arXiv research

We propose a deep learning based method, the Deep Ritz Method, for numerically solving variational problems, particularly the ones that arise from partial differential equations. The Deep Ritz method is naturally nonlinear, naturally adaptive and has the potential to work in rather high dimensions. The framework is qui…

Paper uses deep Ritz method for solving stationary Schrödinger equation, proving convergence and feature emergence.

Paper studies deep learning for solving elliptic PDEs, proving optimal bounds and neural scaling laws.

Paper analyzes DRM for solving high-dimensional elliptic PDEs with generalization bounds.

Study analyzes error in neural network solving PDEs, providing convergence and error bounds.

This paper compares deeper and wider neural networks for optimal generalization error in Sobolev losses.

Paper develops IFTRR to solve sparse generalized eigenvalue problems efficiently.

In this paper, we propose the idea of radial scaling in frequency domain and activation functions with compact support to produce a multi-scale DNN (MscaleDNN), which will have the multi-scale capability in approximating high frequency and high dimensional functions and speeding up the solution of high dimensional PDEs…

New neural network approach solves Poisson equations efficiently.

For a bounded domain $Ω$ with a piecewise smooth boundary in a complete Riemannian manifold $M$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. By making use of a fact that eigenfunctions form an orthonormal basis of $L^2(Ω)$ in place of the Rayleigh-Ritz formula, we obtain inequalities for …

NWoS solves high-dimensional Poisson equations using neural networks.

We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the Cauchy-Schwarz inequality--is used to produce ``parameter-free'', ``projection-free'' vers…

Gradient descent achieves optimal learning for elliptic PDEs via Sobolev norms.

Fast and accurate methods for low-rank learning problems.

Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices, and so on. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes. Many issues remain, thou…

New algorithm updates eigenvectors of evolving graphs efficiently.

Probabilistic deep learning uses neural networks and models to handle uncertainty.

Improves deep learning robustness by considering task and model.

Deep-RLS uses deep learning to improve PCA for better source separation.

How to understand deep learning systems remains an open problem. In this paper we propose that the answer may lie in the geometrization of deep networks. Geometrization is a bridge to connect physics, geometry, deep network and quantum computation and this may result in a new scheme to reveal the rule of the physical w…

SDF adapts Deep Forest for evolving data streams with active learning.

Deep SSMs use neural networks to identify complex systems.

This paper presents a basic property of region dividing of ReLU (rectified linear unit) deep learning when new layers are successively added, by which two new perspectives of interpreting deep learning are given. The first is related to decision trees and forests; we construct a deep learning structure equivalent to a …

The great success of deep learning shows that its technology contains profound truth, and understanding its internal mechanism not only has important implications for the development of its technology and effective application in various fields, but also provides meaningful insights into the understanding of human brai…

Bayesian methods enhance deep learning models by improving reliability and uncertainty.

NeurIPS 2020 competition seeks to predict deep learning generalization.

This paper analyzes generalization issues in deep reinforcement learning.

This paper explains why ResNets generalize better than FFNets using neural tangent kernels.

This paper provides an overview of deep semi-supervised learning methods.

In this paper, we have proposed a deep quantum SVM formulation, and further demonstrated a quantum-clustering framework based on the quantum deep SVM formulation, deep convolutional neural networks, and quantum K-Means clustering. We have investigated the run time computational complexity of the proposed quantum deep c…

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take consistent and robust decisions in complex environments. The integration of deep learn…

With the growth of deep learning, how to describe deep neural networks unifiedly is becoming an important issue. We first formalize neural networks mathematically with their directed graph representations, and prove a generation theorem about the induced networks of connected directed acyclic graphs. Then, we set up a …

Deep active inference learns policies from sensory inputs.

Deep learning aids causal inference in complex settings.

Deep learning is increasingly being used in high-stake decision making applications that affect individual lives. However, deep learning models might exhibit algorithmic discrimination behaviors with respect to protected groups, potentially posing negative impacts on individuals and society. Therefore, fairness in deep…

In this paper, we investigate the unsupervised deep representation learning issue and technically propose a novel framework called Deep Self-representative Concept Factorization Network (DSCF-Net), for clustering deep features. To improve the representation and clustering abilities, DSCF-Net explicitly considers discov…

This paper introduces Deep Incremental Boosting, a new technique derived from AdaBoost, specifically adapted to work with Deep Learning methods, that reduces the required training time and improves generalisation. We draw inspiration from Transfer of Learning approaches to reduce the start-up time to training each incr…

Proposes model-based robust deep learning to handle natural variation in data.

In this paper we introduce ZhuSuan, a python probabilistic programming library for Bayesian deep learning, which conjoins the complimentary advantages of Bayesian methods and deep learning. ZhuSuan is built upon Tensorflow. Unlike existing deep learning libraries, which are mainly designed for deterministic neural netw…

Deep ReLU networks can approximate matrix-vector products with error bounds.

Deep RL applied for Indian stock trading strategies.

Hashing has been widely used for large-scale approximate nearest neighbor search because of its storage and search efficiency. Recent work has found that deep supervised hashing can significantly outperform non-deep supervised hashing in many applications. However, most existing deep supervised hashing methods adopt a …

Deep learning methods are reviewed for preserving structure in neural networks.

Characterizes deep neural network weight space for adversarial attacks.

Although deep learning has shown great success in recent years, researchers have discovered a critical flaw where small, imperceptible changes in the input to the system can drastically change the output classification. These attacks are exploitable in nearly all of the existing deep learning classification frameworks.…

Bayesian interpretation of deep ensembles improves uncertainty quantification.

Study develops efficient nested deep hedging method for derivatives pricing.

Deep learning depends on tuning layers near critical points.