相关论文: Deep Submodular Functions

Deep Neural Networks (DNNs) are widely used for their ability to effectively approximate large classes of functions. This flexibility, however, makes the strict enforcement of constraints on DNNs an open problem. Here we present a framework…

We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…

The scope of research in the domain of activation functions remains limited and centered around improving the ease of optimization or generalization quality of neural networks (NNs). However, to develop a deeper understanding of deep…

Recent techniques that integrate \emph{solver layers} into Deep Neural Networks (DNNs) have shown promise in bridging a long-standing gap between inductive learning and symbolic reasoning techniques. In this paper we present a set of…

Deep learning has been applied to various tasks in the field of machine learning and has shown superiority to other common procedures such as kernel methods. To provide a better theoretical understanding of the reasons for its success, we…

Deep neural networks have become a highly accurate and powerful wavefunction ansatz in combination with variational Monte Carlo methods for solving the electronic Schr\"odinger equation. However, despite their success and favorable scaling,…

The purpose of this article is to develop a machinery to study the capacity of deep neural networks (DNNs) to approximate high-dimensional functions. In particular, we show that DNNs have the expressive power to overcome the curse of…

Collaborative Filtering (CF) is widely used in recommender systems to model user-item interactions. With the great success of Deep Neural Networks (DNNs) in various fields, advanced works recently have proposed several DNN-based models for…

Learning a deep neural network requires solving a challenging optimization problem: it is a high-dimensional, non-convex and non-smooth minimization problem with a large number of terms. The current practice in neural network optimization…

Among the variational wave functions for Fermionic Hamiltonians, neural network backflow (NNBF) and hidden fermion determinant states (HFDS) are two prominent classes to provide accurate approximations to the ground state. Here we develop a…

Submodular function minimization (SFM) is a fundamental discrete optimization problem which generalizes many well known problems, has applications in various fields, and can be solved in polynomial time. Owing to applications in computer…

In the context of deep learning with kernel machines, the deep Restricted Kernel Machine (DRKM) framework allows multiple levels of kernel PCA (KPCA) and Least-Squares Support Vector Machines (LSSVM) to be combined into a deep architecture…

Semi-structured networks (SSNs) merge the structures familiar from additive models with deep neural networks, allowing the modeling of interpretable partial feature effects while capturing higher-order non-linearities at the same time. A…

This paper aims at a better understanding of matrix factorization (MF), factorization machines (FM), and their combination with deep algorithms' application in recommendation systems. Specifically, this paper will focus on Singular Value…

It is frequently observed that overparameterized neural networks generalize well. Regarding such phenomena, existing theoretical work mainly devotes to linear settings or fully-connected neural networks. This paper studies the learning…

Mini-batch gradient descent based methods are the de facto algorithms for training neural network architectures today. We introduce a mini-batch selection strategy based on submodular function maximization. Our novel submodular formulation…

A primary spectral submanifold (SSM) is the unique smoothest nonlinear continuation of a nonresonant spectral subspace $E$ of a dynamical system linearized at a fixed point. Passing from the full nonlinear dynamics to the flow on an…

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…

Deep-learning density functional theory (DFT) shows great promise to significantly accelerate material discovery and potentially revolutionize materials research. However, current research in this field primarily relies on data-driven…

High-dimensional depth separation results for neural networks show that certain functions can be efficiently approximated by two-hidden-layer networks but not by one-hidden-layer ones in high-dimensions $d$. Existing results of this type…