Trust Your Targets: Is Target Propagation Block-Diagonal Gauss-Newton?

Target propagation (TP) is a backpropagation alternative in which local targets carry the global learning signal. Prior works claim that TP performs Gauss-Newton (GN) optimisation on these targets, but the correspondence has only been established under unrealistic assumptions where hitting them exactly is trivial. Practical variants instead descend on a least-squares problem via a single gradient step. In this paper, we rederive TP from a trust region under an implicit, previously unexamined norm, and introduce CGTP (Conjugate Gradient Target Propagation), which uses conjugate gradients to solve the layer-local subproblems in parallel. A single adaptive parameter jointly controls this trust region and a matching bound on the weight update; KFAC emerges exactly as the special case where the per-sample Jacobians are approximated as identical, giving its factored damping a variational grounding. On MNIST and Fashion-MNIST MLPs, CGTP matches the accuracy of ADAM and KFAC, requiring 10x fewer backward-pass-equivalents than the former, while remaining stable across depth.