Related papers: A Geometric Approach to Steerable Convolutions
We propose a spherical kernel for efficient graph convolution of 3D point clouds. Our metric-based kernels systematically quantize the local 3D space to identify distinctive geometric relationships in the data. Similar to the regular grid…
Graph Convolutional Networks (GCNs) have shown to be effective in handling unordered data like point clouds and meshes. In this work we propose novel approaches for graph convolution, pooling and unpooling, inspired from finite differences…
We present a versatile formulation of the convolution operation that we term a "mapped convolution." The standard convolution operation implicitly samples the pixel grid and computes a weighted sum. Our mapped convolution decouples these…
Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors, which can lead to a considerably improved performance. Recent advances in the theoretical description of GCNNs revealed…
Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…
Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints. They leverage concepts from group representation theory, non-commutative harmonic analysis and…
We consider Convolutional Neural Networks (CNNs) with 2D structured features that are symmetric in the spatial dimensions. Such networks arise in modeling pairwise relationships for a sequential recommendation problem, as well as secondary…
We propose an octree guided neural network architecture and spherical convolutional kernel for machine learning from arbitrary 3D point clouds. The network architecture capitalizes on the sparse nature of irregular point clouds, and…
Despite the decomposition of convolutional kernels for lightweight CNNs being well studied, existing works that rely on tensor network diagrams or hyperdimensional abstraction lack geometry intuition. This work devises a new perspective by…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies.…
Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…
Recent advances in depthwise-separable convolutional neural networks (DS-CNNs) have led to novel architectures, that surpass the performance of classical CNNs, by a considerable scalability and accuracy margin. This paper reveals another…
We provide a novel new approach for aligning geometric models using a dual graph structure where local features are mapping probabilities. Alignment of non-rigid structures is one of the most challenging computer vision tasks due to the…
Parametric approaches to Learning, such as deep learning (DL), are highly popular in nonlinear regression, in spite of their extremely difficult training with their increasing complexity (e.g. number of layers in DL). In this paper, we…
Encoder-decoder networks using convolutional neural network (CNN) architecture have been extensively used in deep learning literatures thanks to its excellent performance for various inverse problems. However, it is still difficult to…
Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…
In modern computer vision, images are typically represented as a fixed uniform grid with some stride and processed via a deep convolutional neural network. We argue that deforming the grid to better align with the high-frequency image…
Normalization Layers (NLs) are widely used in modern deep-learning architectures. Despite their apparent simplicity, their effect on optimization is not yet fully understood. This paper introduces a spherical framework to study the…
Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…