10 accepted papers
When the color distribution of input images changes at inference, the performance of conventional neural network architectures drops considerably. A few researchers have begun to incorporate prior knowledge of color geometry in neural network design. These color equivariant architectures have modele…
In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable topological degrees of freedom from learnable geometric dynamics, ena…
From pedestrians to Kuramoto oscillators, interactions between agents govern how dynamical systems evolve in space and time. Discovering how these agents relate to each other has the potential to improve our understanding of the often complex dynamics that underlie these systems. Recent works learn…
We propose GAGrasp, a novel framework for dexterous grasp generation that leverages geometric algebra representations to enforce equivariance to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$S E(3)$</tex> transformations. By encoding the <tex xmlns:m
We propose a new approach to vision-based dexterous grasp translation, which aims to transfer grasp intent across robotic hands with differing morphologies. Given a visual observation of a source hand grasping an object, our goal is to synthesize a functionally equivalent grasp for a target hand wit…
In this paper, we introduce group convolutional neural networks (GCNNs) equivariant to color variation. GCNNs have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale. Despite the improved interpretability, accuracy and generalizabili…
Several popular approaches to 3D vision tasks process multiple views of the input independently with deep neural networks pre-trained on natural images, where view permutation invariance is achieved through a single round of pooling over all views. We argue that this operation discards important inf…
We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we…
Convolutional neural networks (CNNs) are inherently equivariant to translation. Efforts to embed other forms of equivariance have concentrated solely on rotation. We expand the notion of equivariance in CNNs through the Polar Transformer Network (PTN). PTN combines ideas from the Spatial Transformer…
In this paper, we explore the exponential map and its inverse, the logarithm map, for the group SIM(n) of similarity transformations in ℝn which are the composition of a rotation, a translation and a uniform scaling. We give a formula for the exponential map and we prove that it is surjective. We gi…