On Suppressing Range of Adaptive Stepsizes of Adam to Improve Generalisation Performance

A number of recent adaptive optimizers improve the generalisation performance of Adam by essentially reducing the variance of adaptive stepsizes to make a bridge with SGD with momentum. Following the above motivation, we suppress the range of the adaptive stepsizes of Adam by exploiting the layerwise gradient statistics. In particular, at each iteration, we propose to perform three consecutive operations on the second momentum \(\boldsymbol{v}_t\) before using it to update a DNN model: (1): down-scaling, (2): \(\epsilon \) -embedding, and (3): down-translating. The resulting algorithm is referred to as SET-Adam, where SET is a brief notation of the three operations. The down-scaling operation on \(\boldsymbol{v}_t\) is performed layerwise by making use of the angles between the layerwise subvectors of \(\boldsymbol{v}_t\) and the corresponding all-one subvectors. Extensive experimental results show that SET-Adam outperforms eight adaptive optimizers when training transformers and LSTMs for NLP, and VGG and ResNet for image classification over CIAF10 and CIFAR100 while matching the best performance of the eight adaptive methods when training WGAN-GP models for image generation tasks. Furthermore, SET-Adam produces higher validation accuracies than Adam and AdaBelief for training ResNet18 over ImageNet.