Automated Circuit Approximation Method Driven by Data Distribution

We propose an application-tailored data-driven fully automated method for functional approximation of combinational circuits. We demonstrate how an application-level error metric such as the classification accuracy can be translated to a component-level error metric needed for an efficient and fast search in the space of approximate low-level components that are used in the application. This is possible by employing a weighted mean error distance (WMED) metric for steering the circuit approximation process which is conducted by means of genetic programming. WMED introduces a set of weights (calculated from the data distribution measured on a selected signal in a given application) determining the importance of each input vector for the approximation process. The method is evaluated using synthetic benchmarks and application-specific approximate MAC (multiply-and-accumulate) units that are designed to provide the best trade-offs between the classification accuracy and power consumption of two image classifiers based on neural networks.Comment: Accepted for publication at Design, Automation and Test in Europe (DATE 2019). Florence, Ital

A Comprehensive Methodology for Algorithm Characterization, Regularization and Mapping Into Optimal VLSI Arrays.

This dissertation provides a fairly comprehensive treatment of a broad class of algorithms as it pertains to systolic implementation. We describe some formal algorithmic transformations that can be utilized to map regular and some irregular compute-bound algorithms into the best fit time-optimal systolic architectures. The resulted architectures can be one-dimensional, two-dimensional, three-dimensional or nonplanar. The methodology detailed in the dissertation employs, like other methods, the concept of dependence vector to order, in space and time, the index points representing the algorithm. However, by differentiating between two types of dependence vectors, the ordering procedure is allowed to be flexible and time optimal. Furthermore, unlike other methodologies, the approach reported here does not put constraints on the topology or dimensionality of the target architecture. The ordered index points are represented by nodes in a diagram called Systolic Precedence Diagram (SPD). The SPD is a form of precedence graph that takes into account the systolic operation requirements of strictly local communications and regular data flow. Therefore, any algorithm with variable dependence vectors has to be transformed into a regular indexed set of computations with local dependencies. This can be done by replacing variable dependence vectors with sets of fixed dependence vectors. The SPD is transformed into an acyclic, labeled, directed graph called the Systolic Directed Graph (SDG). The SDG models the data flow as well as the timing for the execution of the given algorithm on a time-optimal array. The target architectures are obtained by projecting the SDG along defined directions. If more than one valid projection direction exists, different designs are obtained. The resulting architectures are then evaluated to determine if an improvement in the performance can be achieved by increasing PE fan-out. If so, the methodology provides the corresponding systolic implementation. By employing a new graph transformation, the SDG is manipulated so that it can be mapped into fixed-size and fixed-depth multi-linear arrays. The latter is a new concept of systolic arrays that is adaptable to changes in the state of technology. It promises a bonded clock skew, higher throughput and better performance than the linear implementation

On synthesizing systolic arrays from recurrence equations with linear dependencies

Journal ArticleWe present a technique for synthesizing systolic architectures from Recurrence Equations. A class of such equations (Recurrence Equations with Linear Dependencies) is defined and and the problem of mapping such equations onto a two dimensional architecture is studied. We show that such a mapping is provided by means of a linear allocation and timing function. An important result is that under such a mapping the dependencies remain linear. After obtaining a two-dimensional architecture by applying such a mapping, a systolic array can be derived if t h e communication can be spatially and temporally localized. We show that a simple test consisting of finding the zeroes of a matrix is sufficient to determine whether this localization can be achieved by pipelining and give a construction that generates the array when such a pipelining is possible. The technique is illustrated by automatically deriving a well known systolic array for factoring a band matrix into lower and upper triangular factors

Systolic array synthesis by static analysis of program dependencies

Journal ArticleWe present a technique for mapping recurrence equations to systolic arrays. While this problem has been studied in fairly great detail, the recurrence equations that are analysed here are a generalization of those studied previously. In a n earlier paper (14] we have showed how systolic arrays can be synthesized from such generalized recurrence equations by a combination of affine transformations and explicit pipelining. This paper extends the results in two directions. Firstly, a multistage pipelining technique is proposed, which permits the synthesis of systolic arrays with irregular data flow. Secondly we develop analysis techniques for the synthesis of systolic arrays whose computation is governed by control signals in a systematic manner which is amenable to mechanization. The full paper also discusses how these techniques can be applied to the mapping problem for more general architectures

The Mercury System: Exploiting Truly Fast Hardware in Data Mining

In many data mining applications, the size of the database is not only extremely large, it is also growing rapidly. Even for relatively simple searches, the time required to move the data off magnetic media, cross the system bus into main memory, copy into processor cache, and then execute code to perform a search is prohibitive. We are building a system in which a significant portion of the data mining task (i.e., the portion that examines the bulk of the raw data) is implemented in fast hardware, close to the magnetic media on which it is stored. Furthermore, this hardware can be replicated allowing mining tasks to be performed in parallel, thus providing further speedup for the overall mining application. In this paper, we describe a general framework under which this can be accomplished and provide initial performance results for a set of applications

Systolic Array Implementations With Reduced Compute Time.

The goal of the research is the establishment of a formal methodology to develop computational structures more suitable for the changing nature of real-time signal processing and control applications. A major effort is devoted to the following question: Given a systolic array designed to execute a particular algorithm, what other algorithms can be executed on the same array? One approach for answering this question is based on a general model of array operations using graph-theoretic techniques. As a result, a systematic procedure is introduced that models array operations as a function of the compute cycle. As a consequence of the analysis, the dissertation develops the concept of fast algorithm realizations. This concept characterizes specific realizations that can be evaluated in a reduced number of cycles. It restricts the operations to remain in the same class but with reduced execution time. The concept takes advantage of the data dependencies of the algorithm at hand. This feature allows the modification of existing structures by reordering the input data. Applications of the principle allows optimum time band and triangular matrix product on arrays designed for dense matrices. A second approach for analyzing the families of algorithms implementable in an array, is based on the concept of array time constrained operation. The principle uses the number of compute cycle as an additional degree of freedom to expand the class of transformations generated by a single array. A mathematical approach, based on concepts from multilinear algebra, is introduced to model the recursive transformations implemented in linear arrays at each compute cycle. The proposed representation is general enough to encompass a large class of signal processing and control applications. A complete analytical model of the linear maps implementable by the array at each compute cycle is developed. The proposed methodology results in arrays that are more adaptable to the changing nature of operations. Lessons learned from analyzing existing arrays are used to design smart arrays for special algorithm realizations. Applications of the methodology include the design of flexible time structures and the ability to decompose a full size array into subarrays implementing smaller size problems

Embracing Low-Power Systems with Improvement in Security and Energy-Efficiency

As the economies around the world are aligning more towards usage of computing systems, the global energy demand for computing is increasing rapidly. Additionally, the boom in AI based applications and services has already invited the pervasion of specialized computing hardware architectures for AI (accelerators). A big chunk of research in the industry and academia is being focused on providing energy efficiency to all kinds of power hungry computing architectures. This dissertation adds to these efforts. Aggressive voltage underscaling of chips is one the effective low power paradigms of providing energy efficiency. This dissertation identifies and deals with the reliability and performance problems associated with this paradigm and innovates novel energy efficient approaches. Specifically, the properties of a low power security primitive have been improved and, higher performance has been unlocked in an AI accelerator (Google TPU) in an aggressively voltage underscaled environment. And, novel power saving opportunities have been unlocked by characterizing the usage pattern of a baseline TPU with rigorous mathematical analysis

Design of testbed and emulation tools

The research summarized was concerned with the design of testbed and emulation tools suitable to assist in projecting, with reasonable accuracy, the expected performance of highly concurrent computing systems on large, complete applications. Such testbed and emulation tools are intended for the eventual use of those exploring new concurrent system architectures and organizations, either as users or as designers of such systems. While a range of alternatives was considered, a software based set of hierarchical tools was chosen to provide maximum flexibility, to ease in moving to new computers as technology improves and to take advantage of the inherent reliability and availability of commercially available computing systems