What Does Debiasing Really Remove? A Geometric Study of PCA-Based Gender Debiasing in Word Embeddings
Authors: Alexey Kresin, Tchifou M. Dieffi, Tomer Caspi
Organizations: Department of Computer Science, Hood College, Frederick, MD, United States · Department of Mathematics, Ben-Gurion University of the Negev, Be'er Sheva, Israel
Abstract
Debiasing methods based on principal component analysis (PCA) are broadly used to reduce gender bias in word embeddings used in LLMs, yet it remains unclear what aspects of bias they actually remove and how destructive this process is. These methods are based on the understanding that bias resides in a low-dimensional subspace, with the assumption that most of it can be captured by a few principal components. In this work, we conduct a systematic geometric analysis of PCA-based gender debiasing and investigate what is actually removed from the embedding space. Our experiments across multiple embeddings show that direct gender bias is primarily concentrated in the first principal component, supporting the low-rank bias hypothesis. However, associative bias measured by WEAT does not align with these principal directions and is instead spread across multiple embedding dimensions. Furthermore, as expected, we demonstrate that removing an increasing number of principal components leads to a consistent degradation of the embedding geometry, affecting semantic structure and vector relationships. These results reveal that PCA-based debiasing operates as a trade-off: while it effectively reduces certain forms of direct bias, it fails to eliminate distributed associations and introduces geometric distortion. Moreover, there is no universal optimal level of debiasing, as the balance between bias reduction and semantic preservation depends on the chosen metric and embedding. Overall, our findings suggest that bias in word embeddings is not purely low-rank and that simple subspace removal methods may be insufficient for comprehensive debiasing.
We propose Zero-phase Component Analysis (ZCA) whitening as a geometric pre-processing step for the Word Embedding Association Test (WEAT). WEAT is a bias measurement method widely used in both computational social science and AI fairness research. It relies on cosine similarity as a measure of semantic association, which assumes that the embedding space is approximately isotropic. However, prior work has reported that many widely used language models do not satisfy this assumption, raising concerns about the reliability of bias measurements. ZCA whitening transforms the covariance of the embedding space into the identity matrix while minimizing perturbation to the original vectors. This transformation restores the isotropy condition on which WEAT relies. We evaluate our approach on ten standard WEAT test suites and seven models spanning three architectural families, yielding 70 model-task combinations. The results show that ZCA whitening substantially reduces the anisotropy of the embedding spaces across all models. Particularly for highly anisotropic models, we further observe improvements on standard semantic similarity benchmarks, indicating that the calibrated space better captures semantic associations. After calibration, over 30% of WEAT results change significance status, and effect sizes shift in both directions depending on bias category. These shifts suggest that uncalibrated measurements may both overestimate and underestimate the associations encoded in the embedding space. These findings indicate that previously reported bias measurements in anisotropic embedding spaces should be interpreted with caution and may benefit from re-evaluation with calibrated methods. Our approach contributes to restoring the measurement foundation of WEAT across both computational social science and AI fairness research.
During training, Large Language Models (LLMs) learn social regularities that can lead to gender bias in downstream applications. Most mitigation efforts focus on reducing bias in generated outputs, typically evaluated on structured benchmarks, which raises two concerns: output-level evaluation does not reveal whether alignment modifies the model's underlying representations, and structured benchmarks may not reflect realistic usage scenarios. We propose a unified framework to jointly analyze intrinsic and extrinsic gender bias in LLMs using identical neutral prompts, enabling direct comparison between gender-related information encoded in internal representations and bias expressed in generated outputs. Contrary to prior work reporting weak or inconsistent correlations, we find a consistent association between latent gender information and expressed bias when measured under the unified protocol. We further examine the effect of alignment through supervised fine-tuning aimed at reducing gender bias. Our results suggest that while the latter indeed reduces expressed bias, measurable gender-related associations are still present in internal representations, and can be reactivated under adversarial prompting. Finally, we consider two realistic settings and show that debiasing effects observed on structured benchmarks do not necessarily generalize, e.g., to the case of story generation.
The social biases and unwelcome stereotypes revealed by pretrained language models are becoming obstacles to their application. Compared to numerous debiasing methods targeting word level, there has been relatively less attention on biases present at phrase level, limiting the performance of debiasing in discipline domains. In this paper, we propose an automatic multi-token debiasing pipeline called \textbf{General Phrase Debiaser}, which is capable of mitigating phrase-level biases in masked language models. Specifically, our method consists of a \textit{phrase filter stage} that generates stereotypical phrases from Wikipedia pages as well as a \textit{model debias stage} that can debias models at the multi-token level to tackle bias challenges on phrases. The latter searches for prompts that trigger model's bias, and then uses them for debiasing. State-of-the-art results on standard datasets and metrics show that our approach can significantly reduce gender biases on both career and multiple disciplines, across models with varying parameter sizes.