Related papers: Level set learning with pseudo-reversible neural n…
We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications,…
A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Leveraging geometric information provided by the Implicit…
Deep neural networks (DNNs) provide useful models of visual representational transformations. We present a method that enables a DNN (student) to learn from the internal representational spaces of a reference model (teacher), which could be…
Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer…
Deep Reinforcement Learning (RL) powered by neural net approximation of the Q function has had enormous empirical success. While the theory of RL has traditionally focused on linear function approximation (or eluder dimension) approaches,…
Most image super-resolution (SR) methods are developed on synthetic low-resolution (LR) and high-resolution (HR) image pairs that are constructed by a predetermined operation, e.g., bicubic downsampling. As existing methods typically learn…
We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is…
Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on…
This paper proposes a novel pixel-level distribution regularization scheme (DRSL) for self-supervised domain adaptation of semantic segmentation. In a typical setting, the classification loss forces the semantic segmentation model to…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
Variational Level Set (LS) has been a widely used method in medical segmentation. However, it is limited when dealing with multi-instance objects in the real world. In addition, its segmentation results are quite sensitive to initial…
Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with…
Sparse representations has shown to be a very powerful model for real world signals, and has enabled the development of applications with notable performance. Combined with the ability to learn a dictionary from signal examples,…
Deep neural networks (DNNs) usually contain massive parameters, but there is redundancy such that it is guessed that the DNNs could be trained in low-dimensional subspaces. In this paper, we propose a Dynamic Linear Dimensionality Reduction…
Recursive least squares (RLS) algorithms were once widely used for training small-scale neural networks, due to their fast convergence. However, previous RLS algorithms are unsuitable for training deep neural networks (DNNs), since they…
This paper introduces deep super ReLU networks (DSRNs) as a method for approximating functions in Sobolev spaces measured by Sobolev norms $W^{m,p}$ for $m\in\mathbb{N}$ with $m\ge 2$ and $1\le p\le +\infty$. Standard ReLU deep neural…
Parametric approaches to Learning, such as deep learning (DL), are highly popular in nonlinear regression, in spite of their extremely difficult training with their increasing complexity (e.g. number of layers in DL). In this paper, we…
High dimensional data reduction techniques are provided by using partial least squares within deep learning. Our framework provides a nonlinear extension of PLS together with a disciplined approach to feature selection and architecture…
Deep Neural Network (DNN)-based image reconstruction, despite many successes, often exhibits uneven fidelity between high and low spatial frequency bands. In this paper we propose the Learning Synthesis by DNN (LS-DNN) approach where two…
We introduce a deep learning (DL) framework for inverse problems in imaging, and demonstrate the advantages and applicability of this approach in passive synthetic aperture radar (SAR) image reconstruction. We interpret image recon-…