinate frames that evolve with the predicted trajectory. We present MoCAR (Motion-code Coordinate-aware AutoRegression), a decoder-only framework that casts trajectory forecasting as next-code prediction in a coordinate-aware continuous latent space. MoCAR learns a continuous motion-code space from endpoint-normalized trajectory segments, where each code jointly captures local trajectory geometry and the reference-frame transition induced by that segment. Historical motion codes are used as a teacher-forced prefix, future codes are generated autoregressively under temporal, map, agent, and mode interactions, and predicted codes persist in latent memory while decoded endpoints update the local scene context. This enables rollout without trajectory-space re-tokenization, trajectory queries, goal candidates, or proposal-and-refinement pipelines. On Argoverse (AV) benchmarks, MoCAR achieves top-tier performance with a simple single-stage architecture, transfers strongly from AV2 to AV1 in zero-shot evaluation, and improves on turn-heavy scenarios. Ablations confirm that the learned continuous motion-code space, latent alignment, weak KL regularization, and joint tokenizer-predictor optimization are essential for stable latent autoregression.

All the objects composing our world are enclosed within surfaces. Yet, most robot learning and motion generation frameworks treat surfaces as constraints ignoring their intrinsic geometry. This gap is acute for polyhedral meshes--the standard output of CAD and 3D reconstruction--whose discrete geometric structure remains unexploited. In this paper, we propose a unified discrete Riemannian framework that enables robot learning directly on polyhedral surface meshes. Using discrete differential geometry, we define logarithmic and exponential maps, parallel transport, and ambient-space projections that remain well-defined across faces, edges, and vertices. We instantiate the framework in three learning paradigms: (i) Dynamic Movement Primitives (DMPs), an improved exponential-map computation and a fixed-tangent-cone forcing-term encoding with parallel transport yield better cross-surface generalisation and stability over prior mesh-based approaches. (ii) Gaussian Process (GP), a geodesic-based kernel with practical admissibility control, enables regression at arbitrary mesh locations without smoothness assumptions. (iii) Riemannian Flow Matching (RFM), mesh-native operators improve generative quality over spectral baselines while reducing training time. The framework is validated in simulation against state-of-the-art methods and demonstrated on two real-robot scenarios: generalising user-drawn trajectories across different surfaces and planning polishing motions on RGB-D-reconstructed surfaces.

Dynamic Movement Primitives (DMPs) provide a compact and stable formulation for trajectory representation and generalization in robot skill learning. However, their predefined basis layout limits the allocation of approximation capacity according to stage-dependent precision requirements. To address this issue, this article proposes Stage-Criticality-Guided Dynamic Movement Primitives (SC-DMPs) with adaptive basis allocation for precision-critical skill learning. Operator-robot interaction stiffness and a trajectory-consistency cue derived from cross-demonstration task-space variability are integrated to construct a stage-criticality index. Guided by this index, basis centers are redistributed in normalized time through inverse cumulative criticality and mapped to the canonical phase domain, while their bandwidths are refined to adjust local approximation support. This enables denser and more flexible representation at high-criticality stages while retaining sparser allocation elsewhere. Experiments on handwriting trajectories and three real-robot tasks show that the inferred criticality is concentrated in geometrically demanding and task-constrained regions. Comparisons with DMPs, ProMPs, ProDMP, GP-MP, and KMP demonstrate improved trajectory reproduction, endpoint generalization, and task-critical accuracy while retaining a compact model and the stable structure of classical DMPs.

Unsupervised skill discovery has emerged as a promising approach for leveraging reward-free datasets to pretrain general-purpose policies. However, current skill discovery methods either require access to expert data or exhibit limited generalization, failing to transfer effectively to previously unseen layouts. A key challenge is to learn representations that capture the temporal structure of the environment while remaining robust to variations across layouts. To address this issue, we present an objective for learning action-aware temporal representations that satisfy the functional equivariance property while preserving the local temporal structure of the environment. Building upon this embedding, we further propose unsupervised skill discovery using bisimulation, which learns transferable skills by conditioning the behavior of skills exclusively on the subset of state features that directly affect their execution. This enforces invariant behavior across different layouts, enabling skills to transfer effectively to other configurations. Finally, through comprehensive empirical evaluations, we show that skills learned in a given environment can be effectively applied to solve downstream tasks in various environment layouts, demonstrating strong out-of-distribution generalization.

World Action Models (WAMs) couple visual dynamics prediction with action generation, yet they do not explicitly support the reuse of action experience across manipulation tasks. Furthermore, existing WAMs struggle to capture underlying cross-task semantic relationships that could guide target action prediction, as redundant background elements interfere with the extraction of key visual information. To address these challenges, we develop a novel Action Experience Dictionary (AED) that encodes historical physical action trajectories into shared action embeddings to support skill reuse and model cross-task relationships. Specifically, we first aggregate historical actions to align with visual observations and retrieve action embeddings from the AED using a pretrained action tokenizer. Subsequently, we visually condition the pooled embeddings through cross-attention and prepend them to noisy action tokens, providing interaction context and action intent for prediction. To model action-related motion and reduce reliance on irrelevant background cues, we introduce a motion-aware transition loss that supervises visual feature change prediction over random temporal intervals. Experiments on simulation benchmarks and in real-world cross-embodiment settings verify the effectiveness of our AED. The anonymous project website is available at AED.

Graphical User Interface (GUI) Agents autonomously interact with software to fulfill user requests, where GUI navigation stands out as the most critical and challenging capability. Mastering this capability demands a complex synergy of step-wise decision-making, state-action alignment, and long-horizon planning. While directly mixing these corresponding navigation tasks seems intuitive to simultaneously acquire these skills, such a direct combination is severely bottlenecked by inconsistent optimization objectives and profound data heterogeneity. To overcome these barriers, we propose the MaP (stands for ``\textbf{M}asked Tr\textbf{a}jectory \textbf{P}rediction''), a unified framework that seamlessly harmonizes divergent GUI navigation tasks. By modeling multi-turn GUI interactions as a trajectory and defining training objectives through component masking and prediction, MaP shifts the optimization from task-specific marginal distributions to a consistent objective. Furthermore, to handle the data heterogeneity across multiple navigation tasks, we design a role-aware adapter learning module that dynamically routes each token to a specialized representation space. Extensive experiments on five representative GUI navigation benchmarks demonstrate that MaP effectively mitigates gradient conflicts and significantly outperforms the direct mixture training, establishing a robust paradigm for multi-task GUI navigation.

Humans often observe others before interacting and adjust their behavior accordingly. Robot navigation in crowds, however, often represents pedestrians mainly by observed geometric states, leaving individual differences in interaction tendencies implicit. We propose PRISM (Predictive Representation of Interaction Style and Motion), a framework that infers interaction traits from passive observations of human-human interactions. PRISM encodes human trajectories into a continuous ordinal latent space with a transformer encoder trained by Rank-N-Contrast loss, and pairs each inferred trait with a temporal-stability score supplied to the navigation policy. In randomized crowd simulations, PRISM reduces collision rates over the geometry-only baseline and yields small improvements in navigation-time and path-length metrics. These results suggest the utility of passive latent-trait inference for social navigation in dynamic crowds.

Visual goal and dynamics prediction can provide language-conditioned robot policies with both a target outcome and a representation of action-dependent scene changes. We bring these predictions into action generation and selection through a shared trajectory model. Dynin-Robotics implements this formulation on Dynin-Omni, an omnimodal masked-diffusion backbone, representing language, visual observations, goals, and actions as discrete tokens. By varying conditioning and target spans, the same model learns action prediction, action-conditioned next-observation prediction, terminal goal-state prediction, and trajectory-to-instruction reconstruction. These interfaces support test-time scaling through goal prediction, action-candidate evaluation, and joint refinement of action and future-state predictions. We continually pretrain the model on approximately 1.33 million trajectories from 48 Open X-Embodiment datasets and adapt it separately to downstream domains. On two VLABench tasks, robot pretraining improves adaptation within a fixed Stage-2 step budget, and the full objective mixture improves shifted-instruction success over Policy-only post-training under the same coupled decoder. Combining goal guidance with joint action-next-state denoising further improves shifted-instruction success over action-only decoding; the benefit depends on how the predictions are composed. Dynin-Robotics achieves competitive performance on LIBERO and zero-shot LIBERO-Plus, together with a 78.4% average success rate across four manipulation conditions on a Franka Research 3 robot. An optimized block-parallel implementation accelerates model-side action decoding by up to 29.2x relative to the base implementation under the reported profiling setup. These results support shared trajectory modeling as a common interface for learning complementary robot objectives and composing their predictions during control.

Intermediate representations are key to bridging the modality gap between generalizable manipulation policies and large-scale pretrained vision-language models (VLMs). Among these, trajectory-based representations compactly represent motion-relevant cues, yet most existing approaches predict trajectories in 2D image space, resulting in intrinsic 3D ambiguity. Moreover, using 2D trajectories with depth still leaves the free-space waypoints ambiguous, limiting reliable 3D reasoning. To address this, we propose predicting 3D consistent waypoints (3DWay) from multi-view images. By reformulating 3D waypoints prediction as generating multi-view consistent 2D waypoints followed by geometric triangulation, we enable explicit 3D motion specification while preserving the strong priors of pretrained VLMs. The predicted waypoints can guide existing VLA models for better generalization or be directly executed on simple tasks. Extensive experiments show that 3DWay substantially improves 3D spatial grounding and vision-language reasoning, demonstrating strong potential for generalizable robot manipulation. Codes will be released at https://github.com/ziqin-h/3DWay.

Due to the proliferation of vehicle trajectory data enabled by advanced sensing technologies, path representation learning has become a pivotal task in intelligent transportation systems. Although existing self-supervised approaches have achieved promising performance, their dependence on deterministic contrastive learning paradigms and handcrafted view augmentation strategies inherently restricts their cross-scenario generalization capabilities. To address these limitations, we present DGCPath, an innovative Distribution-aware Generative Contrastive learning framework for Path representation. This framework establishes a synergistic connection between generative modeling and distributional contrastive learning, enabling the acquisition of robust and transferable feature embeddings. Specifically, our framework incorporates: (1) a diffusion-based view generator that autonomously produces semantically coherent yet diverse trajectory views from Gaussian noise; (2) a variational contrastive mechanism that enforces latent feature alignment at the distribution level, transcending conventional instance-wise consistency; and (3) a novel generative cross-supervision module that reinforces view-level consistency through cross-view reconstruction learning. Comprehensive evaluations on three real-world trajectory datasets demonstrate that DGCPath outperforms state-of-the-art baselines on two distinct downstream tasks, validating its enhanced generalization capability and representation effectiveness.

Trajectory representation learning underpins a wide range of trajectory analytics tasks; however, most existing self-supervised approaches, whether discriminative or generative, adopt an open-loop paradigm, relying on fixed data augmentations or random masking without feedback, which limits their ability to generalize and scale. We propose REFINE, a simple yet effective Representation lEarning Framework vIa closed-loop traNscription rEfinement for trajectory data. Drawing upon feedback control theory, REFINE tightly couples road-network-aware generative reconstruction with feedback-driven contrastive learning, enabling the model to capture fine-grained local movement semantics and global spatio-temporal dependencies without manually designed augmentation views. We further provide a control-theoretic analysis that establishes convergence guarantees for the proposed closed-loop optimization. Extensive experiments on four real-world datasets demonstrate that REFINE consistently outperforms state-of-the-art methods across multiple downstream tasks while remaining computationally efficient and scalable. This paper is an extended version of REFINE: Trajectory Representation Learning via Closed-Loop Transcription, to appear in KDD 2026.

Embodied agents performing long-horizon tasks require a memory representation in which the state transitions of dynamic objects remain queryable in natural language across hours-to-days observation horizons. Existing systems either drop fine-grained motion (clip-level video-language embeddings), keep it only as raw coordinates (geometric SLAM), or organise it around immediate task context (agent working memories). None of them gives the agent a per-object timeline whose state transitions are themselves queryable in language. Our key contribution is \textbf{Linguistic Trajectory Encoding} (LTE), which compresses dynamic object motion histories via a hybrid representation combining natural language descriptions, sparse spatial anchors, and visual anchors. LTE adapts compression to motion complexity by anchoring periods without reliable observations to the last seen location, while representing motion with geometric waypoints and linguistic descriptions to preserve accuracy. To evaluate these capabilities across extended time horizons, we construct the \textbf{Spatial Memory Benchmark} (SMB) from EgoLife multi-day recordings, targeting capabilities absent in existing benchmarks: semantic trajectory retrieval and long-horizon object retrieval. On SMB, the LTE-based system achieves $45.3\%$ success in semantic trajectory retrieval and $48.7\%$ in long-horizon object retrieval, outperforming structured-memory and VLM baselines (best prior: $31.9\%$ and $34.4\%$). LTE achieves trajectory compression by factors of $8.7\times$ to $26.1\times$ with sub-second query latency on $24$,h video. On Ego4D natural-language queries, the system reaches $28.75\%$ / $55.10\%$ R@1/R@5, $+15.80$ / $+31.30$ pts over EgoVLPv2.

As air traffic volumes in the National Airspace System continue to expand, in particular at low altitude, the need for scalable decision support tools used by air traffic controllers will also require more development. This article introduces Voice-to-Trajectory for Air Traffic Control, a joint voice communication-flight trajectory data embedding framework, that can be a component of situational awareness in congested airspaces, and assist the development of tools for ATC as they reason in real-time over Automatic Dependent Surveillance-Broadcast trajectories, or the intent expressed by pilots in natural language. We show that these data modalities are not independent and represent a common physical referent: an aircraft flying through the airspace. V2TATC maps a voice instruction and the trajectory of the addressed aircraft to nearby points in a single latent space that can be queried in both directions. It combines a self-supervised trajectory encoder, a frozen speech encoder, a contrastive joint embedding, and a bijective lifting via normalizing flows. We demonstrate V2TATC's effectiveness on the San Francisco Bay Area, for its concentration of major airports, and its mix of commercial and general aviation traffic. Lastly, we release a novel paired voice-trajectory dataset, and report experiments on cross-modal retrieval, ablations, and latent-space analysis.

Trajectory-User Linking (TUL) aims to identify the owner of an anonymous trajectory from a set of candidate users, providing a basis for user mobility analysis and personalized location-aware services. Existing methods often learn Point of Interest (POI), temporal, and semantic features independently, make limited use of structural knowledge shared across trajectories, and compress structural and sequential information before classification. To address these issues, we propose Multi-Relational Knowledge Graph Enhanced Embedding for Trajectory-User Linking (MakeTUL), which, to the best of our knowledge, is the first attempt to introduce knowledge graph representation learning into TUL. MakeTUL organizes visit-time, POI-category, and transfer-speed information as typed relations in a multi-relational mobility knowledge graph, allowing heterogeneous mobility semantics to jointly constrain the learned embeddings. The resulting POI representations are further enriched with high-order co-occurrence patterns extracted from the trajectory collection, providing structural prior knowledge for sparse and overlapping trajectories. By integrating these prior-enhanced representations with temporal, category, and transfer information, the trajectory sequence learning module captures ordered mobility patterns, while a dual-branch classification layer preserves and combines global structural evidence and sequential evidence at the decision level.

Standard machine learning training presents data as discrete endpoint pairs, omitting the structure of the space between them. This paper introduces Transition Information Density (TID) -- the information content recoverable from structured intermediate states between categorically distinct training endpoints -- and Positional Identity, the defined location of an intermediate state on the A-to-B continuum. Both constructs are grounded in three empirical contexts: grapheme-color synesthesia, the Synesthesia Grid (a boundary-contour morphing algorithm instantiating TID in visual morphological space), and a four-condition training experiment across four representational mediums. Probes trained on structured interpolation at defined Positional Identities (C3) exhibit substantially lower intrinsic dimensionality than volume-matched controls (C2) in Phonetic/Linguistic (C3: 3.33 vs. C2: 10.81) and Semantic Description (C3: 4.59 vs. C2: 8.67) mediums. Visual and cross-modal mediums do not show this effect, establishing a modality boundary condition. A fixed-N=50 comparison confirms that Positional Identity structure, not sample count, drives the effect. Resolution N scales monotonically with representational richness. Pooled TwoNN analysis reveals globally collapsed representations in visual space (0.075) and globally consistent representations in phonetic space (0.977). The paper contributes a formal definition of TID and Positional Identity, a nine-metric shape characterization framework, and a four-condition experimental design isolating trajectory structure, data volume, and Positional Identity as distinct factors.

Vision-Language Models (VLMs) for embodied navigation rely on selecting a fixed number of frames from a growing trajectory history. As episodes extend, this selection grows increasingly sparse, yet prior work shows no accuracy gain when scaling from 8 to 64 frames, suggesting the bottleneck is not frame quantity but the representation itself. Sparse frame selection cannot capture the structured behavioral signal that long-horizon reasoning requires: turning patterns, cumulative displacement, and path topology. We introduce BIT-Nav (Brain-Inspired Trajectory Memory for Navigation), a framework that augments frozen VLM navigation pipelines with a compact learned trajectory memory. Motivated by hippocampal path integration, where spatial experience is compressed into structured episodic traces rather than stored as raw sensory replay, BIT-Nav trains a Bi-GRU encoder over action and relative pose sequences via a multi-positive InfoNCE contrastive objective on trajectory prefixes sharing the same behavioral intent. The resulting embedding is projected into the VLM token space via a lightweight MLP and injected as a single memory token at each decision step, conditioning the model on structured motion history at constant token cost regardless of episode length

Representation learning is a powerful tool for spatio-temporal abstraction within reinforcement learning (RL). Two well established approaches are through the successor representation (SR) and the default representation (DR). The SR encodes states by the future trajectories they induce, capturing information flow decoupled from reward. The DR builds on this by weighting trajectories with reward, integrating credit-assignment structure into the representation. Eigenvectors of both representations have been used to support a range of downstream tasks -- including option discovery, reward shaping, transfer learning, and exploration. We introduce a structurally distinct formulation: the terminal representation (TR). The TR encodes reward-weighted trajectories similarly to the DR, but can be learned as a lower-dimensionality object, and can be used directly for the mentioned applications without eigenvector computations. Eigendecomposition also imposes the assumption of symmetric transition dynamics, which the TR can bypass. In this work we develop the theoretical foundations of the TR: its derivation, convergence of two learning algorithms, its use for zero-shot compositionality, and equivalences between alternative reward formulations. We further show the TR is embedded in the top DR eigenvector, allowing it to capture the same underlying knowledge without eigendecomposition. Additionally, we provide empirical evidence of the TR as a viable alternative to existing representations in subsidiary applications, while requiring less computational overhead to learn, store, and use.

Learning generalizable trajectory representations from raw GPS traces remains difficult because the data is continuous, noisy, and irregularly sampled. Spatial tokenization is also challenging: fine grids yield sparse cells with weak embeddings, while coarse grids merge heterogeneous movement patterns into the same token. We present TrajTok, a trajectory encoder with a simple pretraining recipe for transferable trajectory embeddings. TrajTok first learns a multi-resolution hexagonal cell partition from the spatial distribution of GPS points, converting noisy GPS sequences into discrete cell tokens. To capture both geometry and kinematics, it uses a factorized transformer encoder with early per-modality self-attention blocks, cross-attention fusion layers, and spatiotemporal rotary position embeddings, ST-RoPE, to encode where and when each token occurs. TrajTok is pretrained with masked-token modeling that recovers both geometric structure and kinematic patterns from partial trajectory observations. On the Porto dataset, a frozen TrajTok encoder with lightweight task adapters achieves strong performance across trajectory similarity search, classification, estimated time of arrival, and full travel-time regression, outperforming multiple task-specific methods. The same frozen encoder supports both geometry-dominated and kinematics-dominated tasks, suggesting that TrajTok learns transferable trajectory structure rather than task-specific shortcuts. These results indicate that learned multi-resolution spatial tokenization combined with masked-token pretraining is a promising direction for general-purpose trajectory foundation models.

Compositional generalization in sequential decision-making requires identifying which parts of prior rollouts remain useful for new tasks. Existing methods reuse skills or predictive models, but often overlook rich local transition geometry and dynamics. We propose Matrix-Space Reinforcement Learning (MSRL), a geometric abstraction that represents trajectory segments through positive semidefinite matrix descriptors aggregating first- and second-order statistics of lifted one-step transitions. These descriptors expose shared hidden structure, support algebraic composition in an abstract matrix space, and reveal opportunities for transfer. We prove that the descriptor is well defined up to coordinate gauge, complete for the induced low-order additive signal class, additive under valid segment composition, and minimally sufficient among admissible additive descriptors. We further show that conditioning value functions on the trajectory-segment matrix yields a first-order smooth approximation of action values, enabling source-learned matrix-to-value mappings to bootstrap learning in new tasks. MSRL is plug-in compatible with standard model-free and model-based methods, while obstruction filtering rejects implausible compositions. Empirically, MSRL achieves the best average finite-budget target AUC of 0.73, outperforming MSRL from scratch (0.65), TD-MPC-PT+FT (0.63), and TD-MPC (0.57).

Multimodal self-supervised learning (MSSL) has emerged as a key paradigm for pretraining geospatial foundation models. However, existing geospatial MSSL methods are mainly designed for static pairs of modalities, such as satellite imagery, street-view imagery, and text, where learning is driven by aligning observations from the same or nearby locations. This assumption breaks down for human mobility trajectories, which represent continuous movement along paths rather than discrete observations at individual locations. Although trajectories are important for urban understanding through their ability to capture human activity across roads, neighborhoods, and places over time, they remain largely underexplored in current geospatial MSSL frameworks. We present TrajGANR, a novel trajectory-centric geospatial MSSL framework that aligns continuous movement patterns with static, location-based observations. TrajGANR learns a continuous neural representation of trajectories at arbitrary points along each path, which enables fine-grained alignment with nearby street-view images, even when they are not co-located with any trajectory waypoints. We leverage this capability to introduce an MSSL objective that jointly aligns three modalities: trajectories, street-view images, and their geographic locations. We evaluate TrajGANR on four urban mobility and road understanding tasks. Across these tasks, TrajGANR consistently outperforms existing geospatial MSSL frameworks and a trajectory-specific foundation model. Ablation studies further demonstrate that our proposed MSSL objective and the multimodal learning framework are the primary drivers of these improvements, highlighting the importance of fine-grained geospatial alignment over coarser aggregation, as well as geospatial multimodal learning.

Trajectory representation learning (TRL) aims to encode raw trajectory data into low-dimensional embeddings for downstream tasks such as travel time estimation, mobility prediction, and trajectory similarity analysis. From a behavioral perspective, a trajectory reflects a sequence of route choices within an urban environment. However, most existing TRL methods ignore this underlying decision-making process and instead treat trajectories as static, passive spatiotemporal sequences, thereby limiting the semantic richness of the learned representations. To bridge this gap, we propose CORE, a TRL framework that integrates context-aware route choice semantics into trajectory embeddings. CORE first incorporates a multi-granular Environment Perception Module, which leverages large language models (LLMs) to distill environmental semantics from point of interest (POI) distributions, thereby constructing a context-enriched road network. Building upon this backbone, CORE employs a Route Choice Encoder with a mixture-of-experts (MoE) architecture, which captures route choice patterns by jointly leveraging the context-enriched road network and navigational factors. Finally, a Transformer encoder aggregates the route-choice-aware representations into a global trajectory embedding. Extensive experiments on 4 real-world datasets across 6 downstream tasks demonstrate that CORE consistently outperforms 15 state-of-the-art TRL methods, achieving an average improvement of 9.20% over the best-performing baseline. Our code is available at https://github.com/caoji2001/CORE.

The representation of urban trajectory data plays a critical role in effectively analyzing spatial movement patterns. Despite considerable progress, the challenge of designing trajectory representations that can capture diverse and complementary information remains an open research problem. Existing methods struggle in incorporating trajectory fine-grained details and high-level summary in a single model, limiting their ability to attend to both long-term dependencies while preserving local nuances. To address this, we propose HiT-JEPA (Hierarchical Interactions of Trajectory Semantics via a Joint Embedding Predictive Architecture), a unified framework for learning multi-scale urban trajectory representations across semantic abstraction levels. HiT-JEPA adopts a three-layer hierarchy that progressively captures point-level fine-grained details, intermediate patterns, and high-level trajectory abstractions, enabling the model to integrate both local dynamics and global semantics in one coherent structure. Extensive experiments on multiple real-world datasets for trajectory similarity computation show that HiT-JEPA's hierarchical design yields richer, multi-scale representations. Code is available at: https://anonymous.4open.science/r/HiT-JEPA.