Local Learning Rules for Deep Neural Networks with Two-State Neurons

Doctoral thesis, 2025

The way artificial neural networks are trained with backpropagation requires a degree of synchronization of operations, and non-local knowledge of the computational graph of the network, which is infeasible in noisy asynchronous circuitry (be it biological, analog electronic or optical). Learning algorithms based on temporal or spatial neural activity differences allow estimating gradients, and hence learning, without these problematic requirements. In this thesis, we explore a number of such alternative learning algorithms. Paper A presents a variation of contrastive Hebbian learning, which achieves Lipschitz-1 hidden layers by construction. Paper B focuses on efficient training on traditional digital hardware by presenting a variant of backpropagation compatible with quantized weights. Paper C returns to the topic of contrastive Hebbian learning by presenting a new local learning algorithm for training feedforward networks based on neurons possessing two internal states. These dyadic neurons perform credit assignment by encoding errors as differences and predictions as averages of the internal states. Paper D provides a new variation of dual propagation and provides derivations of both the original and the new variant. Paper E presents a general framework for dyadic learning, which encompasses dual propagation in feedforward models and equilibrium propagation (a well-known variant of contrastive Hebbian learning) on Hopfield models as special cases while also being applicable to arbitrarily connected networks. The case of a skew-symmetric Hopfield network is found to be particularly intriguing as it, like the model from paper A, provides Lipschitz-1 layers by construction.