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Inspired by convolutional neural networks on 1D and 2D data, graph convolutional neural networks (GCNNs) have been developed for various learning tasks on graph data, and have shown superior performance on real-world datasets. Despite their…
We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on…
Data-centric methods have shown great potential in understanding and predicting spatiotemporal dynamics, enabling better design and control of the object system. However, deep learning models often lack interpretability, fail to obey…
Convolutional neural network (CNN), with ability of feature learning and nonlinear mapping, has demonstrated its effectiveness in prognostics and health management (PHM). However, explanation on the physical meaning of a CNN architecture…
Convolutional neural networks (CNNs) leverage the great power in representation learning on regular grid data such as image and video. Recently, increasing attention has been paid on generalizing CNNs to graph or network data which is…
Generative Adversarial Networks (GAN) have demonstrated impressive results in modeling the distribution of natural images, learning latent representations that capture semantic variations in an unsupervised basis. Beyond the generation of…
Recent years have witnessed an increased interest in the application of persistent homology, a topological tool for data analysis, to machine learning problems. Persistent homology is known for its ability to numerically characterize the…
Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the…
Graph Neural Networks (GNNs) have emerged as powerful representation learning tools for capturing complex dependencies within diverse graph-structured data. Despite their success in a wide range of graph mining tasks, GNNs have raised…
Graph Neural Networks (GNNs) is an architecture for structural data, and has been adopted in a mass of tasks and achieved fabulous results, such as link prediction, node classification, graph classification and so on. Generally, for a…
Recently, graph neural networks (GNNs) have proved to be suitable in tasks on unstructured data. Particularly in tasks as community detection, node classification, and link prediction. However, most GNN models still operate with static…
We propose a novel spectral convolutional neural network (CNN) model on graph structured data, namely Distributed Feedback-Looped Networks (DFNets). This model is incorporated with a robust class of spectral graph filters, called…
Modeling the distribution of natural images is challenging, partly because of strong statistical dependencies which can extend over hundreds of pixels. Recurrent neural networks have been successful in capturing long-range dependencies in a…
We present a neural architecture that takes as input a 2D or 3D shape and outputs a program that generates the shape. The instructions in our program are based on constructive solid geometry principles, i.e., a set of boolean operations on…
We propose a generative model of unordered point sets, such as point clouds, in the form of an energy-based model, where the energy function is parameterized by an input-permutation-invariant bottom-up neural network. The energy function…
Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the…
Convolutional Neural Networks (CNNs) excel at extracting local features hierarchically, but their performance in capturing complex correlations hinges heavily on deep architectures, which are usually computationally demanding and difficult…
In recent years, generative adversarial networks (GANs) have demonstrated impressive experimental results while there are only a few works that foster statistical learning theory for GANs. In this work, we propose an infinite dimensional…
Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…
We study the discrete-to-continuum consistency of the training of shallow graph convolutional neural networks (GCNNs) on proximity graphs of sampled point clouds under a manifold assumption. Graph convolution is defined spectrally via the…