Nanjiang Chen

Xuhui Lin, Stephen Law, Nanjiang Chen et al.

Embodied agents that navigate cities rely on world models that predict how their surroundings will change as they move. But for navigation, what matters is not what the buildings look like; it is where the agent can go. Most world models nonetheless predict appearance, learning how a scene looks rather than the space an agent can move through. Those that do target geometry, such as bird's-eye-view occupancy grids, flatten the three-dimensional environment onto a ground plane, discarding the above-ground and multi-level structure that shapes real navigation. What is missing is a predictive target that captures the navigable geometry an agent actually traverses, without photometric entanglement and without collapsing the third dimension. Our key idea is to model the open volume between buildings, the negative space, encoded as a 3D isovist: a spherical visibility-depth map recording the distance to the nearest surface in every direction. We introduce an embodied world model that predicts the next isovist from a short history of past isovists and a movement action. The prediction is formulated as a depth residual so the decoder inherits sharp building edges, trained with self-rollout scheduled sampling to keep corrupted context on the geometry manifold, and equipped with a persistent latent bird's-eye-view spatial map for cross-path consistency. Our central finding is emergent and unexpected: a single city-blind model trained on Manhattan and Paris develops a cross-city spatial signature, with city identity linearly decodable from its temporal latents far above single-frame baselines, so the signature lives in the learned dynamics rather than in appearance. The representation is lightweight, interpretable, and reproducible, offering a geometric substrate for spatial reasoning in embodied AI, robotics, and urban analysis, released with an open dataset and pipeline.

Stephen Law, Tao Yang, Nanjiang Chen et al.

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.