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A simple alternative to the conjugate gradient(CG) method is presented; this method is developed as a special case of the more general iterated Ritz method (IRM) for solving a system of linear equations. This novel algorithm is not based on…
Gradient descent (GD) methods are commonly employed in machine learning problems to optimize the parameters of the model in an iterative fashion. For problems with massive datasets, computations are distributed to many parallel computing…
Multiversioning is widely used in databases, transactional memory, and concurrent data structures. It can be used to support read-only transactions that appear atomic in the presence of concurrent update operations. Any system that…
Winograd convolution is originally proposed to reduce the computing overhead by converting multiplication in neural network (NN) with addition via linear transformation. Other than the computing efficiency, we observe its great potential in…
A long-standing issue in the parallel-in-time community is the poor convergence of standard iterative parallel-in-time methods for hyperbolic partial differential equations (PDEs), and for advection-dominated PDEs more broadly. Here, a…
Scaling supercomputers comes with an increase in failure rates due to the increasing number of hardware components. In standard practice, applications are made resilient through checkpointing data and restarting execution after a failure…
The efficient method for computing the sensitivities is the adjoint method. The cost of solving an adjoint equation is comparable to the cost of solving the governing equation. Once the adjoint solution is obtained, the sensitivities to any…
Background: Recursive reasoning models achieve strong performance through iterative refinement, allowing small networks to match large language models. However, training is computationally expensive, often requiring 36 GPU-hours for Sudoku…
We propose both serial and parallel proximal (linearized) alternating direction method of multipliers (ADMM) algorithms for training residual neural networks. In contrast to backpropagation-based approaches, our methods inherently mitigate…
Generative recommendation (GR) has emerged as a promising paradigm that replaces fragmented, scenario-specific architectures with unified Transformer-based models, exhibiting scaling-law behavior where recommendation quality improves…
Supercomputing systems today often come in the form of large numbers of commodity systems linked together into a computing cluster. These systems, like any distributed system, can have large numbers of independent hardware components…
We develop and analyze new scheduling algorithms for solving sparse triangular linear systems (SpTRSV) in parallel. Our approach produces highly efficient synchronous schedules for the forward- and backward-substitution algorithm. Compared…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
Masked Autoregressive (MAR) models promise better efficiency in visual generation than autoregressive (AR) models for the ability of parallel generation, yet their acceleration potential remains constrained by the modeling complexity of…
This paper delves into a comprehensive analysis of fault-tolerant memory systems, focusing on recovery techniques modeled using Markov chains to address transient errors. The study revolves around the application of scrubbing methods in…
A Generative Adversarial Network (GAN) with generator $G$ trained to model the prior of images has been shown to perform better than sparsity-based regularizers in ill-posed inverse problems. Here, we propose a new method of deploying a…
Prompt engineering is crucial for fully leveraging large language models (LLMs), yet most existing optimization methods follow a single trajectory, resulting in limited adaptability, gradient conflicts, and high computational overhead. We…
Handling faults is a growing concern in HPC. In future exascale systems, it is projected that silent undetected errors will occur several times a day, increasing the occurrence of corrupted results. In this article, we propose SEDAR, which…
In this article, we propose an accuracy-assuring technique for finding a solution for unsymmetric linear systems. Such problems are related to different areas such as image processing, computer vision, and computational fluid dynamics.…
Restoring critical loads after extreme events demands adaptive control to maintain distribution-grid resilience, yet uncertainty in renewable generation, limited dispatchable resources, and nonlinear dynamics make effective restoration…