Related papers: Lipschitz constant estimation for 1D convolutional…
Accurate image reconstruction is at the heart of diagnostics in medical imaging. Supervised deep learning-based approaches have been investigated for solving inverse problems including image reconstruction. However, these trained models…
Convolutional neural networks (CNNs) have found many applications in tasks involving two-dimensional (2D) data, such as image classification and image processing. Therefore, 2D convolution layers have been heavily optimized on CPUs and…
Bilinear pooling of Convolutional Neural Network (CNN) features [22, 23], and their compact variants [10], have been shown to be effective at fine-grained recognition, scene categorization, texture recognition, and visual question-answering…
We propose a neural network architecture that can learn discriminative geometric representations of data from persistence diagrams, common descriptors of Topological Data Analysis. The learned representations enjoy Lipschitz stability with…
This work presents a new approach for premixed turbulent combustion modeling based on convolutional neural networks (CNN). We first propose a framework to reformulate the problem of subgrid flame surface density estimation as a machine…
We present compositional nearest neighbors (CompNN), a simple approach to visually interpreting distributed representations learned by a convolutional neural network (CNN) for pixel-level tasks (e.g., image synthesis and segmentation). It…
Most modern convolutional neural networks (CNNs) used for object recognition are built using the same principles: Alternating convolution and max-pooling layers followed by a small number of fully connected layers. We re-evaluate the state…
Modern multimodal systems deployed in industrial and safety-critical environments must remain reliable under partial sensor failures, signal degradation, or cross-modal inconsistencies. This work introduces a mathematically grounded…
We establish uniform Lipschitz estimates for second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients. We give interior estimates as well as estimates up to the boundary in bounded…
With the widespread applications of deep convolutional neural networks (DCNNs), it becomes increasingly important for DCNNs not only to make accurate predictions but also to explain how they make their decisions. In this work, we propose a…
Depthwise separable convolution has shown great efficiency in network design, but requires time-consuming training procedure with full training-set available. This paper first analyzes the mathematical relationship between regular…
We derive explicit bounds for the computation of normalizing constants $Z$ for log-concave densities $\pi = \exp(-U)/Z$ with respect to the Lebesgue measure on $\mathbb{R}^d$. Our approach relies on a Gaussian annealing combined with recent…
The Lipschitz constant of a response surface function upper bounds the sensitivity of a dependent variable to changes in the independent ones. Traditionally, such constants have found much implicit and abstract use in mathematically…
Convolutional neural network (CNN) and its variants have led to many state-of-art results in various fields. However, a clear theoretical understanding about them is still lacking. Recently, multi-layer convolutional sparse coding (ML-CSC)…
Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…
Phase unwrapping is a classical ill-posed problem which aims to recover the true phase from wrapped phase. In this paper, we introduce a novel Convolutional Neural Network (CNN) that incorporates a Spatial Quad-Directional Long Short Term…
This paper addresses the problem of consistently estimating a continuous-time (CT) diffusively coupled network (DCN) to identify physical components in a physical network. We develop a three-step frequency-domain identification method for…
Recently, many studies have shed light on the high adaptivity of deep neural network methods in nonparametric regression models, and their superior performance has been established for various function classes. Motivated by this…
Iterative algorithms solve problems by taking steps until a solution is reached. Models in the form of Deep Thinking (DT) networks have been demonstrated to learn iterative algorithms in a way that can scale to different sized problems at…
With the rapid development of deep learning, a variety of change detection methods based on deep learning have emerged in recent years. However, these methods usually require a large number of training samples to train the network model, so…