Constructing good representations is critical for learning complex tasks in a\nsample efficient manner. In the context of meta-learning, representations can\nbe constructed from common patterns of previously seen tasks so that a future\ntask can be learned quickly. While recent works show the benefit of\nsubspace-based representations, such results are limited to linear-regression\ntasks. This work explores a more general class of nonlinear tasks with\napplications ranging from binary classification, generalized linear models and\nneural nets. We prove that subspace-based representations can be learned in a\nsample-efficient manner and provably benefit future tasks in terms of sample\ncomplexity. Numerical results verify the theoretical predictions in\nclassification and neural-network regression tasks.\n