相关论文: Weighted Inner Products for GMRES and GMRES-DR

This paper shows that the weighting coefficient matrices of the differential quadrature method (DQM) are centrosymmetric or skew-centrosymmetric if the grid spacings are symmetric irrespective of whether they are equal or unequal. A new…

A multigrid method is proposed in this paper to solve eigenvalue problems by the finite element method based on the shifted-inverse power iteration technique. With this scheme, solving eigenvalue problem is transformed to a series of…

Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the…

Inverse problems are ubiquitous in science and engineering. Many of these are naturally formulated as a PDE-constrained optimization problem. These non-linear, large-scale, constrained optimization problems know many challenges, of which…

We study the volume averaging of inhomogeneous metrics within GR and discuss its shortcomings such as gauge dependence, singular behavior as a result of caustics, and causality violations. To remedy these shortcomings, we suggest some…

The weight matrix (WM) of a neural network (NN) is its program. The programs of many traditional NNs are learned through gradient descent in some error function, then remain fixed. The WM of a self-referential NN, however, can keep rapidly…

We propose $\textit{weighted inner product similarity}$ (WIPS) for neural network-based graph embedding. In addition to the parameters of neural networks, we optimize the weights of the inner product by allowing positive and negative…

Consider a marketplace of AI tools, each with slightly different strengths and weaknesses. By selecting the right model for the task at hand, a user can do better than simply committing to a single model for everything. Routers operate…

Geographically weighted regression (GWR) is a popular tool for modeling spatial heterogeneity in a regression model. However, the current weighting function used in GWR only considers the geographical distance, while the attribute…

If the numerical range of a matrix is contained in the right half of the complex plane, the GMRES algorithm for solving linear systems will reduce the norm of the residual at every iteration. In his Ph.D. dissertation, Howard Elman derived…

We investigate mathematically the notion of incoherence: a structural issue with reinforcement learning policies derived by naive goal-conditioning of autoregressive models. We focus on the process of re-training models on their own…

Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically…

This study proposes a class of augmented subspace schemes for the weak Galerkin (WG) finite element method used to solve eigenvalue problems. The augmented subspace is built with the conforming linear finite element space defined on the…

This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a…

Gradient reconstruction is a key process for the spatial accuracy and robustness of finite volume method, especially in industrial aerodynamic applications in which grid quality affects reconstruction methods significantly. A novel gradient…

Model compression has been introduced to reduce the required hardware resources while maintaining the model accuracy. Lots of techniques for model compression, such as pruning, quantization, and low-rank approximation, have been suggested…

In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of…

In [8] a notion of generalized Hadamard product was introduced. We show that when certain kinds of tensors interact with the eigenvalues of symmetric matrices the resulting formulae can be nicely expressed using the generalized Hadamard…

Recently, the concept of teaching has been introduced into machine learning, in which a teacher model is used to guide the training of a student model (which will be used in real tasks) through data selection, loss function design, etc.…

While normalization techniques are widely used in deep learning, their theoretical understanding remains relatively limited. In this work, we establish the benefits of (generalized) weight normalization (WN) applied to the overparameterized…