Two Tales of Single-Phase Contrastive Hebbian Learning
Rasmus Kjær Høier Christopher Zach
The search for "biologically plausible" learning algorithms has converged on
the idea of representing gradients as activity differences. However, most
approaches require a high degree of synchronization (distinct phases during
learning) and introduce substantial computational overhead, which raises doubts
regarding their biological plausibility as well as their potential utility for
neuromorphic computing. Furthermore, they commonly rely on applying
infinitesimal perturbations (nudges) to output units, which is impractical in
noisy environments. Recently it has been shown that by modelling artificial
neurons as dyads with two oppositely nudged compartments, it is possible for a
fully local learning algorithm named ``dual propagation'' to bridge the
performance gap to backpropagation, without requiring separate learning phases
or infinitesimal nudging. However, the algorithm has the drawback that its
numerical stability relies on symmetric nudging, which may be restrictive in
biological and analog implementations. In this work we first provide a solid
foundation for the objective underlying the dual propagation method, which also
reveals a surprising connection with adversarial robustness. Second, we
demonstrate how dual propagation is related to a particular adjoint state
method, which is stable regardless of asymmetric nudging.