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

Extracting discriminative local features that are invariant to imaging variations is an integral part of establishing correspondences between images. In this work, we introduce a self-supervised learning framework to extract discriminative…

Group equivariant convolutional neural networks (G-CNNs) are generalizations of convolutional neural networks (CNNs) which excel in a wide range of technical applications by explicitly encoding symmetries, such as rotations and…

The introduction of relevant physical information into neural network architectures has become a widely used and successful strategy for improving their performance. In lattice gauge theories, such information can be identified with gauge…

This paper proposes an equivariant neural network that takes data in any semi-simple Lie algebra as input. The corresponding group acts on the Lie algebra as adjoint operations, making our proposed network adjoint-equivariant. Our framework…

Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…

Group Equivariant Convolutions (GConvs) enable convolutional neural networks to be equivariant to various transformation groups, but at an additional parameter and compute cost. We investigate the filter parameters learned by GConvs and…

Equivariant neural networks incorporate symmetries through group actions, embedding them as an inductive bias to improve performance. Existing methods learn an equivariant action on the latent space, or design architectures that are…

Although group convolutional networks are able to learn powerful representations based on symmetry patterns, they lack explicit means to learn meaningful relationships among them (e.g., relative positions and poses). In this paper, we…

Weight sharing in convolutional neural networks (CNNs) ensures that their feature maps will be translation-equivariant. However, although conventional convolutions are equivariant to translation, they are not equivariant to other isometries…

The ability to generalize compositionally is key to understanding the potentially infinite number of sentences that can be constructed in a human language from only a finite number of words. Investigating whether NLP models possess this…

We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model such as an MLP or a transformer and…

Convolutional neural networks revolutionized computer vision and natrual language processing. Their efficiency, as compared to fully connected neural networks, has its origin in the architecture, where convolutions reflect the translation…

We view disentanglement learning as discovering an underlying structure that equivariantly reflects the factorized variations shown in data. Traditionally, such a structure is fixed to be a vector space with data variations represented by…

We present a neural network architecture that is fully equivariant with respect to transformations under the Lorentz group, a fundamental symmetry of space and time in physics. The architecture is based on the theory of the…

Equivariant neural networks are a class of neural networks designed to preserve symmetries inherent in the data. In this paper, we introduce a general method for modifying a neural network to enforce equivariance, a process we refer to as…

In this paper we study the spontaneous development of symmetries in the early layers of a Convolutional Neural Network (CNN) during learning on natural images. Our architecture is built in such a way to mimic the early stages of biological…

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…

Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to…

Discovering new phenomena at the Large Hadron Collider (LHC) involves the identification of rare signals over conventional backgrounds. Thus binary classification tasks are ubiquitous in analyses of the vast amounts of LHC data. We develop…

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…