Related papers: A Computationally Efficient Neural Network Invaria…

Equivariant quantum neural networks (QNNs) are promising variational models that exploit symmetries to improve machine learning capabilities. Despite theoretical developments in equivariant QNNs, their implementation on near-term quantum…

Recent studies show that deep neural networks are vulnerable to adversarial examples which can be generated via certain types of transformations. Being robust to a desired family of adversarial attacks is then equivalent to being invariant…

Invariant and equivariant networks are useful in learning data with symmetry, including images, sets, point clouds, and graphs. In this paper, we consider invariant and equivariant networks for symmetries of finite groups. Invariant and…

We propose symmetric power transformation to enhance the capacity of Implicit Neural Representation~(INR) from the perspective of data transformation. Unlike prior work utilizing random permutation or index rearrangement, our method…

Message-passing has proved to be an effective way to design graph neural networks, as it is able to leverage both permutation equivariance and an inductive bias towards learning local structures in order to achieve good generalization.…

We construct and evaluate group-equivariant neural networks for the prediction of the two-dimensional $Q$-tensor order parameter of nematic liquid crystals from synthetically generated microscopic textures. Seven architectures, equivariant…

Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of…

Recent improvements in generative adversarial visual synthesis incorporate real and fake image transformation in a self-supervised setting, leading to increased stability and perceptual fidelity. However, these approaches typically involve…

Many scientific and geometric problems exhibit general linear symmetries, yet most equivariant neural networks are built for compact groups or simple vector features, limiting their reuse on matrix-valued data such as covariances, inertias,…

Recurrent neural networks (RNNs) have represented for years the state of the art in neural machine translation. Recently, new architectures have been proposed, which can leverage parallel computation on GPUs better than classical RNNs.…

Computational Intelligence (CI) techniques have shown great potential as a surrogate model of expensive physics simulation, with demonstrated ability to make fast predictions, albeit at the expense of accuracy in some cases. For many…

We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…

$G$-equivariant convolutional neural networks (GCNNs) is a geometric deep learning model for data defined on a homogeneous $G$-space $\mathcal{M}$. GCNNs are designed to respect the global symmetry in $\mathcal{M}$, thereby facilitating…

The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…

Many machine learning tasks are invariant under the action of a group $G$ of transformations: signal classification can be invariant under translations, image classification under 2D rotations, and spherical-image classification under 3D…

Computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. A particular way for combining these approaches within a framework called vector symbolic architectures leads to neural automata. An…

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…

This work studies the design of neural networks that can process the weights or gradients of other neural networks, which we refer to as neural functional networks (NFNs). Despite a wide range of potential applications, including learned…

The study of representations invariant to common transformations of the data is important to learning. Most techniques have focused on local approximate invariance implemented within expensive optimization frameworks lacking explicit…

Collaborative Inference (CI) optimizes the latency and energy consumption of deep learning inference through the inter-operation of edge and cloud devices. Albeit beneficial for other tasks, CI has never been applied to the sequence-…