相关论文: Automatic Symmetry Discovery with Lie Algebra Conv…

Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries…

Deep convolutional networks (convnets) show a remarkable ability to learn disentangled representations. In recent years, the generalization of deep learning to Lie groups beyond rigid motion in $\mathbb{R}^n$ has allowed to build convnets…

Although provably robust to translational perturbations, convolutional neural networks (CNNs) are known to suffer from extreme performance degradation when presented at test time with more general geometric transformations of inputs.…

Symmetry is widely applied in problems such as the design of equivariant networks and the discovery of governing equations, but in complex scenarios, it is not known in advance. Most previous symmetry discovery methods are limited to linear…

Equivariance guarantees that a model's predictions capture key symmetries in data. When an image is translated or rotated, an equivariant model's representation of that image will translate or rotate accordingly. The success of…

Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…

The weight-sharing mechanism of convolutional kernels ensures translation-equivariance of convolution neural networks (CNNs). Recently, rotation-equivariance has been investigated. However, research on scale-equivariance or simultaneous…

Group convolutional neural networks (G-CNNs) have been shown to increase parameter efficiency and model accuracy by incorporating geometric inductive biases. In this work, we investigate the properties of representations learned by regular…

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…

We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…

By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…

Permutation equivariant neural networks are typically used to learn from data that lives on a graph. However, for any graph $G$ that has $n$ vertices, using the symmetric group $S_n$ as its group of symmetries does not take into account the…

The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks…

Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints. They leverage concepts from group representation theory, non-commutative harmonic analysis and…

The quest for robust and generalizable machine learning models has driven recent interest in exploiting symmetries through equivariant neural networks. In the context of PDE solvers, recent works have shown that Lie point symmetries can be…

This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that…

Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and…

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 symmetry transformations and the corresponding…

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…

We present the group equivariant conditional neural process (EquivCNP), a meta-learning method with permutation invariance in a data set as in conventional conditional neural processes (CNPs), and it also has transformation equivariance in…