Approximate hardware generation using symbolic computer algebra employing grobner basis

Froehlich, Saman; Grose, Daniel; Drechsler, Rolf

doi:10.23919/date.2018.8342133

Cited by 19 publications

(8 citation statements)

References 9 publications

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“…BDD packages represent the circuits using reduced ordered BDDs (ROBDDs). Symbolic computation approaches require to specify the problem using algebraic equations [18].…”

Section: A Methods For Computation Of Error Metricsmentioning

confidence: 99%

“…Due to scalability issues, the results were presented for small sequential multipliers based on an 8-bit adder and some less complex circuits only. In addition, Symbolic Computer Algebra (SCA) has been used to determine various error metrics [18], [19]. The latter approach uses Algebraic Decision Diagrams (ADDs) that has the ability to determine the mean relative error for which no other formal technique exists.…”

Section: B Exact Error Analysis Of Approximate Circuitsmentioning

confidence: 99%

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Formal Methods for Exact Analysis of Approximate Circuits

Vašíček

2019

IEEE Access

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Approximate circuits are digital circuits that are intentionally designed in such a way that the specification is violated in terms of functionality in order to obtain some improvements in power consumption, performance or area, in comparison with fully functional circuits. To design the approximate circuits, the synthesis tools rely on the availability of a procedure checking, whether the synthesized circuits meet a specification and/or provides information about circuit quality. Compared to the traditional circuit design flow, the nature of the approximate circuits involves replacing the strict functional equivalence checking with a more advanced approach that enables us to quantify or guarantee the degree of similarity. The most common technique is to employ a circuit simulator for analysing responses for all input vectors. This approach allows us to simultaneously perform checking and quality assessment, but the exhaustive enumeration of the input vectors is tractable only for a small number of inputs. To avoid excessive runtimes, a subset of all possible input vectors is typically used for complex circuits. This causes us, however, to lose the ability to guarantee that the quality of the synthesized circuits is within an acceptable range given in the specification. The main goal of this paper is to show how to adopt formal methods such as binary decision diagrams and satisfiability solvers for exhaustive analysis of approximate circuits without explicit enumeration of all input vectors. We survey the methods for exact computation of the most important error parameters used in the context of approximate computing, propose improved algorithms and provide a detailed analysis of their performance. The methods are benchmarked on a large set of key approximate circuits consisting of nearly 2,000 unique arithmetic instances with 8-, 12-, 16-, and 32-bit operands which helps us to identify the best algorithm and method for computation of a desired error parameter.

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“…BDD packages represent the circuits using reduced ordered BDDs (ROBDDs). Symbolic computation approaches require to specify the problem using algebraic equations [18].…”

Section: A Methods For Computation Of Error Metricsmentioning

confidence: 99%

Section: B Exact Error Analysis Of Approximate Circuitsmentioning

confidence: 99%

Formal Methods for Exact Analysis of Approximate Circuits

Vašíček

2019

IEEE Access

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“…Integrating given approximate components (e.g. adders, multipliers [20]- [22]) into LeFlow has been considered in [23]. In [24], the authors proposed an approximation resilience exploration metric and an approximate accelerator for convolutional layers targeted for edge devices.…”

Section: Related Workmentioning

confidence: 99%

XbNN: Enabling CNNs on Edge Devices by Approximate On-Chip Dot Product Encoding

Klemmer

Froehlich

Drechsler

et al. 2021

2021 IEEE International Symposium on Circuits and Systems (ISCAS)

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Only a few trends have gained as much traction as Edge Computing and Neural Networks (NN). Both have the potential to radically change how technology influences us. However, since edge devices feature only very limited resources, the sheer amount of performance required by modern NNs limits their use on the edge. Especially, the conversion of Convolutional Neural Networks (CNN) into feasible on-chip designs remains a hard task. Currently, hand-crafted and most-often very heavy architectures have to be used as existing High-Level Synthesis (HLS) frameworks provide only inefficient solutions.In this paper, we introduce the Crossbar Neural Network (XbNN) architecture. Our architecture employs a novel approximate on-chip dot product encoding for the efficient synthesis of CNNs on hardware. This encoding embeds the weights used in CNNs into the hardware design itself, significantly reducing the required memory and computation time. In addition, we present a methodology for the automated conversion of traditional CNNs given in TensorFlow into accelerators on top of the XbNN architecture. To demonstrate the effectiveness of XbNN, we conduct experiments on a common CNN test dataset and analyze the accuracy and performance of the resulting XbNN accelerators. We show that XbNN (a) achieves similar accuracies compared to TensorFlow CNNs and (b) provides much better area and performance results in comparison to a state-of-the-art HLS flow.

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“…On the other hand, BDDs allow one to efficiently examine the set of satisfying truth assignments which represents a key feature of model counting essential for calculating average-case error, error probability, or Hamming distance [33]. Recently, model checking-based techniques lev-ering the approximate miter [15] as well as symbolic computer algebra has also been applied in evaluating and quantifying errors of approximate circuits [16]. However, the above mentioned approaches do still have a problem to scale above multipliers with 12-bit operands and adders with 16-bit operands.…”

Section: Evaluating the Error Of Approximate Circuitsmentioning

confidence: 99%