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Temporal point process (TPP) is an important tool for modeling and predicting irregularly timed events across various domains. Recently, the recurrent neural network (RNN)-based TPPs have shown practical advantages over traditional…
Binary Neural Networks (BNNs) show great promise for real-world embedded devices. As one of the critical steps to achieve a powerful BNN, the scale factor calculation plays an essential role in reducing the performance gap to their…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
Accurate probabilistic predictions are essential for optimal decision making. While neural network miscalibration has been studied primarily in classification, we investigate this in the less-explored domain of regression. We conduct the…
This technical note proposes the decentralized-partial-consensus optimization with inequality constraints, and a continuous-time algorithm based on multiple interconnected recurrent neural networks (RNNs) is derived to solve the obtained…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
Fast and accurate MRI image reconstruction from undersampled data is crucial in clinical practice. Deep learning based reconstruction methods have shown promising advances in recent years. However, recovering fine details from undersampled…
Employing two distinct types of regularization terms, we propose two regularized extragradient methods for solving equilibrium problems on Hadamard manifolds. The sequences generated by these extragradient algorithms converge to a solution…
A new numerical domain decomposition method is proposed for solving elliptic equations on compact Riemannian manifolds. The advantage of this method is to avoid global triangulations or grids on manifolds. Our method is numerically tested…
In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…
In this paper, we propose Selective Output Smoothing Regularization, a novel regularization method for training the Convolutional Neural Networks (CNNs). Inspired by the diverse effects on training from different samples, Selective Output…
Physics-informed neural networks have attracted significant attention in scientific machine learning for their capability to solve forward and inverse problems governed by partial differential equations. However, the accuracy of PINN…
Floating point error is an inevitable drawback of embedded systems implementation. Computing rigorous upper bounds of roundoff errors is absolutely necessary to the validation of critical software. This problem is even more challenging when…
We consider optimization problems on Riemannian manifolds with equality and inequality constraints, which we call Riemannian nonlinear optimization (RNLO) problems. Although they have numerous applications, the existing studies on them are…
A new recalibration post-processing method is presented to improve the quality of the posterior approximation when using Approximate Bayesian Computation (ABC) algorithms. Recalibration may be used in conjunction with existing…
The Bunch-Kaufman algorithm and Aasen's algorithm are two of the most widely used methods for solving symmetric indefinite linear systems, yet they both are known to suffer from occasional numerical instability due to potentially…
Random backpropagation (RBP) is a variant of the backpropagation algorithm for training neural networks, where the transpose of the forward matrices are replaced by fixed random matrices in the calculation of the weight updates. It is…
We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…
Doubly nonnegative (DNN) relaxation usually provides a tight lower bound for a mixed-binary quadratic program (MBQP). However, solving DNN problems is challenging because: (1) the problem size is $\Omega((n+l)^2)$ for an MBQP with $n$…
Neural network ensembles, such as Bayesian neural networks (BNNs), have shown success in the areas of uncertainty estimation and robustness. However, a crucial challenge prohibits their use in practice. BNNs require a large number of…