Title: On Why Form Shapes Reasoning: Structuring Latent Program Networks with Category-Theoretic Constraints
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: Compositional Reasoning, Category Theory, Latent Program Networks

Abstract: Human reasoning is inherently structured: we perceive, compose, and abstract patterns to make sense of the world. Following Kant’s view that cognition imposes structure on experience, we ask how neural networks can acquire structured, compositional reasoning. We present a category-theoretic formulation of Latent Program Networks (LPNs), neural architectures that represent programs as continuous latent vectors optimized at test time. We treat latent transformations as categorical morphisms and introduce differentiable constraints enforcing associativity, identity, and closure, thereby shaping the latent space into a compositional system without explicit symbolic rules. On structured grid-transformation tasks, these constraints significantly improve compositional generalization, latent alignment, and interpretability. Our results demonstrate that category-theoretic structure can be imposed on latent representations to induce compositional reasoning in neural networks.

TL;DR: When form is imposed categorically on latent programs, reasoning emerges compositionally — enabling neural networks to generalize more systematically.