Exponentiated gradient learning yields brain-like synaptic distributions

Artificial neural networks trained with gradient descent (GD) are widely used to model brain learning, but GD allows synapses to switch between excitatory and inhibitory and produces weight distributions unlike those observed experimentally. We show that an alternative rule, exponentiated gradient (EG), avoids these problems because its multiplicative, exponential weight updates mathematically prohibit synapses from changing sign and preferentially scale already-large weights, naturally generating log-normal distributions. This mechanism also concentrates task-relevant computation onto a smaller subset of strong connections, which we show makes EG-trained recurrent neural networks more robust to synaptic pruning and better able to learn from sparsely relevant inputs than GD-trained networks, while matching GD's performance on standard cognitive tasks. These findings tie a normative optimization principle directly to observed features of synaptic organization in the brain.