Improving Deep Learning Speed and Performance through Synaptic Neural Balance

We present experiments and their corresponding theory, demonstrating that synaptic neural balancing can significantly enhance deep learning speed, accuracy, and generalization due to the symmetry that it creates in the synaptic weights. Given an additive cost function (regularizer) of the synaptic weights, a neuron is said to be in balance if the total cost of it incoming weights is equal to the total cost of its outgoing weights. For large classes of networks, activation functions, and regularizers, neurons can be balanced fully or partially using scaling operations that do not change their functionality. Furthermore, these balancing operations are associated with a strictly convex optimization problem with a single optimum and can be carried in any order. In our simulations, we systematically observe that: (1) Fully balancing before training results in better performance as compared to several other training approaches; (2) Interleaving partial (layer-wise) balancing and stochastic gradient descent steps during training results in faster learning convergence and better overall accuracy (with $L_1 $ balancing converging faster than $L_2$ balancing; and (3) When given limited training data, neural balanced models outperform plain or regularized models. and this is true both for both feedforward and recurrent networks. In short, the evidence supports that neural balancing operations with their symmetry ought to be added to the arsenal of methods used to regularize and train neural networks.