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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. 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