  Descent methods for deep networks are notoriously capricious: they require
careful tuning of step size, momentum and weight decay, and which method will
work best on a new benchmark is a priori unclear. To address this problem, this
paper conducts a combined study of neural architecture and optimisation,
leading to a new optimiser called Nero: the neuronal rotator. Nero trains
reliably without momentum or weight decay, works in situations where Adam and
SGD fail, and requires little to no learning rate tuning. Also, Nero's memory
footprint is ~ square root that of Adam or LAMB. Nero combines two ideas: (1)
projected gradient descent over the space of balanced networks; (2)
neuron-specific updates, where the step size sets the angle through which each
neuron's hyperplane turns. The paper concludes by discussing how this geometric
connection between architecture and optimisation may impact theories of
generalisation in deep learning.
