On Exploiting Layerwise Gradient Statistics for Effective Training of Deep Neural Networks

Adam and AdaBelief compute and make use of elementwise adaptive stepsizes in training deep neural networks (DNNs) by tracking the exponential moving average (EMA) of the squared-gradient g_t^2 and the squared prediction error (m_t-g_t)^2, respectively, where m_t is the first momentum at iteration t and can be viewed as a prediction of g_t. In this work, we investigate if layerwise gradient statistics can be expoited in Adam and AdaBelief to allow for more effective training of DNNs. We address the above research question in two steps. Firstly, we slightly modify Adam and AdaBelief by introducing layerwise adaptive stepsizes in their update procedures via either pre- or post-processing. Our empirical results indicate that the slight modification produces comparable performance for training VGG and ResNet models over CIFAR10 and CIFAR100, suggesting that layer-wise gradient statistics play an important role towards the success of Adam and AdaBelief for at least certian DNN tasks. In the second step, we propose Aida, a new optimisation method, with the objective that the elementwise stepsizes within each layer have significantly smaller statistical variances, and the layerwise average stepsizes are much more compact across all the layers. Motivated by the fact that (m_t-g_t)^2 in AdaBelief is conservative in comparison to g_t^2 in Adam in terms of layerwise statistical averages and variances, Aida is designed by tracking a more conservative function of m_t and g_t than (m_t-g_t)^2 via layerwise vector projections. Experimental results show that Aida produces either competitive or better performance with respect to a number of existing methods including Adam and AdaBelief for a set of challenging DNN tasks.