Expected path length on random manifolds
This work addresses the lack of operational tools in representation learning for researchers and practitioners, though it appears incremental as it builds on existing generative models.
The paper tackles the problem of enabling meaningful operations on low-dimensional representations in manifold learning by endowing latent spaces with random Riemannian metrics, and it derives deterministic approximations with tight error bounds on expected distances.
Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provide a meaningful set of operations that are associated with the representation. Working towards operational representation learning, we endow the latent space of a large class of generative models with a random Riemannian metric, which provides us with elementary operators. As computational tools are unavailable for random Riemannian manifolds, we study deterministic approximations and derive tight error bounds on expected distances.