Invariant Tensor Feature Coding

We propose a novel feature coding method that exploits invariance. We consider the setting where the transformations that preserve the image contents compose a finite group of orthogonal matrices. This is the case in many image transformations, such as image rotations and image flipping. We prove that the group-invariant feature vector contains sufficient discriminative information when learning a linear classifier using convex loss minimization. From this result, we propose a novel feature modeling for principal component analysis and k-means clustering, which are used for most feature coding methods, and global feature functions that explicitly consider the group action. Although the global feature functions are complex nonlinear functions in general, we can calculate the group action on this space easily by constructing the functions as the tensor product representations of basic representations, resulting in the explicit form of invariant feature functions. We demonstrate the effectiveness of our methods on several image datasets.Comment: 14 pages, 5 figure

A General Theory of Equivariant CNNs on Homogeneous Spaces

We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base space, and layers are equivariant maps between spaces of fields. The theory enables a systematic classification of all existing G-CNNs in terms of their symmetry group, base space, and field type. We also consider a fundamental question: what is the most general kind of equivariant linear map between feature spaces (fields) of given types? Following Mackey, we show that such maps correspond one-to-one with convolutions using equivariant kernels, and characterize the space of such kernels

Learning to Convolve: A Generalized Weight-Tying Approach

Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated, flipped, etc. However, coming up with exact models of how to rotate a 3 x 3 filter on a square pixel-grid is difficult. In this paper, we learn how to transform filters for use in the group convolution, focussing on roto-translation. For this, we learn a filter basis and all rotated versions of that filter basis. Filters are then encoded by a set of rotation invariant coefficients. To rotate a filter, we switch the basis. We demonstrate we can produce feature maps with low sensitivity to input rotations, while achieving high performance on MNIST and CIFAR-10.Comment: Accepted to ICML 201

CB2: Collaborative Natural Language Interaction Research Platform

CB2 is a multi-agent platform to study collaborative natural language interaction in a grounded task-oriented scenario. It includes a 3D game environment, a backend server designed to serve trained models to human agents, and various tools and processes to enable scalable studies. We deploy CB2 at https://cb2.ai as a system demonstration with a learned instruction following model