Group Equivariant Convolutional Networks (2016-02-24T00:00:00.000000Z)

TL;DR

Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries and achieves state of the art results on CI- FAR10 and rotated MNIST.

Abstract

We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that enjoys a substantially higher degree of weight sharing than regular convolution layers. G-convolutions increase the expressive capacity of the network without increasing the number of parameters. Group convolution layers are easy to use and can be implemented with negligible computational overhead for discrete groups generated by translations, reflections and rotations. G-CNNs achieve state of the art results on CI- FAR10 and rotated MNIST.

Authors

Taco Cohen

5 papers

M. Welling

17 papers

TL;DR

Abstract

Authors

References56 items

Wide Residual Networks

Identity Mappings in Deep Residual Networks

Exploiting Cyclic Symmetry in Convolutional Neural Networks

Deep Residual Learning for Image Recognition

Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)

Generalizing Pooling Functions in Convolutional Neural Networks: Mixed, Gated, and Tree

Fast Algorithms for Convolutional Neural Networks

Training Very Deep Networks

Spatial Transformer Networks

Learning to See by Moving

Rotation-invariant convolutional neural networks for galaxy morphology prediction

On Invariance and Selectivity in Representation Learning

Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

Deep roto-translation scattering for object classification

Transformation Properties of Learned Visual Representations

Fast Convolutional Nets With fbfft: A GPU Performance Evaluation

Adam: A Method for Stochastic Optimization

Striving for Simplicity: The All Convolutional Net

Fractional Max-Pooling

Deep Symmetry Networks

Understanding Image Representations by Measuring Their Equivariance and Equivalence

Deeply-Supervised Nets

Learning the Irreducible Representations of Commutative Lie Groups

Fast Training of Convolutional Networks through FFTs

Network In Network

Unsupervised learning of invariant representations with low sample complexity: the magic of sensory cortex or a new framework for machine learning?

Unsupervised Learning of Invariant Representations in Hierarchical Architectures

Distributed Representations of Words and Phrases and their Compositionality

Regularization of Neural Networks using DropConnect

Rotation, Scaling and Deformation Invariant Scattering for Texture Discrimination

Maxout Networks

ImageNet classification with deep convolutional neural networks

Learning Invariant Representations with Local Transformations

Learning rotation-aware features: From invariant priors to equivariant descriptors

Learning Intermediate-Level Representations of Form and Motion from Natural Movies

Invariant Scattering Convolution Networks

Learning hierarchical invariant spatio-temporal features for action recognition with independent subspace analysis

Transforming Auto-Encoders

Transformation Equivariant Boltzmann Machines

Learning to Represent Spatial Transformations with Factored Higher-Order Boltzmann Machines

An empirical evaluation of deep architectures on problems with many factors of variation

A novel set of rotationally and translationally invariant features for images based on the non-commutative bispectrum

Integral Invariants for Shape Matching

Distinctive Image Features from Scale-Invariant Keypoints

Emergence of Phase- and Shift-Invariant Features by Decomposition of Natural Images into Independent Feature Subspaces

Emergence of invariant-feature detectors in the adaptive-subspace self-organizing map

International Conference on Learning Representations (ICLR)

Deep Learning

Discriminative template learning in group-convolutional networks for invariant speech representations

Proceedings of the 30th International Conference on Machine Learning, ICML 2013, Atlanta, GA, USA, 16-21 June 2013

Spherical tensor algebra for biomedical image analysis = Sphärische Tensor Algebra für die Biomedizinische Bildanalyse

Proceedings of The 28th International Conference on Machine Learning

Group integration techniques in pattern analysis - a kernel view

Monthly Notices of the Royal Astronomical Society

Uber die Erzeugung von Invarianten durch Integration Nachrichten von der Kgl

Nervana Systems reproduction of Springenberg et al., 2016. URL https

Field of Study

Journal Information

Name

Volume

Venue Information

Name

Type

URL

Alternate Names