Related papers: Constructing 3D Rotational Invariance and Equivari…
Equivariance to permutations and rigid motions is an important inductive bias for various 3D learning problems. Recently it has been shown that the equivariant Tensor Field Network architecture is universal -- it can approximate any…
Incorporating symmetries can lead to highly data-efficient and generalizable models by defining equivalence classes of data samples related by transformations. However, characterizing how transformations act on input data is often…
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.…
Learning and reasoning about 3D molecular structures with varying size is an emerging and important challenge in machine learning and especially in drug discovery. Equivariant Graph Neural Networks (GNNs) can simultaneously leverage the…
Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…
Equivariance of neural networks to transformations helps to improve their performance and reduce generalization error in computer vision tasks, as they apply to datasets presenting symmetries (e.g. scalings, rotations, translations). The…
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…
We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…
While using invariant and equivariant maps, it is possible to apply deep learning to a range of primitive data structures, a formalism for dealing with hierarchy is lacking. This is a significant issue because many practical structures are…
Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we…
We propose a general architecture that combines the coefficient learning scheme with a residual operator layer for learning mappings between continuous functions in the 3D Euclidean space. Our proposed model is guaranteed to achieve…
In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While…
Rotation equivariant graph neural networks, i.e. networks designed to guarantee certain geometric relations between their inputs and outputs, yield state of the art performance on spatial deep learning tasks. They exhibit high data…
Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only…
We approach the well-studied problem of supervised group invariant and equivariant machine learning from the point of view of geometric topology. We propose a novel approach using a pre-processing step, which involves projecting the input…
A wide range of techniques have been proposed in recent years for designing neural networks for 3D data that are equivariant under rotation and translation of the input. Most approaches for equivariance under the Euclidean group…
We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We…
In certain situations, neural networks are trained upon data that obey underlying symmetries. However, the predictions do not respect the symmetries exactly unless embedded in the network structure. In this work, we introduce architectures…
Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map…
This paper introduces a 3D shape generative model based on deep neural networks. A new image-like (i.e., tensor) data representation for genus-zero 3D shapes is devised. It is based on the observation that complicated shapes can be well…