Related papers: Deep Submodular Functions

Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…

Deep learning is also known as hierarchical learning, where the learner _learns_ to represent a complicated target function by decomposing it into a sequence of simpler functions to reduce sample and time complexity. This paper formally…

Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…

Improving the generalization ability of Deep Neural Networks (DNNs) is critical for their practical uses, which has been a longstanding challenge. Some theoretical studies have uncovered that DNNs have preferences for some frequency…

Feature discrimination is a crucial aspect of neural network design, as it directly impacts the network's ability to distinguish between classes and generalize across diverse datasets. The accomplishment of achieving high-quality feature…

The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Neural Networks perform much better in function approximation…

Positive semidefinite matrix factorization (PSDMF) expresses each entry of a nonnegative matrix as the inner product of two positive semidefinite (psd) matrices. When all these psd matrices are constrained to be diagonal, this model is…

Submodular functions can be exactly minimized in polynomial time, and the special case that graph cuts solve with max flow \cite{KZ:PAMI04} has had significant impact in computer vision \cite{BVZ:PAMI01,Kwatra:SIGGRAPH03,Rother:GrabCut04}.…

The problem of maximizing nonnegative monotone submodular functions under a certain constraint has been intensively studied in the last decade, and a wide range of efficient approximation algorithms have been developed for this problem.…

We introduce a new class of non-linear function-on-function regression models for functional data using neural networks. We propose a framework using a hidden layer consisting of continuous neurons, called a continuous hidden layer, for…

We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…

Deep neural networks (DNNs) exhibit a surprising structure in their final layer known as neural collapse (NC), and a growing body of works has currently investigated the propagation of neural collapse to earlier layers of DNNs -- a…

Deep learning (DL) enables deep neural networks (DNNs) to automatically learn complex tasks or rules from given examples without instructions or guiding principles. As we do not engineer DNNs' functions, it is extremely difficult to…

Deep Neural Networks (DNNs) became the standard tool for function approximation with most of the introduced architectures being developed for high-dimensional input data. However, many real-world problems have low-dimensional inputs for…

Deep convolutional neural networks (DCNNs) have shown remarkable performance in image classification tasks in recent years. Generally, deep neural network architectures are stacks consisting of a large number of convolutional layers, and…

Submodular functions are discrete analogs of convex functions, which have applications in various fields, including machine learning and computer vision. However, in large-scale applications, solving Submodular Function Minimization (SFM)…

In the architecture of deep learning models, inspired by biological neurons, activation functions (AFs) play a pivotal role. They significantly influence the performance of artificial neural networks. By modulating the non-linear properties…

Multi-scale deep neural networks (MscaleDNNs) with downing-scaling mapping have demonstrated superiority over traditional DNNs in approximating target functions characterized by high frequency features. However, the performance of…

Deep Neural Networks (DNNs) have already become a crucial computational approach to revealing the spatial patterns in the human brain; however, there are three major shortcomings in utilizing DNNs to detect the spatial patterns in…