Seonglae ChoAdds a Lagrange multiplier at each layer to accumulate prediction error and feed it back into the local activation/weight updates. At convergence, effectively becomes the BP adjoint/gradient signal.
In linear networks it recovers the exact BP gradient at equilibrium, and in nonlinear MLPs it nearly matches BP performance under the same inference budget — with the largest gains in the deep + narrow regime where standard PC breaks down. Instead of error diffusing slowly as in PC, the primal-dual dynamics propagate it to deep layers quickly, like a ballistic wave. The downsides: the multiplier state roughly doubles activation memory, and experiments are still limited to MNIST/Fashion-MNIST + residual MLP + 1 epoch.
