Equivariant Symmetry Breaking Sets

• URL: http://arxiv.org/abs/2402.02681v3
• Date: Thu, 14 Nov 2024 16:30:13 GMT
• Title: Equivariant Symmetry Breaking Sets
• Authors: YuQing Xie, Tess Smidt,
• Abstract summary: 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.
• Score: 0.6475999521931204
• License:
• Abstract: Equivariant neural networks (ENNs) have been shown to be extremely effective in applications involving underlying symmetries. By construction ENNs cannot produce lower symmetry outputs given a higher symmetry input. However, symmetry breaking occurs in many physical systems and we may obtain a less symmetric stable state from an initial highly symmetric one. Hence, it is imperative that we understand how to systematically break symmetry in ENNs. In this work, we propose a novel symmetry breaking framework that is fully equivariant and is the first which fully addresses spontaneous symmetry breaking. We emphasize that our approach is general and applicable to equivariance under any group. To achieve this, we introduce the idea of symmetry breaking sets (SBS). Rather than redesign existing networks, we design sets of symmetry breaking objects which we feed into our network based on the symmetry of our inputs and outputs. We show there is a natural way to define equivariance on these sets, which gives an additional constraint. Minimizing the size of these sets equates to data efficiency. We prove that minimizing these sets translates to a well studied group theory problem, and tabulate solutions to this problem for the point groups. Finally, we provide some examples of symmetry breaking to demonstrate how our approach works in practice. The code for these examples is available at \url{https://github.com/atomicarchitects/equivariant-SBS}.

Related papers

• Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networks [43.88179780450706]
  We investigate the impact of weight space permutation symmetries on variational inference. We devise a symmetric symmetrization mechanism for constructing permutation invariant variational posteriors. We show that the symmetrized distribution has a strictly better fit to the true posterior, and that it can be trained using the original ELBO objective.
  arXiv  Detail & Related papers  (2024-08-10T09:06:34Z)
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak [4.41737598556146]
  We show that strong symmetry always spontaneously breaks into the corresponding weak symmetry. We conjecture that this relation among strong-to-weak symmetry breaking, gapless modes, and symmetry-charge diffusion is general for continuous symmetries.
  arXiv  Detail & Related papers  (2024-06-27T17:55:36Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• Symmetry Breaking and Equivariant Neural Networks [17.740760773905986]
  We introduce a novel notion of'relaxed equiinjection' We show how to incorporate this relaxation into equivariant multilayer perceptronrons (E-MLPs) The relevance of symmetry breaking is then discussed in various application domains.
  arXiv  Detail & Related papers  (2023-12-14T15:06:48Z)
• Asymmetry activation and its relation to coherence under permutation operation [53.64687146666141]
  A Dicke state and its decohered state are invariant for permutation. When another qubits state to each of them is attached, the whole state is not invariant for permutation, and has a certain asymmetry for permutation.
  arXiv  Detail & Related papers  (2023-11-17T03:33:40Z)
• Learning Layer-wise Equivariances Automatically using Gradients [66.81218780702125]
  Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and can not be adapted. Our goal is to allow flexible symmetry constraints that can automatically be learned from data using gradients.
  arXiv  Detail & Related papers  (2023-10-09T20:22:43Z)
• 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)
• The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetry [6.716931832076628]
  We show that imposing symmetry constraints that do not exactly match the domain symmetry is very helpful in learning the true symmetry in the environment. We demonstrate that an equivariant model can significantly outperform non-equivariant methods on domains with latent symmetries both in supervised learning and in reinforcement learning for robotic manipulation and control problems.
  arXiv  Detail & Related papers  (2022-11-16T21:51:55Z)
• Towards Antisymmetric Neural Ansatz Separation [48.80300074254758]
  We study separations between two fundamental models of antisymmetric functions, that is, functions $f$ of the form $f(x_sigma(1), ldots, x_sigma(N)) These arise in the context of quantum chemistry, and are the basic modeling tool for wavefunctions of Fermionic systems.
  arXiv  Detail & Related papers  (2022-08-05T16:35:24Z)
• Entanglement-enabled symmetry-breaking orders [0.0]
  A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state.
  arXiv  Detail & Related papers  (2022-07-18T18:00:00Z)
• Handling Object Symmetries in CNN-based Pose Estimation [7.1577508803778045]
  We investigate the problems that Convolutional Neural Networks (CNN)-based pose estimators have with symmetric objects. In particular, we find that the popular min-over-symmetries approach for creating a symmetry-aware loss tends not to work well with gradient-based optimization. We propose a representation called "closed symmetry loop" (csl) from these insights, where the angle of relevant vectors is multiplied by the symmetry order and then generalize it to 6-DOF.
  arXiv  Detail & Related papers  (2020-11-26T10:10:25Z)

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.