Related papers: 3D-Rotation-Equivariant Quaternion Neural Networks
Equivariant neural networks enforce symmetry within the structure of their convolutional layers, resulting in a substantial improvement in sample efficiency when learning an equivariant or invariant function. Such models are applicable to…
Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which…
We explain equivariant neural networks, a notion underlying breakthroughs in machine learning from deep convolutional neural networks for computer vision to AlphaFold 2 for protein structure prediction, without assuming knowledge of…
Equivariant neural networks are neural networks with symmetry. Motivated by the theory of group representations, we decompose the layers of an equivariant neural network into simple representations. The nonlinear activation functions lead…
A symmetry on rigid motion is one of the salient factors in efficient learning of 3D point cloud problems. Group convolution has been a representative method to extract equivariant features, but its realizations have struggled to retain…
Numerous studies have recently focused on incorporating different variations of equivariance in Convolutional Neural Networks (CNNs). In particular, rotation-equivariance has gathered significant attention due to its relevance in many…
Point cloud analysis is a fundamental task in 3D computer vision. Most previous works have conducted experiments on synthetic datasets with well-aligned data; while real-world point clouds are often not pre-aligned. How to achieve rotation…
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…
Learning rotation-invariant distinctive features is a fundamental requirement for point cloud registration. Existing methods often use rotation-sensitive networks to extract features, while employing rotation augmentation to learn an…
We propose a novel quaternion product unit (QPU) to represent data on 3D rotation groups. The QPU leverages quaternion algebra and the law of 3D rotation group, representing 3D rotation data as quaternions and merging them via a weighted…
Despite the importance of image representations such as histograms of oriented gradients and deep Convolutional Neural Networks (CNN), our theoretical understanding of them remains limited. Aiming at filling this gap, we investigate three…
Various recent methods attempt to implement rotation-invariant 3D deep learning by replacing the input coordinates of points with relative distances and angles. Due to the incompleteness of these low-level features, they have to undertake…
In this work we investigate how to achieve equivariance to input transformations in deep networks, purely from data, without being given a model of those transformations. Convolutional Neural Networks (CNNs), for example, are equivariant to…
Recent investigations on rotation invariance for 3D point clouds have been devoted to devising rotation-invariant feature descriptors or learning canonical spaces where objects are semantically aligned. Examinations of learning frameworks…
The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries…
This paper introduces Quaternion Approximate Networks (QUAN), a novel deep learning framework that leverages quaternion algebra for rotation equivariant image classification and object detection. Unlike conventional quaternion neural…
Spherical equivariant graph neural networks (EGNNs) provide a principled framework for learning on three-dimensional molecular and biomolecular systems, where predictions must respect the rotational symmetries inherent in physics. These…
Despite the progress on 3D point cloud deep learning, most prior works focus on learning features that are invariant to translation and point permutation, and very limited efforts have been devoted for rotation invariant property. Several…
This paper presents a novel framework combining group equivariant convolutional neural networks (G-CNNs) with equivariant-aware structured pruning to produce compact, transformation-invariant models for resource-constrained environments.…
The ability of convolutional neural networks (CNNs) to recognize objects regardless of their position in the image is due to the translation-equivariance of the convolutional operation. Group-equivariant CNNs transfer this equivariance to…