Title: Fair Representation Learning through Implicit Path Alignment. Abstract: We considered a fair representation learning perspective, where optimal predictors, on top of the data representation, are ensured to be invariant with respect to different subgroups.  Specifically, we formulated the problem as a bi-level optimization, where the representation is learned in the outer-level, and invariant optimal group predictors are updated in the inner-level. To avoid the high computational and memory cost of differentiating in the inner-level optimization, we proposed the implicit path alignment algorithm, which only relies on the solution of inner optimization and the implicit differentiation rather than the exact optimization path. Moreover, the proposed bi-level objective is demonstrated to fulfill the sufficient rule, which is desirable in various practical scenarios but was not commonly studied in fair representation learning. We further analyzed the error gap of the implicit approach and empirically validated the proposed method in both classification and regression settings. Experimental results show the consistently better trade-off in prediction performance and fairness measurement.     