Kernelizing the gender bias-subspace finds no benefit from nonlinearity

Vargas & Cotterell prove Bolukbasi et al. hard-debiasing bias-subspace construction is exactly PCA on a mean-centered design matrix, making explicit the untested linear-subspace hypothesis for gender bias [vargas-cotterell-2020-linear-subspace-hypothesis-gender-bias] They generalize it to kernel PCA and test five kernels against the linear method on word2vec and GloVe across four benchmarks (WEAT, analogy correlation, indirect-bias SVM, SimLex) [vargas-cotterell-2020-linear-subspace-hypothesis-gender-bias] Across every benchmark and kernel, nonlinear kernels perform on par with or worse than the linear kernel, so added nonlinearity buys no extra bias removal [vargas-cotterell-2020-linear-subspace-hypothesis-gender-bias] This gives direct empirical support for treating the gender-bias subspace as linear; no novel causal intervention is performed [vargas-cotterell-2020-linear-subspace-hypothesis-gender-bias]