相关论文: Learning from Frustration: Torsor CNNs on Graphs

Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems.…

Convolutional neural networks (CNNs) have had great success in many real-world applications and have also been used to model visual processing in the brain. However, these networks are quite brittle - small changes in the input image can…

Convolutional neural networks (CNNs) allow for parameter sharing and translational equivariance by using convolutional kernels in their linear layers. By restricting these kernels to be SO(3)-steerable, CNNs can further improve parameter…

This paper deals with the unification of local and non-local signal processing on graphs within a single convolutional neural network (CNN) framework. Building upon recent works on graph CNNs, we propose to use convolutional layers that…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be $SO(3)$ equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for…

Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to graph-structured data, in which convolution is guided by the graph topology. In many cases where graphs are unavailable, existing methods manually construct graphs…

Graph convolutional neural networks (GCNs) generalize tradition convolutional neural networks (CNNs) from low-dimensional regular graphs (e.g., image) to high dimensional irregular graphs (e.g., text documents on word embeddings). Due to…

Learning to reason about relations and dynamics over multiple interacting objects is a challenging topic in machine learning. The challenges mainly stem from that the interacting systems are exponentially-compositional, symmetrical, and…

Convolutional neural networks (CNN's) are powerful and widely used tools. However, their interpretability is far from ideal. One such shortcoming is the difficulty of deducing a network's ability to generalize to unseen data. We use…

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 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…

Current research in Computer Vision has shown that Convolutional Neural Networks (CNN) give state-of-the-art performance in many classification tasks and Computer Vision problems. The embedding of CNN, which is the internal representation…

Convolutional neural networks (CNNs) have achieved breakthrough performances in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterizing the generalization…

Federated graph learning collaboratively learns a global graph neural network with distributed graphs, where the non-independent and identically distributed property is one of the major challenges. Most relative arts focus on traditional…

Convolutional Neural Networks (CNNs) have shown remarkable performance in general object recognition tasks. In this paper, we propose a new model called EnsNet which is composed of one base CNN and multiple Fully Connected SubNetworks…

We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where geometrically meaningful PDE-coefficients become the…

Despite the phenomenal success of deep neural networks in a broad range of learning tasks, there is a lack of theory to understand the way they work. In particular, Convolutional Neural Networks (CNNs) are known to perform much better than…

Spherical equivariant graph neural networks (EGNNs) provide a principled framework for learning on three-dimensional molecular and biomolecular systems, where predictions must respect the rotational symmetries inherent in physics. These…

Equivariant network architectures are a well-established tool for predicting invariant or equivariant quantities. However, almost all learning problems considered in this context feature a global symmetry, i.e. each point of the underlying…