相关论文: Equivariant Symmetry Breaking Sets

The inclusion of symmetries as an inductive bias, known as equivariance, often improves generalization on geometric data (e.g. grids, sets, and graphs). However, equivariant architectures are usually highly constrained, designed for…

Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However, the relationship between symmetry and the imperative for equivariance in neural networks is not…

Equivariance encodes known symmetries into neural networks, often enhancing generalization. However, equivariant networks cannot break symmetries: the output of an equivariant network must, by definition, have at least the same…

Artificial Neural Networks (ANN) comprise important symmetry properties, which can influence the performance of Monte Carlo methods in Neuroevolution. The problem of the symmetries is also known as the competing conventions problem or…

Incorporating symmetries can lead to highly data-efficient and generalizable models by defining equivalence classes of data samples related by transformations. However, characterizing how transformations act on input data is often…

We propose a novel framework to analyze symmetry breaking in dynamical systems through the lens of entropy and information transfer. Information transfer quantifies the directional exchange of entropy between observables, allowing us to…

Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…

Motivated by questions originating from the study of a class of shallow student-teacher neural networks, methods are developed for the analysis of spurious minima in classes of gradient equivariant dynamics related to neural nets. In the…

Learning from unordered sets is a fundamental learning setup, recently attracting increasing attention. Research in this area has focused on the case where elements of the set are represented by feature vectors, and far less emphasis has…

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…

Symmetry breaking--the phenomenon in which the symmetry of a system is not inherited by its stable states--underlies pattern formation, superconductivity, and numerous other effects. Recent theoretical work has established the possibility…

Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized…

We develop an entropy based framework for analyzing symmetry breaking in dynamical systems. Information transfer, which measures the directional exchange of entropy between observables, provides a quantitative early indicator of symmetry…

Understanding the mechanisms behind neural network optimization is crucial for improving network design and performance. While various optimization techniques have been developed, a comprehensive understanding of the underlying principles…

The Symmetric group $S_{n}$ manifests itself in large classes of quantum systems as the invariance of certain characteristics of a quantum state with respect to permuting the qubits. The subgroups of $S_{n}$ arise, among many other…

We propose a framework to understand the unprecedented performance and robustness of deep neural networks using field theory. Correlations between the weights within the same layer can be described by symmetries in that layer, and networks…

If supersymmetric particles are discovered, an important problem will be to determine how supersymmetry has been broken. At collider energies, supersymmetry breaking can be parameterised by soft supersymmetry breaking parameters. Several…

In the context of answer set programming, this work investigates symmetry detection and symmetry breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We contribute a reduction of symmetry…

In constraint programming and related paradigms, a modeller specifies their problem in a modelling language for a solver to search and return its solution(s). Using high-level modelling languages such as Essence, a modeller may express…

In this paper we show how Group Equivariant Convolutional Neural Networks use subsampling to learn to break equivariance to their symmetries. We focus on 2D rotations and reflections and investigate the impact of broken equivariance on…