Learning disentangled representations via product manifold projection
This addresses the challenge of learning disentangled representations for various data types, such as images and 3D surfaces, with potential applications in fields like computer vision and machine learning, though it appears incremental as it builds on existing manifold-based ideas.
The paper tackles the problem of disentangling generative factors of variation in data by modeling the underlying manifold as a product of submanifolds, resulting in a weakly-supervised algorithm that performs favorably compared to state-of-the-art methods on synthetic and real-world benchmarks.
We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly modeled as a product of submanifolds. This definition of disentanglement gives rise to a novel weakly-supervised algorithm for recovering the unknown explanatory factors behind the data. At training time, our algorithm only requires pairs of non i.i.d. data samples whose elements share at least one, possibly multidimensional, generative factor of variation. We require no knowledge on the nature of these transformations, and do not make any limiting assumption on the properties of each subspace. Our approach is easy to implement, and can be successfully applied to different kinds of data (from images to 3D surfaces) undergoing arbitrary transformations. In addition to standard synthetic benchmarks, we showcase our method in challenging real-world applications, where we compare favorably with the state of the art.