Related papers: Symmetry Discovery for Different Data Types
Lie symmetry transformations that leave a differential equation invariant play a fundamental role in science and mathematics. Such Lie symmetry groups uniquely determine their Lie symmetry algebras. Exact differential elimination algorithms…
We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is equivariant with respect to group actions on the input and…
We propose a simple method to identify a continuous Lie algebra symmetry in a dataset through regression by an artificial neural network. Our proposal takes advantage of the $ \mathcal{O}(\epsilon^2)$ scaling of the output variable under…
Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries,…
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…
We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…
The quest for robust and generalizable machine learning models has driven recent interest in exploiting symmetries through equivariant neural networks. In the context of PDE solvers, recent works have shown that Lie point symmetries can be…
Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…
With the rapid proliferation of autonomous driving, there has been a heightened focus on the research of lidar-based 3D semantic segmentation and object detection methodologies, aiming to ensure the safety of traffic participants. In recent…
Permutation symmetries of deep networks make basic operations like model merging and similarity estimation challenging. In many cases, aligning the weights of the networks, i.e., finding optimal permutations between their weights, is…
A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to…
Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
This paper proposes an equivariant neural network that takes data in any semi-simple Lie algebra as input. The corresponding group acts on the Lie algebra as adjoint operations, making our proposed network adjoint-equivariant. Our framework…
Group equivariant neural networks are growing in importance owing to their ability to generalise well in applications where the data has known underlying symmetries. Recent characterisations of a class of these networks that use high-order…
Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their…
We review a novel neural network architecture called lattice gauge equivariant convolutional neural networks (L-CNNs), which can be applied to generic machine learning problems in lattice gauge theory while exactly preserving gauge…
Incorporating equivariance to symmetry groups as a constraint during neural network training can improve performance and generalization for tasks exhibiting those symmetries, but such symmetries are often not perfectly nor explicitly…
We present a geometric neural network-based tracking controller for systems evolving on matrix Lie groups under unknown dynamics, actuator faults, and bounded disturbances. Leveraging the left-invariance of the tangent bundle of matrix Lie…
Equivariant neural networks are designed to respect symmetries through their architecture, boosting generalization and sample efficiency when those symmetries are present in the data distribution. Real-world data, however, often departs…