The power-law approximation for the frequency distribution of words postulated by Zipf has been extensively studied for decades, which led to many variations on the theme. However, comparatively less attention has been paid to the investigation of the case of word frequencies. In this paper, we derive its analytical expression from the inverse of the underlying rank-size distribution as a function of total word count, vocabulary size and the shape parameter, thereby providing a unified framework to explain the nonlinear behavior of low frequencies on the log-log scale. We also present an efficient method based on relative entropy minimization for a robust estimation of the shape parameter using a small number of empirical low-frequency probabilities. Experiments were carried out for a selected set of languages with varying degrees of inflection in order to demonstrate the effectiveness of the proposed approach.

Abstract In training deep learning networks, the optimizer and related learning rate are often used without much thought or with minimal tuning, even though it is crucial in ensuring a fast convergence to a good quality minimum of the loss function that can also generalize well on the test dataset. Drawing inspiration from the successful application of cyclical learning rate policy to computer vision tasks, we explore how cyclical learning rate can be applied to train transformer-based neural networks for neural machine translation. From our carefully designed experiments, we show that the choice of optimizers and the associated cyclical learning rate policy can have a significant impact on the performance. In addition, we establish guidelines when applying cyclical learning rates to neural machine translation tasks.