Natural Gradient Learning in Predictive Coding through Lateral Circuits

Predictive coding (PC) trains neural networks through local energy-minimization dynamics without depending on a global error signal that backpropagation (BP) requires. Although PC is a promising alternative algorithm for efficient learning, the computational cost of inference dynamics currently outweighs the resulting learning benefits in practice. In this work, we take inspiration from optimization theory to extract more learning benefit from each inference phase. We introduce Natural PC, which augments standard PC with a lateral circuit, enabling exact and efficient natural gradient learning locally in space and time. Our lateral circuit learns the activity correlations that determine the Fisher information matrix and implicitly computes its inverse, avoiding expensive matrix inversion. Across all tested image reconstruction benchmarks, Natural PC achieves state of the art in terms of sample and compute efficiency compared to existing PC approaches. Most notably, Natural PC scales to ImageNet and matches the performance of BP trained with AdamW and various second-order optimizers at an order of magnitude lower computational cost while also using two orders of magnitude fewer training samples. Our results demonstrate that local natural gradient learning makes PC competitive with BP in both sample efficiency and computational cost in reconstruction tasks.