Convex Representation Learning for Generalized Invariance in Semi-Inner-Product Space
This work addresses the challenge of nonconvex optimization in representation learning for machine learning practitioners, offering a convex alternative for generalized invariances.
The authors tackled the problem of learning invariant representations, which is typically nonconvex with regularization methods, by developing a convex algorithm for generalized invariances modeled as semi-norms. They introduced novel Euclidean embeddings in a semi-inner-product space, established approximation bounds, and demonstrated efficient learning with accurate predictions in experiments.
Invariance (defined in a general sense) has been one of the most effective priors for representation learning. Direct factorization of parametric models is feasible only for a small range of invariances, while regularization approaches, despite improved generality, lead to nonconvex optimization. In this work, we develop a convex representation learning algorithm for a variety of generalized invariances that can be modeled as semi-norms. Novel Euclidean embeddings are introduced for kernel representers in a semi-inner-product space, and approximation bounds are established. This allows invariant representations to be learned efficiently and effectively as confirmed in our experiments, along with accurate predictions.