Neural Bregman Divergences for Distance Learning

Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis), and the algorithm must learn to embed points into the pre-chosen space. The study of non-Euclidean geometries or appropriateness is often not explored, which we believe is due to a lack of tools for learning non-Euclidean measures of distance. Under the belief that the use of asymmetric methods in particular have lacked sufficient study, we propose a new approach to learning arbitrary Bergman divergences in a differentiable manner via input convex neural networks. Over a set of both new and previously studied tasks, including asymmetric regression, ranking, and clustering, we demonstrate that our method more faithfully learns divergences than prior Bregman learning approaches. In doing so we obtain the first method for learning neural Bregman divergences and with it inherit the many nice mathematical properties of Bregman divergences, providing the foundation and tooling for better developing and studying asymmetric distance learning.