Related papers: Symmetry Discovery for Different Data Types

Incorporating permutation equivariance into neural networks has proven to be useful in ensuring that models respect symmetries that exist in data. Symmetric tensors, which naturally appear in statistics, machine learning, and graph theory,…

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

We present a new class of equivariant neural networks, hereby dubbed Lattice-Equivariant Neural Networks (LENNs), designed to satisfy local symmetries of a lattice structure. Our approach develops within a recently introduced framework…

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…

Recent work has applied supervised deep learning to derive continuous symmetry transformations that preserve the data labels and to obtain the corresponding algebras of symmetry generators. This letter introduces two improved algorithms…

Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…

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…

The inherent challenge of detecting symmetries stems from arbitrary orientations of symmetry patterns; a reflection symmetry mirrors itself against an axis with a specific orientation while a rotation symmetry matches its rotated copy with…

Unsupervised skill discovery aims to acquire behavior primitives that improve exploration and accelerate downstream task learning. However, existing approaches often ignore the geometric symmetries of physical environments, leading to…

We study the problem of learning equivariant neural networks via gradient descent. The incorporation of known symmetries ("equivariance") into neural nets has empirically improved the performance of learning pipelines, in domains ranging…

Existing symmetry discovery methods predominantly focus on global transformations across the entire system or space, but they fail to consider the symmetries in local neighborhoods. This may result in the reported symmetry group being a…

Parameter-space and function-space provide two different duality frames in which to study neural networks. We demonstrate that symmetries of network densities may be determined via dual computations of network correlation functions, even…

The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under…

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…

Group equivariance has emerged as a valuable inductive bias in deep learning, enhancing generalization, data efficiency, and robustness. Classically, group equivariant methods require the groups of interest to be known beforehand, which may…

Despite the successes of deep learning in computer vision, difficulties persist in recognizing objects that have undergone group-symmetric transformations rarely seen during training$\unicode{x2013}$for example objects seen in unusual…

Equivariant neural networks have proven to be effective for tasks with known underlying symmetries. However, optimizing equivariant networks can be tricky and best training practices are less established than for standard networks. In…

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…

Extensive work has demonstrated that equivariant neural networks can significantly improve sample efficiency and generalization by enforcing an inductive bias in the network architecture. These applications typically assume that the domain…

The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical…