Local Predictions, Global Learning: Radial Basis Function Networks for Spatially-Aware Predictive Coding

Predictive coding networks offer a biologically plausible alternative to backpropagation through local error minimization. However, standard implementations rely on fully connected layers, unlike the sparse, spatially organized connectivity of the brain. We introduce Radial Basis Predictive Coding Networks (RBF-PCN), which use Gaussian receptive fields to enforce spatial locality in predictions and error propagation, reducing computational complexity. Experiments show that RBF-PCN maintains competitive performance with standard predictive coding in shallow models, and that both predictive coding variants exhibit superior equivariance to translations and rotations compared to backpropagation.