  Can models with particular structure avoid being biased towards spurious
correlation in out-of-distribution (OOD) generalization? Peters et al. (2016)
provides a positive answer for linear cases. In this paper, we use a functional
modular probing method to analyze deep model structures under OOD setting. We
demonstrate that even in biased models (which focus on spurious correlation)
there still exist unbiased functional subnetworks. Furthermore, we articulate
and demonstrate the functional lottery ticket hypothesis: full network contains
a subnetwork that can achieve better OOD performance. We then propose Modular
Risk Minimization to solve the subnetwork selection problem. Our algorithm
learns the subnetwork structure from a given dataset, and can be combined with
any other OOD regularization methods. Experiments on various OOD generalization
tasks corroborate the effectiveness of our method.
