Spatial Context Networks: Geometric Semantic Routing in Neural Architectures

We introduce Spatial Context Networks (SCN), a novel
neural architecture that treats neurons as geometric entities in a learned semantic space. Unlike traditional neural networks that rely on weighted summations, SCN employs distance-based activation functions where each neuron operates as a point-mass with a learnable centroid
in d-dimensional space. The architecture implements
three key innovations: (1) geometric activation functions
based on Euclidean distance, (2) semantic routing that
selectively activates neurons based on spatial proximity,
and (3) connection density weighting with adaptive scaling. Our experiments demonstrate stable training dynamics, interpretable neuron specialization, and efficient
sparse activation patterns. Notably, all experiments were
conducted on consumer-grade hardware (gaming laptop),
demonstrating the accessibility and computational efficiency of this approach. The architecture achieves 91%
network efficiency with only 32 hidden neurons while
maintaining numerical stability through principled geometric constraints.