Transformation Properties of Learned Visual Representations
arXiv:1412.7659
Abstract
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).
T.S. Cohen & M. Welling, Transformation Properties of Learned Visual Representations. In International Conference on Learning Representations (ICLR), 2015
References in corpus (1)
Cited by in corpus (10)
- Why do deep convolutional networks generalize so poorly to small image transformations?
- Inferring low-dimensional microstructure representations using convolutional neural networks
- Unsupervised Learning of 3D Structure from Images
- Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations
- Deferred Neural Rendering: Image Synthesis using Neural Textures
- Projecting Trouble: Light Based Adversarial Attacks on Deep Learning Classifiers
- The Effect of Learning Strategy versus Inherent Architecture Properties on the Ability of Convolutional Neural Networks to Develop Transformation Invariance
- On the effect of pooling on the geometry of representations
- Dynamic Variational Autoencoders for Visual Process Modeling
- Quantifying the Effects of Enforcing Disentanglement on Variational Autoencoders