Related papers: A Geometric Approach to Steerable Convolutions
Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph…
Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we…
It is well known that vision classification models suffer from poor calibration in the face of data distribution shifts. In this paper, we take a geometric approach to this problem. We propose Geometric Sensitivity Decomposition (GSD) which…
Convolutional Neural Networks (CNNs) have been widely applied. But as the CNNs grow, the number of arithmetic operations and memory footprint also increase. Furthermore, typical non-linear activation functions do not allow associativity of…
Despite advances in feature representation, leveraging geometric relations is crucial for establishing reliable visual correspondences under large variations of images. In this work we introduce a Hough transform perspective on…
Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…
An important goal in visual recognition is to devise image representations that are invariant to particular transformations. In this paper, we address this goal with a new type of convolutional neural network (CNN) whose invariance is…
This paper introduces a generalization of Convolutional Neural Networks (CNNs) from low-dimensional grid data, such as images, to graph-structured data. We propose a novel spatial convolution utilizing a random walk to uncover the relations…
We introduce, TextureNet, a neural network architecture designed to extract features from high-resolution signals associated with 3D surface meshes (e.g., color texture maps). The key idea is to utilize a 4-rotational symmetric (4-RoSy)…
The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…
Image guided depth completion aims to recover per-pixel dense depth maps from sparse depth measurements with the help of aligned color images, which has a wide range of applications from robotics to autonomous driving. However, the 3D…
Despite advances in feature representation, leveraging geometric relations is crucial for establishing reliable visual correspondences under large variations of images. In this work we introduce a Hough transform perspective on…
Neural networks are omnipresent, but remain poorly understood. Their increasing complexity and use in critical systems raises the important challenge to full interpretability. We propose to address a simple well-posed learning problem:…
Very deep convolutional neural networks (CNNs) have been firmly established as the primary methods for many computer vision tasks. However, most state-of-the-art CNNs are large, which results in high inference latency. Recently, depth-wise…
Applying convolutional neural networks to spherical images requires particular considerations. We look to the millennia of work on cartographic map projections to provide the tools to define an optimal representation of spherical images for…
We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…
Convolutional neural networks use regular quadrilateral convolution kernels to extract features. Since the number of parameters increases quadratically with the size of the convolution kernel, many popular models use small convolution…
Predicting the evolution of a representative sample of a material with microstructure is a fundamental problem in homogenization. In this work we propose a graph convolutional neural network that utilizes the discretized representation of…
The ability to design complex neural network architectures which enable effective training by stochastic gradient descent has been the key for many achievements in the field of deep learning. However, developing such architectures remains a…
This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…