- Keywords: orthogonal classifier, invariance
- Abstract: We propose to identify directions invariant to a given classifier so that these directions can be controlled in tasks such as style transfer. While orthogonal decomposition is directly identifiable when the given classifier is linear, we formally define a notion of orthogonality, and when it exists, in the non-linear case. We also provide a surprisingly simple method for constructing the orthogonal classifier (a classifier utilizing directions other than the given classifier). Empirically, we present three use cases where controlling orthogonal variation is important: style transfer, domain adaptation, and fairness. The orthogonal classifier enables partial style transfer, improves domain adaptation with label shifts, and mitigates the unfairness as a predictor.
- One-sentence Summary: We develop a notion of orthogonality in classifier, and the corresponding construction and utility.
- Supplementary Material: zip