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Recent work has improved the training stability of deep PC networks (PCNs) by leveraging some BP-inspired reparameterisations. However, the full scalability and theoretical basis of these methods remain unclear. To address this gap, we study the infinite width and depth limits of PCNs. For linear residual networks, we show that the set of width- and depth-stable feature-learning parameterisations for PC is exactly the same as for BP. Moreover, under any of these parameterisations, the PC energy with equilibrated activities converges to the quadratic BP loss when the model width is much larger than the depth, resulting in PC computing the same gradients as BP. Experiments show that, as long as an activity equilibrium is reached, convergence t","title":"On the Infinite Width and Depth Limits of Predictive Coding Networks","url":"https://arxiv.org/abs/2602.07697","vendor":"arxiv_cs_ai"},"summary":"arXiv:2602.07697v2 Announce Type: replace-cross \nAbstract: Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights. Recent work has improved the training stability of deep PC networks (PCNs) by leveraging some BP-inspired reparameterisations. However, the full scalability and theoretical basis of these methods remain unclear. To address this gap, we study the infinite width and depth limits of PCNs. For linear residual networks, we show that the set of width- and depth-stable feature-learning parameterisations for PC is exactly the same as for BP. Moreover, under any of these parameterisations, the PC energy with equilibrated activities converges to the quadratic BP loss when the model width is much larger than the depth, resulting in PC computing the same gradients as BP. 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