# Re-evaluating Word Mover's Distance

arXiv: https://arxiv.org/abs/2105.14403 · HTML: https://mlsanity.com/paper/2105.14403/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 100 references that are in the map.
- First posted on arXiv 30 May 2021.

## Builds on (most cited first, 30 of 51)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [MoverScore: Text Generation Evaluating with Contextualized Embeddings and Earth Mover Distance](https://mlsanity.com/paper/1909.02622/) (2019)
- [RocketQA: An Optimized Training Approach to Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2010.08191/) (2020)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Word Alignment by Fine-tuning Embeddings on Parallel Corpora](https://mlsanity.com/paper/2101.08231/) (2021)
- [Are We Really Making Much Progress? A Worrying Analysis of Recent Neural Recommendation Approaches](https://mlsanity.com/paper/1907.06902/) (2019)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Unsupervised Alignment of Embeddings with Wasserstein Procrustes](https://mlsanity.com/paper/1805.11222/) (2018)
- [Subspace Robust Wasserstein Distances](https://mlsanity.com/paper/1901.08949/) (2019)
- [SUPERT: Towards New Frontiers in Unsupervised Evaluation Metrics for Multi-Document Summarization](https://mlsanity.com/paper/2005.03724/) (2020)
- [Sliced Wasserstein Kernels for Probability Distributions](https://mlsanity.com/paper/1511.03198/) (2015)
- [Reinforcement Learning Based Graph-to-Sequence Model for Natural Question Generation](https://mlsanity.com/paper/1908.04942/) (2019)
- [Tree-Sliced Variants of Wasserstein Distances](https://mlsanity.com/paper/1902.00342/) (2019)
- [Baseline Needs More Love: On Simple Word-Embedding-Based Models and Associated Pooling Mechanisms](https://mlsanity.com/paper/1805.09843/) (2018)
- [Hierarchical Optimal Transport for Document Representation](https://mlsanity.com/paper/1906.10827/) (2019)
- [Re-evaluating Automatic Metrics for Image Captioning](https://mlsanity.com/paper/1612.07600/) (2016)
- [Projection Robust Wasserstein Distance and Riemannian Optimization](https://mlsanity.com/paper/2006.07458/) (2020)
- [On the Limitations of Cross-lingual Encoders as Exposed by Reference-Free Machine Translation Evaluation](https://mlsanity.com/paper/2005.01196/) (2020)
- [Discrete Adversarial Attacks and Submodular Optimization with Applications to Text Classification](https://mlsanity.com/paper/1812.00151/) (2018)
- [Improving Sequence-to-Sequence Learning via Optimal Transport](https://mlsanity.com/paper/1901.06283/) (2019)
- [Word Rotator's Distance](https://mlsanity.com/paper/2004.15003/) (2020)
- [Structured Optimal Transport](https://mlsanity.com/paper/1712.06199/) (2017)
- [A Riemannian Block Coordinate Descent Method for Computing the Projection Robust Wasserstein Distance](https://mlsanity.com/paper/2012.05199/) (2020)

## Built on by (most cited first, 10 of 10)

- [WikiWhy: Answering and Explaining Cause-and-Effect Questions](https://mlsanity.com/paper/2210.12152/) (2022)
- [Approximating 1-Wasserstein Distance with Trees](https://mlsanity.com/paper/2206.12116/) (2022)
- [Optimal Transport for Measures with Noisy Tree Metric](https://mlsanity.com/paper/2310.13653/) (2023)
- [Word Tour: One-dimensional Word Embeddings via the Traveling Salesman Problem](https://mlsanity.com/paper/2205.01954/) (2022)
- [Twin Papers: A Simple Framework of Causal Inference for Citations via Coupling](https://mlsanity.com/paper/2208.09862/) (2022)
- [Characterizing and Measuring Linguistic Dataset Drift](https://mlsanity.com/paper/2305.17127/) (2023)
- [Moving Other Way: Exploring Word Mover Distance Extensions](https://mlsanity.com/paper/2202.03119/) (2022)
- [An Empirical Study of Self-supervised Learning with Wasserstein Distance](https://mlsanity.com/paper/2310.10143/) (2023)
- [Advanced Machine Learning Framework for Efficient Plant Disease Prediction](https://mlsanity.com/paper/2409.05174/) (2024)
- [Global Ground Metric Learning with Applications to scRNA data](https://mlsanity.com/paper/2506.15383/) (2025)

## Abstract (arXiv)

The word mover's distance (WMD) is a fundamental technique for measuring the similarity of two documents. As the crux of WMD, it can take advantage of the underlying geometry of the word space by employing an optimal transport formulation. The original study on WMD reported that WMD outperforms classical baselines such as bag-of-words (BOW) and TF-IDF by significant margins in various datasets. In this paper, we point out that the evaluation in the original study could be misleading. We re-evaluate the performances of WMD and the classical baselines and find that the classical baselines are competitive with WMD if we employ an appropriate preprocessing, i.e., L1 normalization. In addition, we introduce an analogy between WMD and L1-normalized BOW and find that not only the performance of WMD but also the distance values resemble those of BOW in high dimensional spaces.