Injecting Qualitative Spatial Reasoning into World Models via Logic Tensor Networks

摘要

World models (WM) learn predictive representations from high-dimensional sensory input. However, their internal knowledge is implicit and often inadequate for systematic reasoning about object structure. Qualitative Spatial Reasoning (QSR) models provide explicit human-readable object descriptions under transformations. This paper shows that these two forms of modeling can be combined by injecting a QSR model into a WM to improve the WM reasoning abilities. Using a cube rotation setting inspired by the cube comparison test used in mental rotation tasks as a case study, we use a QSR model that captures the geometric relationships and transformation rules describing how features move across faces under discrete rotations. We translate this QSR model into differentiable constraints using Logic Tensor Networks (LTNs) to guide gradient based learning. These constraints are injected into the WM loss function to regularize its latent dynamics to satisfy the spatial constraints of rotation. The results show that under an extreme data scarce regime (10%), baseline model's performance collapses to near zero, whereas our approach achieves above 90% better performance relative to baseline. Our method consistently maintains high scores across all data regimes (~80%), for both in-distribution and out-of-distribution observations. This paper proposes a novel framework to infuse QSR knowledge inside WM to make learned latent dynamics logical. Code is available at: https:// github.com/ajayrao80/LtnDreamer/