5 research outputs found
Transformation Properties of Learned Visual Representations
When a three-dimensional object moves relative to an observer, a change
occurs on the observer's image plane and in the visual representation computed
by a learned model. Starting with the idea that a good visual representation is
one that transforms linearly under scene motions, we show, using the theory of
group representations, that any such representation is equivalent to a
combination of the elementary irreducible representations. We derive a striking
relationship between irreducibility and the statistical dependency structure of
the representation, by showing that under restricted conditions, irreducible
representations are decorrelated. Under partial observability, as induced by
the perspective projection of a scene onto the image plane, the motion group
does not have a linear action on the space of images, so that it becomes
necessary to perform inference over a latent representation that does transform
linearly. This idea is demonstrated in a model of rotating NORB objects that
employs a latent representation of the non-commutative 3D rotation group SO(3).Comment: T.S. Cohen & M. Welling, Transformation Properties of Learned Visual
Representations. In International Conference on Learning Representations
(ICLR), 201
Symmetry Regularization
The properties of a representation, such as smoothness, adaptability, generality, equivari- ance/invariance, depend on restrictions imposed during learning. In this paper, we propose using data symmetries, in the sense of equivalences under transformations, as a means for learning symmetry- adapted representations, i.e., representations that are equivariant to transformations in the original space. We provide a sufficient condition to enforce the representation, for example the weights of a neural network layer or the atoms of a dictionary, to have a group structure and specifically the group structure in an unlabeled training set. By reducing the analysis of generic group symmetries to per- mutation symmetries, we devise an analytic expression for a regularization scheme and a permutation invariant metric on the representation space. Our work provides a proof of concept on why and how to learn equivariant representations, without explicit knowledge of the underlying symmetries in the data.This material is based upon work supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF-1231216
Efficient Methods for Unsupervised Learning of Probabilistic Models
In this thesis I develop a variety of techniques to train, evaluate, and
sample from intractable and high dimensional probabilistic models. Abstract
exceeds arXiv space limitations -- see PDF