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Representing and reasoning about 3D structures of macromolecules is emerging as a distinct challenge in machine learning. Here, we extend recent work on geometric vector perceptrons and apply equivariant graph neural networks to a wide…
To improve the robustness of graph neural networks (GNN), graph structure learning (GSL) has attracted great interest due to the pervasiveness of noise in graph data. Many approaches have been proposed for GSL to jointly learn a clean graph…
Graph Neural Networks (GNNs) have shown remarkable performance in structured data modeling tasks such as node classification. However, mainstream approaches generally rely on a large number of trainable parameters and fixed aggregation…
The inherent diversity of computation types within the deep neural network (DNN) models often requires a variety of specialized units in hardware processors, which limits computational efficiency, increasing both inference latency and power…
Equivariant neural networks have proven to be effective for tasks with known underlying symmetries. However, optimizing equivariant networks can be tricky and best training practices are less established than for standard networks. In…
Edge intelligence has arisen as a promising computing paradigm for supporting miscellaneous smart applications that rely on machine learning techniques. While the community has extensively investigated multi-tier edge deployment for…
Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where…
In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free…
In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle…
We present a framework for the multiscale modeling of finite strain magneto-elasticity based on physics-augmented neural networks (NNs). By using a set of problem specific invariants as input, an energy functional as the output and by…
We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model such as an MLP or a transformer and…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
This paper proposes a Fast Graph Convolutional Neural Network (FGRNN) architecture to predict sequences with an underlying graph structure. The proposed architecture addresses the limitations of the standard recurrent neural network (RNN),…
Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches,…
In reinforcement learning (RL), exploiting environmental symmetries can significantly enhance efficiency, robustness, and performance. However, ensuring that the deep RL policy and value networks are respectively equivariant and invariant…
Heterogeneous graph neural networks (HGNNs) have powerful capability to embed rich structural and semantic information of a heterogeneous graph into node representations. Existing HGNNs inherit many mechanisms from graph neural networks…
Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes…
$n$-particle reduced density matrices ($n$-RDMs) play a central role in understanding correlated phases of matter, but their calculation is often computationally inefficient for strongly-correlated states at large system sizes. In this…
Graph Neural Networks (GNNs) have emerged as powerful tools for learning representations of graph-structured data. In addition to real-valued GNNs, quaternion GNNs also perform well on tasks on graph-structured data. With the aim of…
True-time-delay (TTD) beamformers can produce wideband, squint-free beams in both analog and digital signal domains, unlike frequency-dependent FFT beams. Our previous work showed that TTD beamformers can be efficiently realized using the…