Related papers: Riemannian Residual Neural Networks
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean…
Deep Neural Networks are widely used for solving complex problems in several scientific areas, such as speech recognition, machine translation, image analysis. The strategies employed to investigate their theoretical properties mainly rely…
In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…
Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…
Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean…
Although Deep Learning (DL) has achieved success in complex Artificial Intelligence (AI) tasks, it suffers from various notorious problems (e.g., feature redundancy, and vanishing or exploding gradients), since updating parameters in…
Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…
Deep neural networks demonstrate to have a high performance on image classification tasks while being more difficult to train. Due to the complexity and vanishing gradient problem, it normally takes a lot of time and more computational…
Deep residual networks (ResNets) made a recent breakthrough in deep learning. The core idea of ResNets is to have shortcut connections between layers that allow the network to be much deeper while still being easy to optimize avoiding…
Convolutional Neural Networks (CNNs) has revolutionized computer vision, but training very deep networks has been challenging due to the vanishing gradient problem. This paper explores Residual Networks (ResNet), introduced by He et al.…
This paper addresses the understanding and characterization of residual networks (ResNet), which are among the state-of-the-art deep learning architectures for a variety of supervised learning problems. We focus on the mapping component of…
Residual networks (Resnets) have become a prominent architecture in deep learning. However, a comprehensive understanding of Resnets is still a topic of ongoing research. A recent view argues that Resnets perform iterative refinement of…
Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be…
Neural networks are playing a crucial role in everyday life, with the most modern generative models able to achieve impressive results. Nonetheless, their functioning is still not very clear, and several strategies have been adopted to…
Many tasks require mapping continuous input data (e.g. images) to discrete task outputs (e.g. class labels). Yet, how neural networks learn to perform such discrete computations on continuous data manifolds remains poorly understood. Here,…
Deep neural networks (DNNs) on Riemannian manifolds have garnered increasing interest in various applied areas. For instance, DNNs on spherical and hyperbolic manifolds have been designed to solve a wide range of computer vision and nature…
We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued…
Deep neural networks have become the main work horse for many tasks involving learning from data in a variety of applications in Science and Engineering. Traditionally, the input to these networks lie in a vector space and the operations…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…