  Learning rate, batch size and momentum are three important hyperparameters in
the SGD algorithm. It is known from the work of Jastrzebski et al.
arXiv:1711.04623 that large batch size training of neural networks yields
models which do not generalize well. Yao et al. arXiv:1802.08241 observe that
large batch training yields models that have poor adversarial robustness. In
the same paper, the authors train models with different batch sizes and compute
the eigenvalues of the Hessian of loss function. They observe that as the batch
size increases, the dominant eigenvalues of the Hessian become larger. They
also show that both adversarial training and small-batch training leads to a
drop in the dominant eigenvalues of the Hessian or lowering its spectrum. They
combine adversarial training and second order information to come up with a new
large-batch training algorithm and obtain robust models with good
generalization. In this paper, we empirically observe the effect of the SGD
hyperparameters on the accuracy and adversarial robustness of networks trained
with unperturbed samples. Jastrzebski et al. considered training models with a
fixed learning rate to batch size ratio. They observed that higher the ratio,
better is the generalization. We observe that networks trained with constant
learning rate to batch size ratio, as proposed in Jastrzebski et al., yield
models which generalize well and also have almost constant adversarial
robustness, independent of the batch size. We observe that momentum is more
effective with varying batch sizes and a fixed learning rate than with constant
learning rate to batch size ratio based SGD training.
