Mapping Movement: The Rise of Trajectory Foundation Models

Author: Denis Avetisyan

A new generation of AI is learning to predict and understand motion, opening doors for advanced applications across robotics, autonomous systems, and beyond.

The framework establishes a mathematical foundation for modeling and analyzing space-time trajectory data, enabling precise representation of movement through a formalized system.

This review explores recent advances in trajectory foundation models, covering data modalities, self-supervised learning techniques, and key research challenges.

While foundation models have revolutionized data analytics, a systematic understanding of their application to dynamic, real-world phenomena remains a critical gap. This tutorial, ‘Spatio-Temporal Trajectory Foundation Model – Recent Advances and Future Directions’, addresses this by providing a comprehensive overview of trajectory foundation models (TFMs), a crucial subset for analyzing spatio-temporal data. We present a taxonomy of existing methodologies, critically assessing their strengths and limitations across diverse tasks, and highlight advancements in self-supervised and contrastive learning. Ultimately, this work asks: how can we build truly transferable and responsible TFMs to unlock the full potential of spatio-temporal general intelligence?

The Epistemic Challenge of Movement: Beyond Superficial Observation

Historically, analyzing movement – whether of vehicles, pedestrians, or even animals – has been hampered by the need for researchers to manually define what aspects of a trajectory are important. This reliance on hand-crafted features, such as speed, direction, or turning angles, creates a significant bottleneck, as these features may not adequately capture the nuances of complex behaviors. Consequently, traditional methods often struggle to generalize beyond the specific scenarios they were designed for, exhibiting poor performance when faced with novel or unpredictable movement patterns. This limited generalization stems from an inability to learn underlying principles directly from the data itself, instead being constrained by the pre-defined, and potentially incomplete, understanding embedded within the chosen features. The result is a fragmented approach, hindering a comprehensive understanding of movement and limiting the potential for accurate prediction in real-world applications.

Trajectory Foundation Models represent a significant departure from conventional movement analysis techniques, which historically depended on manually designed features to interpret patterns in positional data. These new models instead learn directly from the raw data streams that define trajectories – sequences of points denoting location over time. By foregoing the need for pre-defined characteristics, these models can autonomously discover intricate relationships and underlying structures within movement, enabling them to generalize to previously unseen scenarios and datasets. This capacity for self-discovery yields robust representations of motion, capable of capturing nuances often lost in traditional methods, and paving the way for more accurate predictions and a deeper comprehension of dynamic processes across a multitude of fields.

Trajectory Foundation Models are poised to revolutionize fields reliant on understanding and anticipating motion. Beyond simply tracking where something is, these models learn the underlying principles of movement, enabling remarkably accurate predictions across a spectrum of applications. Autonomous vehicles stand to benefit from improved navigation and collision avoidance, while robotic systems could achieve more fluid and adaptive behaviors. The implications extend far beyond robotics, however; urban planners can leverage these models to optimize traffic flow, predict pedestrian congestion, and design more efficient public transportation systems. Even in fields like wildlife biology, understanding animal movement patterns – from migration routes to foraging behaviors – becomes significantly more refined. Ultimately, this technology promises to move beyond reactive responses to movement and towards proactive anticipation, unlocking entirely new levels of efficiency and insight.

Self-Supervision: An Algorithmic Imperative

Self-Supervised Learning (SSL) offers a methodology for training Trajectory Foundation Models by leveraging inherent structure within unlabeled trajectory data, thereby circumventing the need for expensive and time-consuming manual labeling. Instead of requiring external annotations, SSL algorithms formulate predictive tasks from the data itself – for example, predicting future trajectory segments given past observations, or reconstructing masked portions of a trajectory. This process allows the model to learn meaningful representations of movement patterns directly from the data, effectively using the data as its own source of supervision. The resulting models exhibit performance comparable to, and sometimes exceeding, supervised approaches, while significantly reducing the dependence on labeled datasets, which are often a bottleneck in robotics and motion planning applications.

Contrastive and generative learning techniques facilitate the development of robust trajectory representations in Foundation Models by leveraging inherent data structure. Contrastive learning algorithms train models to distinguish between similar and dissimilar trajectory segments, embedding trajectories in a feature space where related movements are closer together. Generative approaches, conversely, focus on reconstructing or predicting trajectory patterns, often employing techniques like masked autoencoders or variational autoencoders to learn a latent space capturing essential trajectory characteristics. Both methodologies enable the model to learn meaningful features from unlabeled trajectory data by establishing relationships between different parts of the trajectory or by learning to generate plausible future states, ultimately leading to improved performance on downstream tasks.

TrajRL and Toast represent distinct approaches to pre-training Trajectory Foundation Models utilizing unlabeled data. TrajRL employs reinforcement learning techniques, treating trajectory prediction as a reward maximization problem where the model learns to generate likely future states. Toast, conversely, focuses on masked trajectory reconstruction; it randomly masks portions of observed trajectories and trains the model to predict the missing segments. Both methods leverage trajectory augmentation – creating modified versions of existing trajectories – to increase the diversity of the training data and improve model robustness. Empirical results demonstrate that pre-training with either TrajRL or Toast significantly enhances downstream task performance, reducing the reliance on labeled datasets and improving generalization capabilities.

The reduction in reliance on labeled data achieved through self-supervised learning directly contributes to improved model adaptability and generalization capabilities. Labeled datasets are often limited in scope and can introduce biases specific to the labeling process or environment. By learning directly from the inherent structure of trajectory data, models develop a more robust understanding of underlying movement principles, independent of specific task constraints. This allows the model to more effectively transfer learned knowledge to novel scenarios, variations in environment, or previously unseen movement patterns, ultimately resulting in enhanced performance and broader applicability compared to models heavily reliant on labeled examples.

From Correlation to Comprehension: Applying Trajectory Foundation Models

Trajectory Foundation Models are increasingly utilized for both real-time and historical transportation analysis. Accurate Travel Time Estimation leverages these models to predict the duration of trips based on current and anticipated traffic conditions, going beyond simple speed-distance calculations by factoring in complex interactions and potential disruptions. Detailed Traffic Analysis benefits from the models’ ability to process large volumes of trajectory data, identifying congestion patterns, origin-destination flows, and anomalous events with greater precision than traditional methods. This allows transportation planners and traffic management systems to make data-driven decisions regarding infrastructure improvements, signal timing optimization, and incident response strategies, ultimately improving overall network efficiency and reducing delays.

Trajectory Recovery utilizes Trajectory Foundation Models to reconstruct plausible movement paths from incomplete observational data. This process addresses common data challenges such as sensor failures, signal occlusion, or limited tracking periods. By leveraging the learned patterns of movement encoded within the model, gaps in trajectories can be filled with statistically likely paths, effectively imputing missing data points. The resulting complete trajectories improve the accuracy of downstream tasks, including more reliable movement prediction and enhanced analysis of historical movement patterns. This capability is particularly valuable in scenarios where continuous, uninterrupted tracking is not feasible or practical.

Trajectory Clustering and Classification leverage Trajectory Foundation Models to analyze movement data beyond simple forecasting. Clustering algorithms group similar trajectories together based on shared characteristics – such as speed, direction, or spatial location – revealing common travel behaviors. Classification, conversely, assigns predefined labels to trajectories, categorizing them into distinct types – for example, identifying routes used by public transportation, distinguishing between pedestrian and vehicular movement, or flagging anomalous trajectories indicative of unusual activity. These capabilities rely on the models’ learned representations of movement, allowing for automated identification and categorization of complex patterns within trajectory datasets.

Trajectory Generation leverages trained models to synthesize plausible movement paths, enabling the simulation of future scenarios for applications such as autonomous vehicle planning and urban mobility modeling. This capability extends beyond simple extrapolation; the models can generate diverse trajectories conditioned on specific starting points, goals, and constraints, allowing for the exploration of multiple possible outcomes. Furthermore, generated trajectories can be used for “what-if” analysis, evaluating the impact of different interventions – like altered traffic light timings or the introduction of new infrastructure – on overall system performance. The fidelity of these simulations is directly related to the quality of the training data and the model’s ability to capture complex, real-world movement dynamics.

Beyond Observation: The Pursuit of Causal Understanding

Establishing a relationship between two events, such as a specific body movement and a subsequent action, is often the first step in scientific inquiry, but correlation alone provides an incomplete picture. Simply observing that events frequently occur together doesn’t illuminate the underlying mechanisms driving that association; it fails to answer why a movement happens. A truly comprehensive understanding necessitates shifting from identifying that movements and actions are linked, to building a causal model – a framework that explains the generative process, detailing how and why one event reliably leads to another. This approach moves beyond passive observation to actively discerning the cause-and-effect relationships governing dynamic systems, allowing for prediction and intervention beyond what correlational studies permit. Recognizing this distinction is crucial for fields ranging from robotics and biomechanics to clinical analysis and behavioral science, as it underpins the development of interventions and technologies that don’t just react to observed patterns, but proactively influence outcomes.

The pursuit of understanding movement extends beyond simply observing what happens to discerning why. Traditional trajectory analysis often relies on correlations, which can be misleading due to spurious relationships; just because two movement patterns occur together doesn’t mean one causes the other. Recent advancements integrate Structural Causal Models (SCMs) with Trajectory Foundation Models (TFMs) to address this limitation. By explicitly modeling causal relationships-for instance, how a specific muscle activation leads to a joint rotation-these combined models can filter out noise and identify genuine drivers of movement. This approach allows researchers to move beyond prediction and towards explanation, building systems that not only recognize patterns but also understand the underlying mechanisms governing dynamic behavior and ultimately, offer more robust and interpretable insights into complex movement phenomena.

Sophisticated trajectory representation learning is achieved through techniques like Predictive Information Maximization (PIM) and Representation Disentanglement (RED). PIM focuses on learning representations that maximize predictive power, enabling the model to anticipate future states based on past movements and thus capture the inherent dynamics of a trajectory. Meanwhile, RED aims to separate underlying factors of variation within the movement data – such as speed, direction, or style – into independent, interpretable components. By combining these approaches, models move beyond simply recognizing patterns in movement to understanding why those patterns occur, leading to more robust and generalizable predictions about complex behaviors and ultimately a richer understanding of underlying movement dynamics. These enhancements are crucial for applications ranging from robotics and animation to behavioral analysis and predictive healthcare.

This work delivers a thorough tutorial on trajectory foundation models (TFMs), serving as a consolidated resource for researchers entering this rapidly evolving field. It details recent progress in data-modality-oriented methods – techniques specifically designed to leverage the unique characteristics of movement data – and comprehensively outlines the core principles of foundation model learning as applied to trajectories. The paper doesn’t simply present these advancements; it systematically breaks down the key concepts and methodologies, offering a clear pathway for understanding how these models are built, trained, and applied to diverse movement analysis tasks. By synthesizing these developments, this tutorial aims to accelerate innovation and broader adoption of TFMs across multiple disciplines, from robotics and biomechanics to behavioral science and clinical analysis.

The pursuit of robust trajectory foundation models, as detailed in the study, echoes a fundamental principle of mathematical elegance. The models strive for a generalized understanding of spatio-temporal data, aiming to predict and generate plausible trajectories beyond the training set. This resonates with Tim Berners-Lee’s assertion: “The Web is more a social creation than a technical one.” Just as the web’s strength lies in interconnectedness and shared understanding, these models aim to establish a coherent ‘understanding’ of movement patterns. The success of self-supervised learning and contrastive learning methods hinges on establishing consistent boundaries within the data, ensuring predictable and provable representations of motion, mirroring the consistency demanded by pure mathematical solutions.

What Lies Ahead?

The proliferation of trajectory foundation models, while exhibiting promise, has largely skirted the fundamental question of reproducibility. The current reliance on empirical validation – demonstrating performance on curated datasets – feels… insufficient. A model capable of generating plausible trajectories is not necessarily a correct model. The field must confront the issue of deterministic outcomes; if a model, given identical inputs, yields divergent results, its utility diminishes rapidly, particularly in applications demanding verifiable predictions.

Further investigation into the very nature of ‘representation learning’ is crucial. Many approaches implicitly assume a universal, modality-agnostic trajectory structure. This feels… optimistic. A rigorous mathematical framework defining the inherent limitations of spatio-temporal representation-what can, and cannot, be faithfully encoded-remains conspicuously absent. Without such a framework, progress will remain largely empirical, a cycle of iterative refinement devoid of true theoretical grounding.

Ultimately, the true test of these models will not be their ability to mimic observed data, but their capacity to extrapolate correctly into novel scenarios. Generative learning, divorced from provable constraints, risks producing elegant illusions. The pursuit of statistically plausible trajectories should not overshadow the demand for logically sound ones.

Original article: https://arxiv.org/pdf/2511.20729.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

The Epistemic Challenge of Movement: Beyond Superficial Observation

Self-Supervision: An Algorithmic Imperative

From Correlation to Comprehension: Applying Trajectory Foundation Models

Beyond Observation: The Pursuit of Causal Understanding

What Lies Ahead?

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