Accelerated Predictive Coding Networks via Direct Kolen-–Pollack Feedback Alignment

Predictive coding (PC) is a brain-inspired optimization algorithm for training neural networks relying on local updates, thereby enabling parallel learning across layers. However, its practical implementations face two key optimization challenges: the error signal must still propagate from the output to early layers through multiple inference-phase steps, and it decays exponentially during this process, leading to vanishing updates in early layers. We propose direct Kolen--Pollack predictive coding (DKP--PC), a PC variant that addresses both error delay and exponential decay while preserving update locality. It enables direct error transmission from the output layer to all hidden layers by leveraging direct feedback connections, learned using the DKP update rule. This results in an optimization algorithm that decouples error propagation from network depth, achieving a theoretically depth-independent error propagation time. Empirically, compared to standard PC and some of its variants, DKP--PC reduces training time and computational overhead while performing comparably or better across different benchmarks. In the most complex scenario, that is, a ResNet-18 network trained on Tiny ImageNet, it achieves a 5\% absolute improvement in test accuracy while reducing training time by over 40\%, compared to the best PC variant. In addition, we demonstrate that DKP--PC's parallel execution enables training speedups compared to backpropagation on fully-connected networks.