Representation Transfer by Optimal Transport

Deep learning currently provides the best representations of complex objects for a wide variety of tasks. However, learning these representations is an expensive process that requires very large training samples and significant computing resources. Thankfully, sharing these representations is a common practice, enabling to solve new tasks with relatively little training data and few computing resources; the transfer of representations is nowadays an essential ingredient in numerous real-world applications of deep learning. Transferring representations commonly relies on the parameterized form of the features making up the representation, as encoded by the computational graph of these features. In this paper, we propose to use a novel non-parametric metric between representations. It is based on a functional view of features, and takes into account certain invariances of representations, such as the permutation of their features, by relying on optimal transport. This distance is used as a regularization term promoting similarity between two representations. We show the relevance of this approach in two representation transfer settings, where the representation of a trained reference model is transferred to another one, for solving a new related task (inductive transfer learning), or for distilling knowledge to a simpler model (model compression).