Understanding How Inference Shapes Weight Updates in Predictive Coding: From Label Noise to the State-to-Weight Interface

Predictive coding networks infer neural activities through iterative energy minimization and learn network parameters through local synaptic updates. In this work, we find that, under symmetric label noise, PC maintains its fit to clean samples while memorizing fewer incorrect labels than backpropagation. By analyzing state inference and weight updates separately, we find that inference absorbs an incorrect label into the hidden states rather than passing it on to the weights. For the same image, an incorrect label induces a larger feedforward prediction error than the true label, yet the residuals after inference are similar, yielding a higher state absorption ratio. Our theoretical analysis characterizes this separation, showing how inference absorbs prediction errors through state changes and how the resulting states shape both the residuals and parameter gradients used for weight updates. At fixed weights and inference states, using inferred inputs attenuates the weight-gradient response to label changes and alters its direction; replacing these inputs with feedforward states leads to greater noise memorization during training. PC also memorizes more class-structured incorrect labels than those from symmetric corruption. Together, these results show how inference filters target-induced changes before local updates accumulate in shared weights.