Related papers: Rotation-Invariant Point Convolution With Multiple…
Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…
Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction.…
Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…
Objects in aerial images have greater variations in scale and orientation than in typical images, so detection is more difficult. Convolutional neural networks use a variety of frequency- and orientation-specific kernels to identify objects…
The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In…
Despite the successes of deep learning in computer vision, difficulties persist in recognizing objects that have undergone group-symmetric transformations rarely seen during training$\unicode{x2013}$for example objects seen in unusual…
We investigate the optimization of neural networks on symmetric data, and compare the strategy of constraining the architecture to be equivariant to that of using data augmentation. Our analysis reveals that that the relative geometry of…
This work is about understanding the impact of invariance and equivariance on generalisation in supervised learning. We use the perspective afforded by an averaging operator to show that for any predictor that is not equivariant, there is…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…
This work introduces E3x, a software package for building neural networks that are equivariant with respect to the Euclidean group $\mathrm{E}(3)$, consisting of translations, rotations, and reflections of three-dimensional space. Compared…
Rectifying the orientation of images represents a daily task for every photographer. This task may be complicated even for the human eye, especially when the horizon or other horizontal and vertical lines in the image are missing. In this…
Deep learning with 3D data such as reconstructed point clouds and CAD models has received great research interests recently. However, the capability of using point clouds with convolutional neural network has been so far not fully explored.…
Vision Transformers (ViTs) have gained rapid adoption in computational pathology for their ability to model long-range dependencies through self-attention, addressing the limitations of convolutional neural networks that excel at local…
Incorporating equivariance as an inductive bias into deep learning architectures to take advantage of the data symmetry has been successful in multiple applications, such as chemistry and dynamical systems. In particular, roto-translations…
Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…
Wavelet scattering networks, which are convolutional neural networks (CNNs) with fixed filters and weights, are promising tools for image analysis. Imposing symmetry on image statistics can improve human interpretability, aid in…
To better address challenging issues of the irregularity and inhomogeneity inherently present in 3D point clouds, researchers have been shifting their focus from the design of hand-craft point feature towards the learning of 3D point…
Invariance and equivariance to the rotation group have been widely discussed in the 3D deep learning community for pointclouds. Yet most proposed methods either use complex mathematical tools that may limit their accessibility, or are tied…
We propose a framework for rotation and translation covariant deep learning using $SE(2)$ group convolutions. The group product of the special Euclidean motion group $SE(2)$ describes how a concatenation of two roto-translations results in…
Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and…