Tell a robot to go to “the red chair near the window.” It needs to connect language to space. The standard approach: store a language feature vector at every grid cell in the map. This works for small rooms. For a building, it's computationally prohibitive — millions of vectors, most of them redundant, all consuming memory.
LAMP (arXiv:2602.11862) replaces explicit storage with an implicit neural field. Instead of a language vector per location, a continuous function maps coordinates to semantic features. The field is learned, compressed, and — critically — differentiable. This means the robot can use gradient descent to find the location that best matches “red chair near the window” without exhaustively searching the map.
The navigation pipeline is coarse-to-fine. A sparse graph handles rough path planning — “go to that area of the building.” Gradient-based optimization then refines the position within the learned field near the goal — “actually, 2 meters left.” A Bayesian layer using von Mises-Fisher distributions adds uncertainty estimates, allowing the robot to reason about goals in unobserved regions by leveraging semantic similarities.
The structural insight: explicit maps store answers. Implicit maps store the function that generates answers. The function is smaller than the answer set, generalizes to unseen queries, and admits optimization. It's the difference between a lookup table and an equation — same information, different computational affordances. The equation doesn't just save memory. It enables operations (gradient descent, interpolation, uncertainty estimation) that the table can't support.