Related papers: Auto-Differentiating Linear Algebra
Deep learning (DL) techniques have been extensively utilized for medical image classification. Most DL-based classification networks are generally structured hierarchically and optimized through the minimization of a single loss function…
The classification of MRI images according to the anatomical field of view is a necessary task to solve when faced with the increasing quantity of medical images. In parallel, advances in deep learning makes it a suitable tool for computer…
We have repurposed Google Tensor Processing Units (TPUs), application-specific chips developed for machine learning, into large-scale dense linear algebra supercomputers. The TPUs' fast inter-core interconnects (ICI)s, physically…
In machine learning, there is a fundamental trade-off between ease of optimization and expressive power. Neural Networks, in particular, have enormous expressive power and yet are notoriously challenging to train. The nature of that…
Neural networks (NNs) achieve outstanding performance in many domains; however, their decision processes are often opaque and their inference can be computationally expensive in resource-constrained environments. We recently proposed…
Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep…
Deep Learning (DL) models are often black boxes, making their decision-making processes difficult to interpret. This lack of transparency has driven advancements in eXplainable Artificial Intelligence (XAI), a field dedicated to clarifying…
In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the…
Deep convolutional neural networks have revolutionized many machine learning and computer vision tasks, however, some remaining key challenges limit their wider use. These challenges include improving the network's robustness to…
On account of its many successes in inference tasks and denoising applications, Dictionary Learning (DL) and its related sparse optimization problems have garnered a lot of research interest. While most solutions have focused on single…
A novel precoding method based on supervised deep neural networks is introduced for the multiple-input multiple-output Gaussian wiretap channel. The proposed deep learning (DL)-based precoding learns the input covariance matrix through…
We propose the Lanczos network (LanczosNet), which uses the Lanczos algorithm to construct low rank approximations of the graph Laplacian for graph convolution. Relying on the tridiagonal decomposition of the Lanczos algorithm, we not only…
The deep linear network (DLN) is a model for implicit regularization in gradient based optimization of overparametrized learning architectures. Training the DLN corresponds to a Riemannian gradient flow, where the Riemannian metric is…
We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many…
We investigate deep morphological neural networks (DMNNs). We demonstrate that despite their inherent non-linearity, "linear" activations are essential for DMNNs. To preserve their inherent sparsity, we propose architectures that constraint…
The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…
This paper introduces a meta-learning approach for parameterized pseudo-differential operators with deep neural networks. With the help of the nonstandard wavelet form, the pseudo-differential operators can be approximated in a compressed…
We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…
Decision Trees (DTs) constitute one of the major highly non-linear AI models, valued, e.g., for their efficiency on tabular data. Learning accurate DTs is, however, complicated, especially for oblique DTs, and does take a significant…
Predicting the next activity of a running process is an important aspect of process management. Recently, artificial neural networks, so called deep-learning approaches, have been proposed to address this challenge. This demo paper…