相关论文: Equivariant Symmetry Breaking Sets

Recognizing symmetries in data allows for significant boosts in neural network training. In many cases, however, the underlying symmetry is present only in an idealized dataset, and is broken in the training data, due to effects such as…

The combination of linear and nonlinear potentials, both shaped as a single well, enables competition between the confinement and expulsion induced by the former and latter potentials, respectively. We demonstrate that this setting leads to…

Automatic tumor segmentation is a crucial step in medical image analysis for computer-aided diagnosis. Although the existing methods based on convolutional neural networks (CNNs) have achieved the state-of-the-art performance, many…

Neural network parameterizations exhibit inherent symmetries that yield multiple equivalent minima within the loss landscape. Scale Graph Metanetworks (ScaleGMNs) explicitly leverage these symmetries by proposing an architecture equivariant…

Neural networks are emerging as a tool for scalable data-driven simulation of high-dimensional dynamical systems, especially in settings where numerical methods are infeasible or computationally expensive. Notably, it has been shown that…

We introduce the group-equivariant autoencoder (GE-autoencoder) -- a deep neural network (DNN) method that locates phase boundaries by determining which symmetries of the Hamiltonian have spontaneously broken at each temperature. We use…

Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…

Self-supervised learning for inverse problems allows to train a reconstruction network from noise and/or incomplete data alone. These methods have the potential of enabling learning-based solutions when obtaining ground-truth references for…

State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…

Spontaneous symmetry breaking (SSB) is responsible for structure formation in scenarios ranging from condensed matter to cosmology. SSB is broadly understood in terms of perturbations to the Hamiltonian governing the dynamics or to the…

Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely…

Spontaneous symmetry breaking (SSB) is a key concept in physics that for decades has played a crucial role in the description of many physical phenomena in a large number of different areas, like particle physics, cosmology, and…

Ensembles of quantum chaotic systems are expected to exhibit energy eigenvalues with random-matrix-like level repulsion between pairs of energies separated by less than the inverse Thouless time. Recent research has shown that exact and…

Group equivariance can overly constrain models if the symmetries in the group differ from those observed in data. While common methods address this by determining the appropriate level of symmetry at the dataset level, they are limited to…

Steerable convolutional neural networks (SCNNs) enhance task performance by modelling geometric symmetries through equivariance constraints on weights. Yet, unknown or varying symmetries can lead to overconstrained weights and decreased…

Learning policies for multi-entity systems in 3D environments is far more complicated against single-entity scenarios, due to the exponential expansion of the global state space as the number of entities increases. One potential solution of…

Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the…

The concept of spontaneous symmetry breaking (SSB) generally lacks a simple and intuitive introduction in the literature. This gap is filled by defining SSB in a universal context beyond its usual applications in physics and by discussing…

Traditional supervised learning aims to learn an unknown mapping by fitting a function to a set of input-output pairs with a fixed dimension. The fitted function is then defined on inputs of the same dimension. However, in many settings,…

In this work, we explore the trade-offs of explicit structural priors, particularly group equivariance. We address this through theoretical analysis and a comprehensive empirical study. To enable controlled and fair comparisons, we…