# Sakana AI Researchers Introduce PC-ALM, a Layer-Local Alternative to Backpropagation That Trains 1000-Layer Networks

> Source: <https://www.marktechpost.com/2026/09/14/sakana-ai-researchers-introduce-pc-alm-a-layer-local-alternative-to-backpropagation-that-trains-1000-layer-networks/>
> Published: 2026-09-14 20:46:16+00:00

Sakana AI researchers Jeffrey Seely and Julian Gould introduce Augmented Lagrangian Predictive Coding (PC-ALM), a local-learning alternative to backpropagation. By attaching a Lagrange multiplier to each layer constraint, PC-ALM keeps predictive coding's layer-local updates while recovering exact backprop gradients in linear networks. It matches BP across widths and depths from 8 to 128 at an inference budget of T = 2L, lifts gradient cosine to BP from 0.604 to 0.909 in the reference cell, and trains 1000-layer residual MLPs within about 2 points of backprop on MNIST. MIT-licensed JAX code is available.

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