Debiasing Word Embeddings with Nonlinear Geometry (2022)

Abstract: Debiasing word embeddings has been largely limited to individual and independent social categories. However, real-world corpora typically present multiple social categories that possibly correlate or intersect with each other. For instance, “hair weaves” is stereotypically associated with African American females, but neither African American nor females alone. Therefore, this work studies biases associated with multiple social categories: joint biases induced by the union of different categories and intersectional biases that do not overlap with the biases of the constituent categories. We first empirically observe that individual biases intersect non-trivially (i.e., over a one-dimensional subspace). Drawing from the intersectional theory in social science and the linguistic theory, we then construct an intersectional subspace to debias for multiple social categories using the nonlinear geometry of individual biases. Empirical evaluations corroborate the efficacy of our approach.

## introduction due to the reliance on the large-scale text corpora for training, it has been observed that word embeddings are prone to express social biases inherent in the data @xcite . prior research (e.g. @xcite in debiasing word embeddings mitigates biases associated with individual social categories and treats each category in isolation. for example, the seminal hard-debiasing approach @xcite identifies the bias direction of a category (e.g., gender) and then removes the direction from the target word such that it is equidistant to all groups (e.g., female and male at a binary level with gender) in the category. however, real-world training corpora typically present multiple social categories (e.g., gender and race), possibly with higher cardinality. these social categories can further correlate or intersect with each other @xcite . despite the promising results, debiasing for individual social categories limits our understanding of the complex nature of social biases. alternatively, we might consider biases in the presence of multiple social categories @xcite @xcite . this can result in at least two scenarios, as depicted in fig. 1 . first, word embeddings can simultaneously present multiple biases that might nontrivially correlate with each other. for example, debiasing for gender can influence the results of racial bias. in the literature of social psychology, a number of works (e.g. @xcite @xcite studied the interrelationship between various biases, a.k.a. "generalized prejudice". we refer to bias induced by the union of different social categories as joint biases. second, a few recent works (e.g. @xcite detected intersectional biases in word embeddings, which is the bias that does not overlap with the biases of their constituent identities. for example, "hair weaves" is stereotypically associated with african american females @xcite . the primary goal of this work is to mitigate the two kinds of biases in word embeddings. there are several challenges: first, it is highly possible that different biases are nonlinearly correlated @xcite . simply taking a linear combination of individual bias subspaces (e.g., sum or mean of all bias subspaces) might lead to ineffective solutions that even amplify individual biases. second, identifying a bias subspace typically needs predefined word sets related to target groups. these sets are curated by experts to most accurately represent each group and the associated social biases. this can be time-consuming and requires great human effort. existing sets for identifying intersectional groups are extremely limited. they are small and exclusively used for the intersectionality of gender and race @xcite . therefore, relying on predefined sets limits the use of debiasing approaches in practice. to address these challenges, we first empirically observe that individual bias subspaces constructed via existing word sets intersect over a onedimensional subspace. we then relate our findings to the intersectionality theory by @xcite and the linguistic theory introduced by @xcite . the result is a hypothesis that the bias subspace for multiple social categories roughly resides in the intersection of all individual bias subspaces. the proposed approach (coined as joint and intersectional debiasing, josec) departs from the linear correlation assumption and leverages the nonlinear geometry of subspace representations to learn an intersectional subspace. josec does not need any additional human-coded defining sets for intersectional groups except for the defining sets for the constituent groups. we contribute to: ## related work early efforts in debiasing word embeddings have been focused on gender. the seminal work by @xcite proposed a post-processing approach that projects gender-neutral words into a gender subspace identified by defining sets of gendered words such as she, he, man, woman. gender bias can then be alleviated through harddebiasing in which the bias components in non-gendered words (e.g., doctor, nurse) are first removed and the gendered words are then centered and equalized. @xcite further extended the hard-debiasing method to multi-class settings such as race. given a corpus, one can also learn gender-neutral word embeddings by modifying the glove @xcite objective function @xcite . this in-processing approach was further extended to a post-processing approach by @xcite , who suggested preserving gender-related information using autoencoder. previous research as well as our work focuses on static word embeddings, however, stereotyped biases have also been found in contextualized word embeddings, e.g., @xcite . despite the fruitful results, most prior works were found to remove biases superficially and fail to deliver gender-neutral embeddings @xcite . therefore, it is increasingly observable that existing bias removal techniques are insufficient to guarantee gender-neural modeling. the majority of existing works were also criticized for not examining the impact of gender bias in real-world applications @xcite . in contrast to prior research focused on one form of bias in debiasing word embeddings, this work aims to provide a simple yet effective approach for bias mitigation in the presence of multiple bias forms. as human-like biases exist in the majority of word embeddings and debiasing approaches are unlikely to largely affect our results, we build our approach upon the seminal hard-debiasing algorithm by @xcite . future research is warranted to investigate other debiasing approaches. for intersectional bias, most of the existing works are in social science and psychology literature, such as @xcite @xcite . comparatively fewer efforts can be found in the computer science field. one such work @xcite examined the intersectional accuracy disparities in commercial gender classification systems. for contextualized word embeddings, @xcite and tan and celis (2019) measured the emergent intersectional biases of african american females using attributes presented in @xcite . in complement to weat, @xcite proposed the contextualized embedding association test (ceat) to measure the intersectional bias. these methods detect intersectional bias using the defining and attribute sets related to intersectional groups. in summary, this work complements prior research by mitigating biases related to multiple social categories. josec does not rely on the humancoded word sets used to define the intersectional groups to identify the bias subspace. while this work focuses on non-contextualized embeddings, research (e.g., @xcite ; lepori, 2020) has found contextualized word embeddings such as bert @xcite display intersectional biases. we leave it for future exploration. ## preliminary in this section, we briefly review the backbone model of this work: the seminal hard-debiasing method @xcite and its extension. it consists of two steps: identifying the bias subspace and removing bias components. ## method existing approaches for debiasing word embeddings work on individual categories, rendering incomplete measurement of various social biases @xcite . to account for biases associated with multiple social categories, we need to address the primary challenges of the potential non-linear correlations between biases and the difficulty of curating defining sets to identify the bias subspace for these categories. in this section, we introduce the proposed approach -josec -for identifying such a subspace without additional human-coded defining set, which we refer to as the intersectional subspace. ## experiments we validate the efficacy of the proposed intersectional subspace for debiasing word embeddings with multiple social categories. we answer the following research questions: how does josec fare against baselines for mitigating (rq. 1) joint biases and (rq. 2) intersectional biases? how does josec influence the (rq. 3) utility of word embeddings in downstream tasks and (rq. 4) biases in downstream tasks such as toxicity detection? ## discussions this work studies joint biases induced by the union of multiple categories and the intersectional biases that do not overlap with biases of the constituent categories. challenges arise from the potential nonlinearity between different biases and the difficulty of curating human-coded word lists for identifying intersectional bias subspace. we first empirically showed that different biases intersect non-trivially. informed by the intersectionality theory and the linguistic theory by firth, we propose a simple yet effective approach (josec) for constructing the intersectional bias subspace using the nonlinear geometry of bias subspaces. josec can reduce intrinsic bias without losing the semantic utility of word embeddings. the broad result of this research is that it is critical to consider biases associated with multiple social categories given the complex nature of human-like biases. we do note several limitations of this study. first, the empirical observation of the nonlinearity be-tween different biases needs more rigorous theoretical proof/evidence. a potential result would be an in-depth analysis of bias correlations in a variety of nlp tasks. questions such as "how are biases correlated? negative or positive correlation?" might be investigated. second, research should be conducted to study how to reduce joint and intersectional biases in contextualized word embeddings such as bert and gpt-3. third, josec focuses on intrinsic measures, which remain good descriptive metrics for computational social science @xcite . however, it might not be relied on to mitigate biases in downstream applications. as real-world scenarios can be more challenging and complicated (e.g., biases induced in the deployment), it is necessary to extend this research to extrinsic measures of biases, which might vary in different applications. meanwhile, research needs to focus on a more rigorous and transparent data collection process (e.g., recording demographic and identity information of annotators) @xcite to help reduce downstream biases. challenging sets to measure application bias such as @xcite need to be created to test the robustness of debiasing methods.