Fault Tolerant and Energy Efficient One-Sided Matrix Decompositions on Heterogeneous Systems with GPUs

Heterogeneous computing system with both CPUs and GPUs has become a class of widely used hardware architecture in supercomputers. As heterogeneous systems delivering higher computational performance, they are being built with an increasing number of complex components. This is anticipated that these systems will be more susceptible to hardware faults with higher power consumption. Numerical linear algebra libraries are used in a wide spectrum of high-performance scientific applications. Among numerical linear algebra operations, one-sided matrix decompositions can sometimes take a large portion of execution time or even dominate the whole scientific application execution. Due to the computational characteristic of one-sided matrix decompositions, they are very suitable for computation platforms such as heterogeneous systems with CPUs and GPUs. Many works have been done to implement and optimize one-sided matrix decompositions on heterogeneous systems with CPUs and GPUs. However, it is challenging to enable stable and high performance one-sided matrix decompositions running on computing platforms that are unreliable and high energy consumption. So, in this thesis, we aim to develop novel fault tolerance and energy efficiency optimizations for one-sided matrix decompositions on heterogeneous systems with CPUs and GPUs.To improve reliability and energy efficiency, extensive researches have been done on developing and optimizing fault tolerance methods and energy-saving strategies for one-sided matrix decompositions. However, current designs still have several limitations: (1) Little has been done on developing and optimizing fault tolerance method for one-sided matrix decompositions on heterogeneous systems with GPUs; (2) Limited by the protection coverage and strength, existing fault tolerance works provide insufficient protection when applied to one-sided matrix decompositions on heterogeneous systems with GPUs; (3) Lack the knowledge of algorithms, existing system level energy saving solutions cannot achieve the optimal energy savings due to potentially inaccurate and high-cost workload prediction they rely on when they are used in one-sided matrix decompositions; (4) It is challenging to apply both fault tolerance techniques and energy saving strategies to one-side matrix decompositions at the same time given that their current designs are not naturally compatible with each other.To address the first problem, based on the original (Algorithm Based Fault Tolerance) ABFT, we develop the first ABFT for matrix decomposition on heterogeneous systems with GPUs together with the novel storage errors protection and several optimization techniques specifically for GPUs. As for the second problem, we design a novel checksum scheme for ABFT that allows data stored in matrices to be encoded in two dimensions. This stronger checksum encoding mechanism enables much stronger protection including enhanced error propagation protection. In addition, we introduce a more efficient checking scheme. By prioritizing the checksum verification according to the sensitivity of matrix operations to soft errors with optimized checksum verification kernel for GPUs, we can achieve strong protect to matrix decompositions with comparable overhead. For the third problem, to improve energy efficiency for one-sided matrix decompositions, we introduce an algorithm-based energy-saving approach designed to maximize energy savings by utilizing algorithmic characteristics. Our approach can predict program execution behavior much more accurately, which is difficult for system level solutions for applications with variable execution characteristics. Experiments show that our approach can lead to much higher energy saving than existing works. Finally, for the fourth problem, we propose a novel energy saving approach for one-sided matrix decompositions on heterogeneous systems with GPUs. It allows energy saving strategies and fault tolerance techniques to be enabled at the same time without brings performance impact or extra energy cost

Improving Energy Saving of One-sided Matrix Decompositions on CPU-GPU Heterogeneous Systems

One-sided dense matrix decompositions (e.g., Cholesky, LU, and QR) are the key components in scientific computing in many different fields. Although their design has been highly optimized for modern processors, they still consume a considerable amount of energy. As CPU-GPU heterogeneous systems are commonly used for matrix decompositions, in this work, we aim to further improve the energy saving of one-sided matrix decompositions on CPU-GPU heterogeneous systems. We first build an Algorithm-Based Fault Tolerance protected overclocking technique (ABFT-OC) to enable us to exploit reliable overclocking for key matrix decomposition operations. Then, we design an energy-saving matrix decomposition framework, Bi-directional Slack Reclamation(BSR), that can intelligently combine the capability provided by ABFT-OC and DVFS to maximize energy saving and maintain performance and reliability. Experiments show that BSR is able to save up to 11.7% more energy compared with the current best energy saving optimization approach with no performance degradation and up to 14.1% Energy * Delay^2 reduction. Also, BSR enables the Pareto efficient performance-energy trade-off, which is able to provide up to 1.43x performance improvement without costing extra energy

Scalable and Reliable Sparse Data Computation on Emergent High Performance Computing Systems

Heterogeneous systems with both CPUs and GPUs have become important system architectures in emergent High Performance Computing (HPC) systems. Heterogeneous systems must address both performance-scalability and power-scalability in the presence of failures. Aggressive power reduction pushes hardware to its operating limit and increases the failure rate. Resilience allows programs to progress when subjected to faults and is an integral component of large-scale systems, but incurs significant time and energy overhead. The future exascale systems are expected to have higher power consumption with higher fault rates. Sparse data computation is the fundamental kernel in many scientific applications. It is suitable for the studies of scalability and resilience on heterogeneous systems due to its computational characteristics. To deliver the promised performance within the given power budget, heterogeneous computing mandates a deep understanding of the interplay between scalability and resilience. Managing scalability and resilience is challenging in heterogeneous systems, due to the heterogeneous compute capability, power consumption, and varying failure rates between CPUs and GPUs. Scalability and resilience have been traditionally studied in isolation, and optimizing one typically detrimentally impacts the other. While prior works have been proved successful in optimizing scalability and resilience on CPU-based homogeneous systems, simply extending current approaches to heterogeneous systems results in suboptimal performance-scalability and/or power-scalability. To address the above multiple research challenges, we propose novel resilience and energy-efficiency technologies to optimize scalability and resilience for sparse data computation on heterogeneous systems with CPUs and GPUs. First, we present generalized analytical and experimental methods to analyze and quantify the time and energy costs of various recovery schemes, and develop and prototype performance optimization and power management strategies to improve scalability for sparse linear solvers. Our results quantitatively reveal that each resilience scheme has its own advantages depending on the fault rate, system size, and power budget, and the forward recovery can further benefit from our performance and power optimizations for large-scale computing. Second, we design a novel resilience technique that relaxes the requirement of synchronization and identicalness for processes, and allows them to run in heterogeneous resources with power reduction. Our results show a significant reduction in energy for unmodified programs in various fault situations compared to exact replication techniques. Third, we propose a novel distributed sparse tensor decomposition that utilizes an asynchronous RDMA-based approach with OpenSHMEM to improve scalability on large-scale systems and prove that our method works well in heterogeneous systems. Our results show our irregularity-aware workload partition and balanced-asynchronous algorithms are scalable and outperform the state-of-the-art distributed implementations. We demonstrate that understanding different bottlenecks for various types of tensors plays critical roles in improving scalability

GPU devices for safety-critical systems: a survey

Graphics Processing Unit (GPU) devices and their associated software programming languages and frameworks can deliver the computing performance required to facilitate the development of next-generation high-performance safety-critical systems such as autonomous driving systems. However, the integration of complex, parallel, and computationally demanding software functions with different safety-criticality levels on GPU devices with shared hardware resources contributes to several safety certification challenges. This survey categorizes and provides an overview of research contributions that address GPU devices’ random hardware failures, systematic failures, and independence of execution.This work has been partially supported by the European Research Council with Horizon 2020 (grant agreements No. 772773 and 871465), the Spanish Ministry of Science and Innovation under grant PID2019-107255GB, the HiPEAC Network of Excellence and the Basque Government under grant KK-2019-00035. The Spanish Ministry of Economy and Competitiveness has also partially supported Leonidas Kosmidis with a Juan de la Cierva Incorporación postdoctoral fellowship (FJCI-2020- 045931-I).Peer ReviewedPostprint (author's final draft

Exploring Winograd Convolution for Cost-effective Neural Network Fault Tolerance

Winograd is generally utilized to optimize convolution performance and computational efficiency because of the reduced multiplication operations, but the reliability issues brought by winograd are usually overlooked. In this work, we observe the great potential of winograd convolution in improving neural network (NN) fault tolerance. Based on the observation, we evaluate winograd convolution fault tolerance comprehensively from different granularities ranging from models, layers, and operation types for the first time. Then, we explore the use of inherent fault tolerance of winograd convolution for cost-effective NN protection against soft errors. Specifically, we mainly investigate how winograd convolution can be effectively incorporated with classical fault-tolerant design approaches including triple modular redundancy (TMR), fault-aware retraining, and constrained activation functions. According to our experiments, winograd convolution can reduce the fault-tolerant design overhead by 55.77\% on average without any accuracy loss compared to standard convolution, and further reduce the computing overhead by 17.24\% when the inherent fault tolerance of winograd convolution is considered. When it is applied on fault-tolerant neural networks enhanced with fault-aware retraining and constrained activation functions, the resulting model accuracy generally shows significant improvement in presence of various faults

Novel Monte Carlo Methods for Large-Scale Linear Algebra Operations

Linear algebra operations play an important role in scientific computing and data analysis. With increasing data volume and complexity in the Big Data era, linear algebra operations are important tools to process massive datasets. On one hand, the advent of modern high-performance computing architectures with increasing computing power has greatly enhanced our capability to deal with a large volume of data. One the other hand, many classical, deterministic numerical linear algebra algorithms have difficulty to scale to handle large data sets. Monte Carlo methods, which are based on statistical sampling, exhibit many attractive properties in dealing with large volume of datasets, including fast approximated results, memory efficiency, reduced data accesses, natural parallelism, and inherent fault tolerance. In this dissertation, we present new Monte Carlo methods to accommodate a set of fundamental and ubiquitous large-scale linear algebra operations, including solving large-scale linear systems, constructing low-rank matrix approximation, and approximating the extreme eigenvalues/ eigenvectors, across modern distributed and parallel computing architectures. First of all, we revisit the classical Ulam-von Neumann Monte Carlo algorithm and derive the necessary and sufficient condition for its convergence. To support a broad family of linear systems, we develop Krylov subspace Monte Carlo solvers that go beyond the use of Neumann series. New algorithms used in the Krylov subspace Monte Carlo solvers include (1) a Breakdown-Free Block Conjugate Gradient algorithm to address the potential rank deficiency problem occurred in block Krylov subspace methods; (2) a Block Conjugate Gradient for Least Squares algorithm to stably approximate the least squares solutions of general linear systems; (3) a BCGLS algorithm with deflation to gain convergence acceleration; and (4) a Monte Carlo Generalized Minimal Residual algorithm based on sampling matrix-vector products to provide fast approximation of solutions. Secondly, we design a rank-revealing randomized Singular Value Decomposition (R3SVD) algorithm for adaptively constructing low-rank matrix approximations to satisfy application-specific accuracy. Thirdly, we study the block power method on Markov Chain Monte Carlo transition matrices and find that the convergence is actually depending on the number of independent vectors in the block. Correspondingly, we develop a sliding window power method to find stationary distribution, which has demonstrated success in modeling stochastic luminal Calcium release site. Fourthly, we take advantage of hybrid CPU-GPU computing platforms to accelerate the performance of the Breakdown-Free Block Conjugate Gradient algorithm and the randomized Singular Value Decomposition algorithm. Finally, we design a Gaussian variant of Freivalds’ algorithm to efficiently verify the correctness of matrix-matrix multiplication while avoiding undetectable fault patterns encountered in deterministic algorithms