Related papers: Revisiting Transformation Invariant Geometric Deep…
We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an…
Inspired by two basic mechanisms in animal visual systems, we introduce a feature transform technique that imposes invariance properties in the training of deep neural networks. The resulting algorithm requires less parameter tuning, trains…
Integrating invariance into data representations is a principled design in intelligent systems and web applications. Representations play a fundamental role, where systems and applications are both built on meaningful representations of…
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.…
Graph transformation that predicts graph transition from one mode to another is an important and common problem. Despite much progress in developing advanced graph transformation techniques in recent years, the fundamental assumption…
Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency…
Equivariant Graph Neural Networks (GNNs) have achieved remarkable success across diverse scientific applications. However, existing approaches face critical efficiency challenges when scaling to large geometric graphs and suffer significant…
Developing robust and interpretable vision systems is a crucial step towards trustworthy artificial intelligence. In this regard, a promising paradigm considers embedding task-required invariant structures, e.g., geometric invariance, in…
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…
It is often said that a deep learning model is "invariant" to some specific type of transformation. However, what is meant by this statement strongly depends on the context in which it is made. In this paper we explore the nature of…
Invariant and equivariant networks have been successfully used for learning images, sets, point clouds, and graphs. A basic challenge in developing such networks is finding the maximal collection of invariant and equivariant linear layers.…
Neural networks that satisfy invariance with respect to input permutations have been widely studied in machine learning literature. However, in many applications, only a subset of all input permutations is of interest. For heterogeneous…
This paper is focused on studying the view-manifold structure in the feature spaces implied by the different layers of Convolutional Neural Networks (CNN). There are several questions that this paper aims to answer: Does the learned CNN…
Training a Convolutional Neural Network (CNN) to be robust against rotation has mostly been done with data augmentation. In this paper, another progressive vision of research direction is highlighted to encourage less dependence on data…
Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (permutation of the input permutes the output). In this paper,…
Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…
Incorporating Euclidean symmetries (e.g. rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling. However, in various…
Although theoretical properties such as expressive power and over-smoothing of graph neural networks (GNN) have been extensively studied recently, its convergence property is a relatively new direction. In this paper, we investigate the…
Deep convolutional neural networks have been shown to be vulnerable to arbitrary geometric transformations. However, there is no systematic method to measure the invariance properties of deep networks to such transformations. We propose…
Graph neural networks (GNNs) are a well-regarded tool for learned control of networked dynamical systems due to their ability to be deployed in a distributed manner. However, current distributed GNN architectures assume that all nodes in…