Related papers: Matrix Manifold Neural Networks++
Our proposed deeply-supervised nets (DSN) method simultaneously minimizes classification error while making the learning process of hidden layers direct and transparent. We make an attempt to boost the classification performance by studying…
Efforts are underway to study ways via which the power of deep neural networks can be extended to non-standard data types such as structured data (e.g., graphs) or manifold-valued data (e.g., unit vectors or special matrices). Often,…
Deep neural networks (DNNs) have found applications in diverse signal processing (SP) problems. Most efforts either directly adopt the DNN as a black-box approach to perform certain SP tasks without taking into account of any known…
In this paper, we propose a new neural architecture search (NAS) problem of Symmetric Positive Definite (SPD) manifold networks, aiming to automate the design of SPD neural architectures. To address this problem, we first introduce a…
Complex nonlinear models such as deep neural network (DNNs) have become an important tool for image classification, speech recognition, natural language processing, and many other fields of application. These models however lack…
Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account…
Currently there is great interest in the utility of deep neural networks (DNNs) for the physical layer of radio frequency (RF) communications. In this manuscript, we describe a custom DNN specially designed to solve problems in the RF…
This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…
This paper introduces an extension of the backpropagation algorithm that enables us to have layers with constrained weights in a deep network. In particular, we make use of the Riemannian geometry and optimization techniques on matrix…
Normalization layers are crucial for deep learning, but their Euclidean formulations are inadequate for data on manifolds. On the other hand, many Riemannian manifolds in machine learning admit gyro-structures, enabling principled…
This article provides an expository account of training dynamics in the Deep Linear Network (DLN) from the perspective of the geometric theory of dynamical systems. Rigorous results by several authors are unified into a thermodynamic…
Deep neural networks (DNN) have achieved unprecedented performance in computer-vision tasks almost ubiquitously in business, technology, and science. While substantial efforts are made to engineer highly accurate architectures and provide…
A very popular model in machine learning is the feedforward neural network (FFN). The FFN can approximate general functions and mitigate the curse of dimensionality. Here we introduce FFNs which represent sections of holomorphic line…
While deep learning algorithms demonstrate a great potential in scientific computing, its application to multi-scale problems remains to be a big challenge. This is manifested by the "frequency principle" that neural networks tend to learn…
We study data-driven representations for three-dimensional triangle meshes, which are one of the prevalent objects used to represent 3D geometry. Recent works have developed models that exploit the intrinsic geometry of manifolds and…
The success of Large Language Models (LLMs), e.g., ChatGPT, is witnessed by their planetary popularity, their capability of human-like communication, and also by their steadily improved reasoning performance. However, it remains unclear…
Graph Neural Networks (GNNs) have attracted increasing attention in recent years and have achieved excellent performance in semi-supervised node classification tasks. The success of most GNNs relies on one fundamental assumption, i.e., the…
Generative networks have shown remarkable success in learning complex data distributions, particularly in generating high-dimensional data from lower-dimensional inputs. While this capability is well-documented empirically, its theoretical…
Artificial Recurrent Neural Networks (RNNs) are widely used in neuroscience to model the collective activity of neurons during behavioral tasks. The high dimensionality of their parameter and activity spaces, however, often make it…
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…