Related papers: e3nn: Euclidean Neural Networks
The neural network and quantum computing are both significant and appealing fields, with their interactive disciplines promising for large-scale computing tasks that are untackled by conventional computers. However, both developments are…
Towards developing effective and efficient brain-computer interface (BCI) systems, precise decoding of brain activity measured by electroencephalogram (EEG), is highly demanded. Traditional works classify EEG signals without considering the…
Convolution is an integral operation that defines how the shape of one function is modified by another function. This powerful concept forms the basis of hierarchical feature learning in deep neural networks. Although performing convolution…
Designing neural network architectures that can handle data symmetry is crucial. This is especially important for geometric graphs whose properties are equivariance under Euclidean transformations. Current equivariant graph neural networks…
Rotation-invariance is a desired property of machine-learning models for medical image analysis and in particular for computational pathology applications. We propose a framework to encode the geometric structure of the special Euclidean…
Deep learning has been shown to be able to recognize data patterns better than humans in specific circumstances or contexts. In parallel, quantum computing has demonstrated to be able to output complex wave functions with a few number of…
Using unitary (instead of general) matrices in artificial neural networks (ANNs) is a promising way to solve the gradient explosion/vanishing problem, as well as to enable ANNs to learn long-term correlations in the data. This approach…
In the last decade, special purpose computing systems, such as Neuromorphic computing, have become very popular in the field of computer vision and machine learning for classification tasks. In 2015, IBM's released the TrueNorth…
Classifying nodes in a graph is a common problem. The ideal classifier must adapt to any imbalances in the class distribution. It must also use information in the clustering structure of real-world graphs. Existing Graph Neural Networks…
We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that…
Modeling the complex three-dimensional (3D) dynamics of relational systems is an important problem in the natural sciences, with applications ranging from molecular simulations to particle mechanics. Machine learning methods have achieved…
Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as physical simulations. A crucial…
Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the…
This paper presents an adaptive convolutional neural network (CNN) architecture that can automate diverse topology optimization (TO) problems having different underlying physics. The architecture uses the encoder-decoder networks with dense…
Developing equivariant neural networks for the E(3) group plays an important role in modeling 3D data across real-world applications. Enforcing this equivariance primarily involves the tensor products of irreducible representations…
Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is…
By folding into particular 3D structures, proteins play a key role in living beings. To learn meaningful representation from a protein structure for downstream tasks, not only the global backbone topology but the local fine-grained…
We present a new class of equivariant neural networks, hereby dubbed Lattice-Equivariant Neural Networks (LENNs), designed to satisfy local symmetries of a lattice structure. Our approach develops within a recently introduced framework…
Geometric deep learning (GDL) models have demonstrated a great potential for the analysis of non-Euclidian data. They are developed to incorporate the geometric and topological information of non-Euclidian data into the end-to-end deep…
This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…