A Physical Theory of Backpropagation: Exact Gradients from the Least-Action Principle

ArXi:2602.02281v2 Announce Type: replace-cross Backpropagation is typically presented as a symbolic procedure: a backward pass topologically distinct from inference, with non-local error signals and synchronous global clocking, features with no clear analog in physical reality. Existing physics-inspired alternatives recover gradients only approximately, in vanishing-perturbation limits, or under weight-symmetry constraints incompatible with feedforward architectures. In this paper, we address this gap by deriving exact backpropagation from Hamilton's least-action principle.