Exploring the Linear Subspace Hypothesis in Gender Bias Mitigation

Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing, pages 2902–2913, November 16–20, 2020. c⃝2020 Association for Computational Linguistics 2902 Exploring the Linear Subspace Hypothesis in Gender Bias Mitigation Francisco VargasD and Ryan CotterellD,Q DUniversity of Cambridge QETH Z¨urich fav25@cam.ac.uk, rcotterell@inf.ethz.ch Abstract Bolukbasi et al. (2016) presents one of the first gender bias mitigation techniques for word embeddings. Their method takes pre-trained word embeddings as input and attempts to iso- late a linear subspace that captures most of the gender bias in the embeddings. As judged by an analogical evaluation task, their method virtually eliminates gender bias in the embed- dings. However, an implicit and untested as- sumption of their method is that the bias sub- space is actually linear. In this work, we gener- alize their method to a kernelized, non-linear version. We take inspiration from kernel prin- cipal component analysis and derive a non- linear bias isolation technique. We discuss and overcome some of the practical drawbacks of our method for non-linear gender bias mitiga- tion in word embeddings and analyze empiri- cally whether the bias subspace is actually lin- ear. Our analysis shows that gender bias is in fact well captured by a linear subspace, justify- ing the assumption of Bolukbasi et al. (2016). 1 Introduction Pre-trained word representations are a necessity for strong performance on modern NLP tasks. These embeddings now serve as input to neural meth- ods (Goldberg, 2017), which recently have become the standard models in the field. However, be- cause these representations are constructed from large, human-created corpora, they naturally con- tain societal biases encoded in that data; gender bias is among the most well studied of these bi- ases (Caliskan et al., 2017). Both a-contextual word embeddings (Mikolov et al., 2013; Penning- ton et al., 2014) and contextual word embeddings (Peters et al., 2018; Devlin et al., 2019) have been shown to encode gender bias (Bolukbasi et al., 2016; Caliskan et al., 2017; Zhao et al., 2019; May et al., 2019; Karve et al., 2019). More im- portantly, the bias in those embeddings has been shown to influence models for downstream tasks where they are used as input, e.g. coreference reso- lution (Rudinger et al., 2018; Zhao et al., 2018). Bolukbasi et al. (2016) present one of the first methods for detecting and mitigating gender bias in word embeddings. They provide a novel linear-algebraic approach that post-processes word embeddings in order to partially remove gender bias. Under their evaluation, they find they can nearly perfectly remove bias in an analogical reasoning task. However, subsequent work (Gonen and Goldberg, 2019; Hall Maudslay et al., 2019) has indicated that gender bias still lingers in the em- beddings, despite Bolukbasi et al. (2016)’s strong experimental results. In the development of their method, Bolukbasi et al. (2016) make a critical and unstated assumption: Gender bias forms a linear subspace of word embedding space. In mathemat- ics, linearity is a strong assumption and there is no reason a-priori why one should expect complex and …

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