Using reconfigurable computing technology to accelerate matrix decomposition and applications

Matrix decomposition plays an increasingly significant role in many scientific and engineering applications. Among numerous techniques, Singular Value Decomposition (SVD) and Eigenvalue Decomposition (EVD) are widely used as factorization tools to perform Principal Component Analysis for dimensionality reduction and pattern recognition in image processing, text mining and wireless communications, while QR Decomposition (QRD) and sparse LU Decomposition (LUD) are employed to solve the dense or sparse linear system of equations in bioinformatics, power system and computer vision. Matrix decompositions are computationally expensive and their sequential implementations often fail to meet the requirements of many time-sensitive applications. The emergence of reconfigurable computing has provided a flexible and low-cost opportunity to pursue high-performance parallel designs, and the use of FPGAs has shown promise in accelerating this class of computation. In this research, we have proposed and implemented several highly parallel FPGA-based architectures to accelerate matrix decompositions and their applications in data mining and signal processing. Specifically, in this dissertation we describe the following contributions: • We propose an efficient FPGA-based double-precision floating-point architecture for EVD, which can efficiently analyze large-scale matrices. • We implement a floating-point Hestenes-Jacobi architecture for SVD, which is capable of analyzing arbitrary sized matrices. • We introduce a novel deeply pipelined reconfigurable architecture for QRD, which can be dynamically configured to perform either Householder transformation or Givens rotation in a manner that takes advantage of the strengths of each. • We design a configurable architecture for sparse LUD that supports both symmetric and asymmetric sparse matrices with arbitrary sparsity patterns. • By further extending the proposed hardware solution for SVD, we parallelize a popular text mining tool-Latent Semantic Indexing with an FPGA-based architecture. • We present a configurable architecture to accelerate Homotopy l1-minimization, in which the modification of the proposed FPGA architecture for sparse LUD is used at its core to parallelize both Cholesky decomposition and rank-1 update. Our experimental results using an FPGA-based acceleration system indicate the efficiency of our proposed novel architectures, with application and dimension-dependent speedups over an optimized software implementation that range from 1.5ÃÂ to 43.6ÃÂ in terms of computation time

Design and resource management of reconfigurable multiprocessors for data-parallel applications

FPGA (Field-Programmable Gate Array)-based custom reconfigurable computing machines have established themselves as low-cost and low-risk alternatives to ASIC (Application-Specific Integrated Circuit) implementations and general-purpose microprocessors in accelerating a wide range of computation-intensive applications. Most often they are Application Specific Programmable Circuiits (ASPCs), which are developer programmable instead of user programmable. The major disadvantages of ASPCs are minimal programmability, and significant time and energy overheads caused by required hardware reconfiguration when the problem size outnumbers the available reconfigurable resources; these problems are expected to become more serious with increases in the FPGA chip size. On the other hand, dominant high-performance computing systems, such as PC clusters and SMPs (Symmetric Multiprocessors), suffer from high communication latencies and/or scalability problems. This research introduces low-cost, user-programmable and reconfigurable MultiProcessor-on-a-Programmable-Chip (MPoPC) systems for high-performance, low-cost computing. It also proposes a relevant resource management framework that deals with performance, power consumption and energy issues. These semi-customized systems reduce significantly runtime device reconfiguration by employing userprogrammable processing elements that are reusable for different tasks in large, complex applications. For the sake of illustration, two different types of MPoPCs with hardware FPUs (floating-point units) are designed and implemented for credible performance evaluation and modeling: the coarse-grain MIMD (Multiple-Instruction, Multiple-Data) CG-MPoPC machine based on a processor IP (Intellectual Property) core and the mixed-mode (MIMD, SIMD or M-SIMD) variant-grain HERA (HEterogeneous Reconfigurable Architecture) machine. In addition to alleviating the above difficulties, MPoPCs can offer several performance and energy advantages to our data-parallel applications when compared to ASPCs; they are simpler and more scalable, and have less verification time and cost. Various common computation-intensive benchmark algorithms, such as matrix-matrix multiplication (MMM) and LU factorization, are studied and their parallel solutions are shown for the two MPoPCs. The performance is evaluated with large sparse real-world matrices primarily from power engineering. We expect even further performance gains on MPoPCs in the near future by employing ever improving FPGAs. The innovative nature of this work has the potential to guide research in this arising field of high-performance, low-cost reconfigurable computing. The largest advantage of reconfigurable logic lies in its large degree of hardware customization and reconfiguration which allows reusing the resources to match the computation and communication needs of applications. Therefore, a major effort in the presented design methodology for mixed-mode MPoPCs, like HERA, is devoted to effective resource management. A two-phase approach is applied. A mixed-mode weighted Task Flow Graph (w-TFG) is first constructed for any given application, where tasks are classified according to their most appropriate computing mode (e.g., SIMD or MIMD). At compile time, an architecture is customized and synthesized for the TFG using an Integer Linear Programming (ILP) formulation and a parameterized hardware component library. Various run-time scheduling schemes with different performanceenergy objectives are proposed. A system-level energy model for HERA, which is based on low-level implementation data and run-time statistics, is proposed to guide performance-energy trade-off decisions. A parallel power flow analysis technique based on Newton\u27s method is proposed and employed to verify the methodology

Accelerating Linear Algebra and Machine Learning Kernels on a Massively Parallel Reconfigurable Architecture

abstract: This thesis presents efficient implementations of several linear algebra kernels, machine learning kernels and a neural network based recommender systems engine onto a massively parallel reconfigurable architecture, Transformer. The linear algebra kernels include Triangular Matrix Solver (TRSM), LU Decomposition (LUD), QR Decomposition (QRD), and Matrix Inversion. The machine learning kernels include an LSTM (Long Short Term Memory) cell, and a GRU (gated Recurrent Unit) cell used in recurrent neural networks. The neural network based recommender systems engine consists of multiple kernels including fully connected layers, embedding layer, 1-D batchnorm, Adam optimizer, etc. Transformer is a massively parallel reconfigurable multicore architecture designed at the University of Michigan. The Transformer configuration considered here is 4 tiles and 16 General Processing Elements (GPEs) per tile. It supports a two level cache hierarchy where the L1 and L2 caches can operate in shared (S) or private (P) modes. The architecture was modeled using Gem5 and cycle accurate simulations were done to evaluate the performance in terms of execution times, giga-operations per second per Watt (GOPS/W), and giga-floating-point-operations per second per Watt (GFLOPS/W). This thesis shows that for linear algebra kernels, each kernel achieves high performance for a certain cache mode and that this cache mode can change when the matrix size changes. For instance, for smaller matrix sizes, L1P, L2P cache mode is best for TRSM, while L1S, L2S is the best cache mode for LUD, and L1P, L2S is the best for QRD. For each kernel, the optimal cache mode changes when the matrix size is increased. For instance, for TRSM, the L1P, L2P cache mode is best for smaller matrix sizes ($N=64, 128, 256, 512$) and it changes to L1S, L2P for larger matrix sizes ($N=1024$). For machine learning kernels, L1P, L2P is the best cache mode for all network parameter sizes. Gem5 simulations show that the peak performance for TRSM, LUD, QRD and Matrix Inverse in the 14nm node is 97.5, 59.4, 133.0 and 83.05 GFLOPS/W, respectively. For LSTM and GRU, the peak performance is 44.06 and 69.3 GFLOPS/W. The neural network based recommender system was implemented in L1S, L2S cache mode. It includes a forward pass and a backward pass and is significantly more complex in terms of both computational complexity and data movement. The most computationally intensive block is the fully connected layer followed by Adam optimizer. The overall performance of the recommender systems engine is 54.55 GFLOPS/W and 169.12 GOPS/W.Dissertation/ThesisMasters Thesis Electrical Engineering 201

Architectural explorations for streaming accelerators with customized memory layouts

El concepto básico de la arquitectura mono-nucleo en los procesadores de propósito general se ajusta bien a un modelo de programación secuencial. La integración de multiples núcleos en un solo chip ha permitido a los procesadores correr partes del programa en paralelo. Sin embargo, la explotación del enorme paralelismo disponible en muchas aplicaciones de alto rendimiento y de los datos correspondientes es difícil de conseguir usando unicamente multicores de propósito general. La aparición de aceleradores tipo streaming y de los correspondientes modelos de programación han mejorado esta situación proporcionando arquitecturas orientadas al proceso de flujos de datos. La idea básica detrás del diseño de estas arquitecturas responde a la necesidad de procesar conjuntos enormes de datos. Estos dispositivos de alto rendimiento orientados a flujos permiten el procesamiento rapido de datos mediante el uso eficiente de computación paralela y comunicación entre procesos. Los aceleradores streaming orientados a flujos, igual que en otros procesadores, consisten en diversos componentes micro-arquitectonicos como por ejemplo las estructuras de memoria, las unidades de computo, las unidades de control, los canales de Entrada/Salida y controles de Entrada/Salida, etc. Sin embargo, los requisitos del flujo de datos agregan algunas características especiales e imponen otras restricciones que afectan al rendimiento. Estos dispositivos, por lo general, ofrecen un gran número de recursos computacionales, pero obligan a reorganizar los conjuntos de datos en paralelo, maximizando la independiencia para alimentar los recursos de computación en forma de flujos. La disposición de datos en conjuntos independientes de flujos paralelos no es una tarea sencilla. Es posible que se tenga que cambiar la estructura de un algoritmo en su conjunto o, incluso, puede requerir la reescritura del algoritmo desde cero. Sin embargo, todos estos esfuerzos para la reordenación de los patrones de las aplicaciones de acceso a datos puede que no sean muy útiles para lograr un rendimiento óptimo. Esto es debido a las posibles limitaciones microarquitectonicas de la plataforma de destino para los mecanismos hardware de prefetch, el tamaño y la granularidad del almacenamiento local, y la flexibilidad para disponer de forma serial los datos en el interior del almacenamiento local. Las limitaciones de una plataforma de streaming de proposito general para el prefetching de datos, almacenamiento y demas procedimientos para organizar y mantener los datos en forma de flujos paralelos e independientes podría ser eliminado empleando técnicas a nivel micro-arquitectonico. Esto incluye el uso de memorias personalizadas especificamente para las aplicaciones en el front-end de una arquitectura streaming. El objetivo de esta tesis es presentar exploraciones arquitectónicas de los aceleradores streaming con diseños de memoria personalizados. En general, la tesis cubre tres aspectos principales de tales aceleradores. Estos aspectos se pueden clasificar como: i) Diseño de aceleradores de aplicaciones específicas con diseños de memoria personalizados, ii) diseño de aceleradores con memorias personalizadas basados en plantillas, y iii) exploraciones del espacio de diseño para dispositivos orientados a flujos con las memorias estándar y personalizadas. Esta tesis concluye con la propuesta conceptual de una Blacksmith Streaming Architecture (BSArc). El modelo de computación Blacksmith permite la adopción a nivel de hardware de un front-end de aplicación específico utilizando una GPU como back-end. Esto permite maximizar la explotación de la localidad de datos y el paralelismo a nivel de datos de una aplicación mientras que proporciona un flujo mayor de datos al back-end. Consideramos que el diseño de estos procesadores con memorias especializadas debe ser proporcionado por expertos del dominio de aplicación en la forma de plantillas.The basic concept behind the architecture of a general purpose CPU core conforms well to a serial programming model. The integration of more cores on a single chip helped CPUs in running parts of a program in parallel. However, the utilization of huge parallelism available from many high performance applications and the corresponding data is hard to achieve from these general purpose multi-cores. Streaming accelerators and the corresponding programing models improve upon this situation by providing throughput oriented architectures. The basic idea behind the design of these architectures matches the everyday increasing requirements of processing huge data sets. These high-performance throughput oriented devices help in high performance processing of data by using efficient parallel computations and streaming based communications. The throughput oriented streaming accelerators ¿ similar to the other processors ¿ consist of numerous types of micro-architectural components including the memory structures, compute units, control units, I/O channels and I/O controls etc. However, the throughput requirements add some special features and impose other restrictions for the performance purposes. These devices, normally, offer a large number of compute resources but restrict the applications to arrange parallel and maximally independent data sets to feed the compute resources in the form of streams. The arrangement of data into independent sets of parallel streams is not an easy and simple task. It may need to change the structure of an algorithm as a whole or even it can require to write a new algorithm from scratch for the target application. However, all these efforts for the re-arrangement of application data access patterns may still not be very helpful to achieve the optimal performance. This is because of the possible micro-architectural constraints of the target platform for the hardware pre-fetching mechanisms, the size and the granularity of the local storage and the flexibility in data marshaling inside the local storage. The constraints of a general purpose streaming platform on the data pre-fetching, storing and maneuvering to arrange and maintain it in the form of parallel and independent streams could be removed by employing micro-architectural level design approaches. This includes the usage of application specific customized memories in the front-end of a streaming architecture. The focus of this thesis is to present architectural explorations for the streaming accelerators using customized memory layouts. In general the thesis covers three main aspects of such streaming accelerators in this research. These aspects can be categorized as : i) Design of Application Specific Accelerators with Customized Memory Layout ii) Template Based Design Support for Customized Memory Accelerators and iii) Design Space Explorations for Throughput Oriented Devices with Standard and Customized Memories. This thesis concludes with a conceptual proposal on a Blacksmith Streaming Architecture (BSArc). The Blacksmith Computing allow the hardware-level adoption of an application specific front-end with a GPU like streaming back-end. This gives an opportunity to exploit maximum possible data locality and the data level parallelism from an application while providing a throughput natured powerful back-end. We consider that the design of these specialized memory layouts for the front-end of the device are provided by the application domain experts in the form of templates. These templates are adjustable according to a device and the problem size at the device's configuration time. The physical availability of such an architecture may still take time. However, simulation framework helps in architectural explorations to give insight into the proposal and predicts potential performance benefits for such an architecture