Relaxed Equivariant Graph Neural Networks
- URL: http://arxiv.org/abs/2407.20471v1
- Date: Tue, 30 Jul 2024 00:16:50 GMT
- Title: Relaxed Equivariant Graph Neural Networks
- Authors: Elyssa Hofgard, Rui Wang, Robin Walters, Tess Smidt,
- Abstract summary: 3D Euclidean symmetry equivariant neural networks have demonstrated notable success in modeling complex physical systems.
We introduce a framework for relaxed $E(3)$ graph equivariant neural networks that can learn and represent symmetry breaking within continuous groups.
- Score: 16.98061967654925
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 3D Euclidean symmetry equivariant neural networks have demonstrated notable success in modeling complex physical systems. We introduce a framework for relaxed $E(3)$ graph equivariant neural networks that can learn and represent symmetry breaking within continuous groups. Building on the existing e3nn framework, we propose the use of relaxed weights to allow for controlled symmetry breaking. We show empirically that these relaxed weights learn the correct amount of symmetry breaking.
Related papers
- The Empirical Impact of Neural Parameter Symmetries, or Lack Thereof [50.49582712378289]
We investigate the impact of neural parameter symmetries by introducing new neural network architectures.
We develop two methods, with some provable guarantees, of modifying standard neural networks to reduce parameter space symmetries.
Our experiments reveal several interesting observations on the empirical impact of parameter symmetries.
arXiv Detail & Related papers (2024-05-30T16:32:31Z) - Enhancing lattice kinetic schemes for fluid dynamics with Lattice-Equivariant Neural Networks [79.16635054977068]
We present a new class of equivariant neural networks, dubbed Lattice-Equivariant Neural Networks (LENNs)
Our approach develops within a recently introduced framework aimed at learning neural network-based surrogate models Lattice Boltzmann collision operators.
Our work opens towards practical utilization of machine learning-augmented Lattice Boltzmann CFD in real-world simulations.
arXiv Detail & Related papers (2024-05-22T17:23:15Z) - Equivariant Symmetry Breaking Sets [0.6475999521931204]
Equivariant neural networks (ENNs) have been shown to be extremely effective in applications involving underlying symmetries.
We propose a novel symmetry breaking framework that is fully equivariant and is the first which fully addresses spontaneous symmetry breaking.
arXiv Detail & Related papers (2024-02-05T02:35:11Z) - A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learning [5.1105250336911405]
We provide a unifying theoretical and methodological framework for incorporating symmetry into machine learning models.
We show that enforcing and discovering symmetry are linear-algebraic tasks that are dual with respect to the bilinear structure of the Lie derivative.
We propose a novel way to promote symmetry by introducing a class of convex regularization functions based on the Lie derivative and nuclear norm relaxation.
arXiv Detail & Related papers (2023-11-01T01:19:54Z) - Symmetry Induces Structure and Constraint of Learning [0.0]
We unveil the importance of the loss function symmetries in affecting, if not deciding, the learning behavior of machine learning models.
Common instances of mirror symmetries in deep learning include rescaling, rotation, and permutation symmetry.
We show that the theoretical framework can explain intriguing phenomena, such as the loss of plasticity and various collapse phenomena in neural networks.
arXiv Detail & Related papers (2023-09-29T02:21:31Z) - Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras
from First Principles [55.41644538483948]
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 transformations symmetry and the corresponding generators.
Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
arXiv Detail & Related papers (2023-01-13T16:25:25Z) - Breaking the Symmetry: Resolving Symmetry Ambiguities in Equivariant
Neural Networks [4.147346416230272]
We present OAVNN: Orientation Aware Vector Neuron Network, an extension of the Vector Neuron Network.
OAVNN is a rotation equivariant network that is robust to planar symmetric inputs.
arXiv Detail & Related papers (2022-10-29T16:28:59Z) - Learning Physical Dynamics with Subequivariant Graph Neural Networks [99.41677381754678]
Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics.
Physical laws abide by symmetry, which is a vital inductive bias accounting for model generalization.
Our model achieves on average over 3% enhancement in contact prediction accuracy across 8 scenarios on Physion and 2X lower rollout MSE on RigidFall.
arXiv Detail & Related papers (2022-10-13T10:00:30Z) - SNeS: Learning Probably Symmetric Neural Surfaces from Incomplete Data [77.53134858717728]
We build on the strengths of recent advances in neural reconstruction and rendering such as Neural Radiance Fields (NeRF)
We apply a soft symmetry constraint to the 3D geometry and material properties, having factored appearance into lighting, albedo colour and reflectivity.
We show that it can reconstruct unobserved regions with high fidelity and render high-quality novel view images.
arXiv Detail & Related papers (2022-06-13T17:37:50Z) - On the Importance of Asymmetry for Siamese Representation Learning [53.86929387179092]
Siamese networks are conceptually symmetric with two parallel encoders.
We study the importance of asymmetry by explicitly distinguishing the two encoders within the network.
We find the improvements from asymmetric designs generalize well to longer training schedules, multiple other frameworks and newer backbones.
arXiv Detail & Related papers (2022-04-01T17:57:24Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.