相关论文: Constructing 3D Rotational Invariance and Equivari…

Many applications require the robustness, or ideally the invariance, of a neural network to certain transformations of input data. Most commonly, this requirement is addressed by either augmenting the training data, using adversarial…

Deep neural networks lack straightforward ways to incorporate domain knowledge and are notoriously considered black boxes. Prior works attempted to inject domain knowledge into architectures implicitly through data augmentation. Building on…

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…

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…

We present a SE(3)-equivariant graph neural network (GNN) approach that directly predicting the formation factor and effective permeability from micro-CT images. FFT solvers are established to compute both the formation factor and effective…

Learning 3D point sets with rotational invariance is an important and challenging problem in machine learning. Through rotational invariant architectures, 3D point cloud neural networks are relieved from requiring a canonical global pose…

Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds. Existing work has primarily focused on a small number of groups, such as the translation, rotation,…

How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…

We construct and evaluate group-equivariant neural networks for the prediction of the two-dimensional $Q$-tensor order parameter of nematic liquid crystals from synthetically generated microscopic textures. Seven architectures, equivariant…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

Equivariant neural networks incorporate symmetries into their architecture, achieving higher generalization performance. However, constructing equivariant neural networks typically requires prior knowledge of data types and symmetries,…

Deep neural networks have achieved great success in the last decade. When designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, it is critical that the model can maintain invariance towards…

In this paper, we utilize hyperspheres and regular $n$-simplexes and propose an approach to learning deep features equivariant under the transformations of $n$D reflections and rotations, encompassed by the powerful group of O$(n)$. Namely,…

We integrate two powerful ideas, geometry and deep visual representation learning, into recurrent network architectures for mobile visual scene understanding. The proposed networks learn to "lift" and integrate 2D visual features over time…

Spherical convolutional networks have been introduced recently as tools to learn powerful feature representations of 3D shapes. Spherical CNNs are equivariant to 3D rotations making them ideally suited to applications where 3D data may be…

In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for…

Graph neural networks (GNNs) have achieved remarkable success in molecular property prediction. However, traditional graph representations struggle to effectively encode the inherent 3D spatial structures of molecules, as molecular…

We introduce a tensor-channel equivariant graph neural network for direct prediction of molecular polarizability tensors. Building on the efficient PaiNN architecture, we augment the hidden representation with explicit symmetric rank-2…

Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is…

The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and…