相关论文: Discretizing Group-Convolutional Neural Networks f…
One of the most fundamental problems in machine learning is to compare examples: Given a pair of objects we want to return a value which indicates degree of (dis)similarity. Similarity is often task specific, and pre-defined distances can…
We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that…
Deep neural networks face many problems in the field of hyperspectral image classification, lack of effective utilization of spatial spectral information, gradient disappearance and overfitting as the model depth increases. In order to…
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…
Although group convolution operators are increasingly used in deep convolutional neural networks to improve the computational efficiency and to reduce the number of parameters, most existing methods construct their group convolution…
Subsampling is used in convolutional neural networks (CNNs) in the form of pooling or strided convolutions, to reduce the spatial dimensions of feature maps and to allow the receptive fields to grow exponentially with depth. However, it is…
We propose a local modelling approach using deep convolutional neural networks (CNNs) for fine-grained image classification. Recently, deep CNNs trained from large datasets have considerably improved the performance of object recognition.…
In this paper, we introduce group convolutional neural networks (GCNNs) equivariant to color variation. GCNNs have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale.…
Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks…
Deep Convolutional Neural Networks (CNNs) are capable of learning unprecedentedly effective features from images. Some researchers have struggled to enhance the parameters' efficiency using grouped convolution. However, the relation between…
Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as…
Graph neural networks (GNNs) demonstrate a robust capability for representation learning on graphs with complex structures, showcasing superior performance in various applications. The majority of existing GNNs employ a graph convolution…
Graph Convolutional Networks (GCNs) have become a crucial tool on learning representations of graph vertices. The main challenge of adapting GCNs on large-scale graphs is the scalability issue that it incurs heavy cost both in computation…
The distance-geometric graph representation adopts a unified scheme (distance) for representing the geometry of three-dimensional(3D) graphs. It is invariant to rotation and translation of the graph and it reflects pair-wise node…
Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…
Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…
Convolutional neural networks (CNNs) have massively impacted visual recognition in 2D images, and are now ubiquitous in state-of-the-art approaches. CNNs do not easily extend, however, to data that are not represented by regular grids, such…
Convolutional Neural Networks (CNNs) traditionally encode translation equivariance via the convolution operation. Generalization to other transformations has recently received attraction to encode the knowledge of the data geometry in group…
Graph Convolutional Neural Networks (GCNNs) extend classical CNNs to graph data domain, such as brain networks, social networks and 3D point clouds. It is critical to identify an appropriate graph for the subsequent graph convolution.…
Building discriminative representations for 3D data has been an important task in computer graphics and computer vision research. Convolutional Neural Networks (CNNs) have shown to operate on 2D images with great success for a variety of…