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Disentangling by Subspace Diffusion
David Pfau · Irina Higgins · Alex Botev · Sébastien Racanière

Tue Dec 08 09:00 AM -- 11:00 AM (PST) @ Poster Session 1 #414

We present a novel nonparametric algorithm for symmetry-based disentangling of data manifolds, the Geometric Manifold Component Estimator (GEOMANCER). GEOMANCER provides a partial answer to the question posed by Higgins et al.(2018): is it possible to learn how to factorize a Lie group solely from observations of the orbit of an object it acts on? We show that fully unsupervised factorization of a data manifold is possible if the true metric of the manifold is known and each factor manifold has nontrivial holonomy – for example, rotation in 3D. Our algorithm works by estimating the subspaces that are invariant under random walk diffusion, giving an approximation to the de Rham decomposition from differential geometry. We demonstrate the efficacy of GEOMANCER on several complex synthetic manifolds. Our work reduces the question of whether unsupervised disentangling is possible to the question of whether unsupervised metric learning is possible, providing a unifying insight into the geometric nature of representation learning.

Author Information

David Pfau (DeepMind)
Irina Higgins (DeepMind)
Alex Botev (DeepMind)
Sébastien Racanière (DeepMind)

Sébastien Racanière is a Staff Research Engineer in DeepMind. His current interests in ML revolve around the interaction between Physics and Machine Learning, with an emphasis on the use of symmetries. He got his PhD in pure mathematics from the Université Louis Pasteur, Strasbourg, in 2002, with co-supervisors Michèle Audin (Strasbourg) and Frances Kirwan (Oxford). This was followed by a two years Marie-Curie Individual Fellowship in Imperial College, London, and another postdoc in Cambridge (UK). His first job in the industry was at the Samsung European Research Institute, investigating the use of Learning Algorithms in mobile phones, followed by UGS, a Cambridge based company, working on a 3D search engine. He afterwards worked for Maxeler, in London, programming FPGAs. He then moved to Google, and finally DeepMind.

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