Related papers: A Geometric Approach to Steerable Convolutions

D shape generation is a fundamental operation in computer graphics. While significant progress has been made, especially with recent deep generative models, it remains a challenge to synthesize high-quality shapes with rich geometric…

Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the…

This paper is concerned with a fundamental problem in geometric deep learning that arises in the construction of convolutional neural networks on surfaces. Due to curvature, the transport of filter kernels on surfaces results in a…

Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…

We propose a generalization of convolutional neural networks (CNNs) to irregular domains, through the use of a translation operator on a graph structure. In regular settings such as images, convolutional layers are designed by translating a…

This paper addresses the challenges of designing mesh convolution neural networks for 3D mesh dense prediction. While deep learning has achieved remarkable success in image dense prediction tasks, directly applying or extending these…

The Gaussian kernel and its derivatives have already been employed for Convolutional Neural Networks in several previous works. Most of these papers proposed to compute filters by linearly combining one or several bases of fixed or slightly…

We introduce a guide to help deep learning practitioners understand and manipulate convolutional neural network architectures. The guide clarifies the relationship between various properties (input shape, kernel shape, zero padding, strides…

In this paper, we propose deformable deep convolutional neural networks for generic object detection. This new deep learning object detection framework has innovations in multiple aspects. In the proposed new deep architecture, a new…

The large spatial/temporal/frequency scale of geoscience and remote-sensing datasets causes memory issues when using convolutional neural networks for (sub-) surface data segmentation. Recently developed fully reversible or fully invertible…

Steerable CNN imposes the prior knowledge of transformation invariance or equivariance in the network architecture to enhance the the network robustness on geometry transformation of data and reduce overfitting. It has been an intuitive and…

The distance-geometric graph representation adopts a unified scheme (distance) for representing the geometry of three-dimensional(3D) graphs. It is invariant to rotation and translation of the graph and it reflects pair-wise node…

Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as…

We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…

We introduce a new framework for manipulating and interacting with deep generative models that we call network bending. We present a comprehensive set of deterministic transformations that can be inserted as distinct layers into the…

We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations.…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…

In this paper, we propose a geometric framework to analyze the convergence properties of gradient descent trajectories in the context of linear neural networks. We translate a well-known empirical observation of linear neural nets into a…

Symmetry-aware architectures are central to geometric deep learning. We present a systematic approach for constructing continuous rotationally invariant and equivariant functions using symmetric tensor networks. The proposed framework…

Recently, non-stationary spectral kernels have drawn much attention, owing to its powerful feature representation ability in revealing long-range correlations and input-dependent characteristics. However, non-stationary spectral kernels are…