# Evaluating Metrics for Bias in Word Embeddings

arXiv: https://arxiv.org/abs/2111.07864 · HTML: https://mlsanity.com/paper/2111.07864/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 32 references that are in the map.
- First posted on arXiv 15 Nov 2021.

## Builds on (most cited first, 25 of 25)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Semantics derived automatically from language corpora contain human-like biases](https://mlsanity.com/paper/1608.07187/) (2016)
- [Gender Bias in Coreference Resolution: Evaluation and Debiasing Methods](https://mlsanity.com/paper/1804.06876/) (2018)
- [Universal Sentence Encoder](https://mlsanity.com/paper/1803.11175/) (2018)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [On Measuring Social Biases in Sentence Encoders](https://mlsanity.com/paper/1903.10561/) (2019)
- [Measuring Bias in Contextualized Word Representations](https://mlsanity.com/paper/1906.07337/) (2019)
- [Lipstick on a Pig: Debiasing Methods Cover up Systematic Gender Biases in Word Embeddings But do not Remove Them](https://mlsanity.com/paper/1903.03862/) (2019)
- [Gender Bias in Contextualized Word Embeddings](https://mlsanity.com/paper/1904.03310/) (2019)
- [Towards Debiasing Sentence Representations](https://mlsanity.com/paper/2007.08100/) (2020)
- [Black is to Criminal as Caucasian is to Police: Detecting and Removing Multiclass Bias in Word Embeddings](https://mlsanity.com/paper/1904.04047/) (2019)
- [Evaluating the Underlying Gender Bias in Contextualized Word Embeddings](https://mlsanity.com/paper/1904.08783/) (2019)
- [Understanding Undesirable Word Embedding Associations](https://mlsanity.com/paper/1908.06361/) (2019)
- [Stereotype and Skew: Quantifying Gender Bias in Pre-trained and Fine-tuned Language Models](https://mlsanity.com/paper/2101.09688/) (2021)
- [Learning General Purpose Distributed Sentence Representations via Large Scale Multi-task Learning](https://mlsanity.com/paper/1804.00079/) (2018)
- [Examining Gender Bias in Languages with Grammatical Gender](https://mlsanity.com/paper/1909.02224/) (2019)
- [What are the biases in my word embedding?](https://mlsanity.com/paper/1812.08769/) (2018)
- [Dictionary-based Debiasing of Pre-trained Word Embeddings](https://mlsanity.com/paper/2101.09525/) (2021)
- [Trans-Encoder: Unsupervised sentence-pair modelling through self- and mutual-distillations](https://mlsanity.com/paper/2109.13059/) (2021)
- [Conceptor Debiasing of Word Representations Evaluated on WEAT](https://mlsanity.com/paper/1906.05993/) (2019)
- [Text Similarity in Vector Space Models: A Comparative Study](https://mlsanity.com/paper/1810.00664/) (2018)

## Built on by (most cited first, 7 of 7)

- [No Word Embedding Model Is Perfect: Evaluating the Representation Accuracy for Social Bias in the Media](https://mlsanity.com/paper/2211.03634/) (2022)
- [AMBEDKAR-A Multi-level Bias Elimination through a Decoding Approach with Knowledge Augmentation for Robust Constitutional Alignment of Language Models](https://mlsanity.com/paper/2509.02133/) (2025)
- [Legally Binding but Unfair? Towards Assessing Fairness of Privacy Policies](https://mlsanity.com/paper/2403.08115/) (2024)
- [The SAME score: Improved cosine based bias score for word embeddings](https://mlsanity.com/paper/2203.14603/) (2022)
- [Detecting and Mitigating Indirect Stereotypes in Word Embeddings](https://mlsanity.com/paper/2305.14574/) (2023)
- [A Bayesian approach to uncertainty in word embedding bias estimation](https://mlsanity.com/paper/2306.09066/) (2023)
- [Semantic Properties of cosine based bias scores for word embeddings](https://mlsanity.com/paper/2401.15499/) (2024)

## Abstract (arXiv)

Over the last years, word and sentence embeddings have established as text preprocessing for all kinds of NLP tasks and improved the performances significantly. Unfortunately, it has also been shown that these embeddings inherit various kinds of biases from the training data and thereby pass on biases present in society to NLP solutions. Many papers attempted to quantify bias in word or sentence embeddings to evaluate debiasing methods or compare different embedding models, usually with cosine-based metrics. However, lately some works have raised doubts about these metrics showing that even though such metrics report low biases, other tests still show biases. In fact, there is a great variety of bias metrics or tests proposed in the literature without any consensus on the optimal solutions. Yet we lack works that evaluate bias metrics on a theoretical level or elaborate the advantages and disadvantages of different bias metrics. In this work, we will explore different cosine based bias metrics. We formalize a bias definition based on the ideas from previous works and derive conditions for bias metrics. Furthermore, we thoroughly investigate the existing cosine-based metrics and their limitations to show why these metrics can fail to report biases in some cases. Finally, we propose a new metric, SAME, to address the shortcomings of existing metrics and mathematically prove that SAME behaves appropriately.