Transformer-based deep neural networks have achieved great success in various sequence applications due to their powerful ability to model long-range dependency. The key module of Transformer is self-attention (SA) which extracts features from the entire sequence regardless of the distance between positions. Although SA helps Transformer performs particularly well on long-range tasks, SA requires quadratic computation and memory complexity with the input sequence length. Recently, attention map reuse, which groups multiple SA layers to share one attention map, has been proposed and achieved significant speedup for speech recognition models. In this paper, we provide a comprehensive study on attention map reuse focusing on its ability to accelerate inference. We compare the method with other SA compression techniques and conduct a breakdown analysis of its advantages for a long sequence. We demonstrate the effectiveness of attention map reuse by measuring the latency on both CPU and GPU platforms.

We propose a fast approximation method of a softmax function with a very large vocabulary using singular value decomposition (SVD). SVD-softmax targets fast and accurate probability estimation of the topmost probable words during inference of neural network language models. The proposed method transforms the weight matrix used in the calculation of the output vector by using SVD. The approximate probability of each word can be estimated with only a small part of the weight matrix by using a few large singular values and the corresponding elements for most of the words. We applied the technique to language modeling and neural machine translation and present a guideline for good approximation. The algorithm requires only approximately 20\% of arithmetic operations for an 800K vocabulary case and shows more than a three-fold speedup on a GPU.