相关论文: $\mathrm{SO}(2)$-Equivariant Reinforcement Learnin…

End-to-end learning for visual robotic manipulation is known to suffer from sample inefficiency, requiring large numbers of demonstrations. The spatial roto-translation equivariance, or the SE(3)-equivariance can be exploited to improve the…

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 of neural networks to transformations helps to improve their performance and reduce generalization error in computer vision tasks, as they apply to datasets presenting symmetries (e.g. scalings, rotations, translations). The…

Invariance under symmetry is an important problem in machine learning. Our paper looks specifically at equivariant neural networks where transformations of inputs yield homomorphic transformations of outputs. Here, steerable CNNs have…

Self-supervised learning (SSL) methods have achieved remarkable success in learning image representations allowing invariances in them - but therefore discarding transformation information that some computer vision tasks actually require.…

Graph neural networks (GNNs) have shown promise in learning unstructured mesh-based simulations of physical systems, including fluid dynamics. In tandem, geometric deep learning principles have informed the development of equivariant…

Model-free reinforcement learning is a promising approach for autonomously solving challenging robotics control problems, but faces exploration difficulty without information of the robot's kinematics and dynamics morphology. The…

Reinforcement Learning algorithms have recently been proposed to learn time-sequential control policies in the field of autonomous driving. Direct applications of Reinforcement Learning algorithms with discrete action space will yield…

Recent work has shown the utility of developing machine learning models that respect the structure and symmetries of eigenvectors. These works promote sign invariance, since for any eigenvector v the negation -v is also an eigenvector.…

Recently, learning equivariant representations has attracted considerable research attention. Dieleman et al. introduce four operations which can be inserted into convolutional neural network to learn deep representations equivariant to…

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…

Distributed optimal control is known to be challenging and can become intractable even for linear-quadratic regulator problems. In this work, we study a special class of such problems where distributed state feedback controllers can give…

In this work we present a novel extension of soft actor critic, a state of the art deep reinforcement algorithm. Our method allows us to combine traditional controllers with learned neural network policies. This combination allows us to…

In this study, we introduce a method for learning group (known or unknown) equivariant functions by learning the associated quadratic form $x^T A x$ corresponding to the group from the data. Certain groups, known as orthogonal groups,…

Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large…

Machine learning, deep learning, has been accelerating computational physics, which has been used to simulate systems on a lattice. Equivariance is essential to simulate a physical system because it imposes a strong induction bias for the…

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…

Pre-trained deep image representations are useful for post-training tasks such as classification through transfer learning, image retrieval, and object detection. Data augmentations are a crucial aspect of pre-training robust…

Equivariant deep learning architectures exploit symmetries in learning problems to improve the sample efficiency of neural-network-based models and their ability to generalise. However, when modelling real-world data, learning problems are…

The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…