Wasserstein distance is a powerful tool for comparing probability distributions and is widely used for document classification and retrieval tasks in NLP. In particular, it is known as the word mover’s distance (WMD) in the NLP community. WMD exhibits excellent performance for various NLP tasks; however, one of its limitations is its computational cost and thus is not useful for large-scale distribution comparisons. In this study, we propose a simple and effective nearest neighbor search based on the Wasserstein distance. Specifically, we employ the L1 embedding method based on the tree-based Wasserstein approximation and subsequently used the nearest neighbor search to efficiently find the k-nearest neighbors. Through benchmark experiments, we demonstrate that the proposed approximation has comparable performance to the vanilla Wasserstein distance and can be computed three orders of magnitude faster than the vanilla Wasserstein distance.

Wasserstein distance, which can be computed by solving the optimal transport problem, is a powerful method for measuring the dissimilarity between documents. In the NLP community, it is referred to as word mover’s distance (WMD). One of the key challenges of Wasserstein distance is its computational cost since it needs cubic time. Although the Sinkhorn algorithm is a powerful tool to speed up to compute the Wasserstein distance, it still requires square time. Recently, a linear time approximation of the Wasserstein distance including the sliced Wasserstein and the tree-Wasserstein distance (TWD) has been proposed. However, a linear time approximation method suffers when the dimensionality of word vectors is high. In this study, we propose a method to combine feature selection and tree approximation of Wasserstein distance to handle high-dimensional problems. More specifically, we use multiple word embeddings and automatically select useful word embeddings in a tree approximation of Wasserstein distance. To this end, we approximate Wasserstein distance for each word vector by tree approximation technique, and select the discriminative (i.e., large Wasserstein distance) word embeddings by solving an entropic regularized maximization problem. Through our experiments on document classification, our proposed method achieved high performance.

The problem of estimating the probability distribution of labels has been widely studied as a label distribution learning (LDL) problem, whose applications include age estimation, emotion analysis, and semantic segmentation. We propose a tree-Wasserstein distance regularized LDL algorithm, focusing on hierarchical text classification tasks. We propose predicting the entire label hierarchy using neural networks, where the similarity between predicted and true labels is measured using the tree-Wasserstein distance. Through experiments using synthetic and real-world datasets, we demonstrate that the proposed method successfully considers the structure of labels during training, and it compares favorably with the Sinkhorn algorithm in terms of computation time and memory usage.

Transformer is a powerful architecture that achieves superior performance on various sequence learning tasks, including neural machine translation, language understanding, and sequence prediction. At the core of the Transformer is the attention mechanism, which concurrently processes all inputs in the streams. In this paper, we present a new formulation of attention via the lens of the kernel. To be more precise, we realize that the attention can be seen as applying kernel smoother over the inputs with the kernel scores being the similarities between inputs. This new formulation gives us a better way to understand individual components of the Transformer’s attention, such as the better way to integrate the positional embedding. Another important advantage of our kernel-based formulation is that it paves the way to a larger space of composing Transformer’s attention. As an example, we propose a new variant of Transformer’s attention which models the input as a product of symmetric kernels. This approach achieves competitive performance to the current state of the art model with less computation. In our experiments, we empirically study different kernel construction strategies on two widely used tasks: neural machine translation and sequence prediction.

Word translation, or bilingual dictionary induction, is an important capability that impacts many multilingual language processing tasks. Recent research has shown that word translation can be achieved in an unsupervised manner, without parallel seed dictionaries or aligned corpora. However, state of the art methods unsupervised bilingual dictionary induction are based on generative adversarial models, and as such suffer from their well known problems of instability and hyper-parameter sensitivity. We present a statistical dependency-based approach to bilingual dictionary induction that is unsupervised – no seed dictionary or parallel corpora required; and introduces no adversary – therefore being much easier to train. Our method performs comparably to adversarial alternatives and outperforms prior non-adversarial methods.