Time-Encoded Values for Highly Efficient Stochastic Circuits

Najafi, M. Hassan; Jamali-Zavareh, Shiva; Lilja, David J.; Riedel, Marc; Bazargan, Kia; Harjani, Ramesh

doi:10.1109/tvlsi.2016.2645902

Cited by 59 publications

(30 citation statements)

References 28 publications

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“…Secondly, accuracy is improved by using circuits with correlated inputs (CSC) [6,19], which reduce the area cost. Thirdly, accuracy can be enhanced by performing SC operations using deterministic bit-streams [20,21]. These works obtained accurate arithmetic operations, but the entire bit-stream should be processed to avoid significant truncation error [22].…”

Section: Related Workmentioning

confidence: 99%

Accurate and compact stochastic computations by exploiting correlation

Abdellatef¹,

Khalil-Hani²,

Shaikh-Husin³

2019

Turk J Elec Eng & Comp Sci

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Recent studies have shown, contrary to what was previously believed, that by exploiting correlation in stochastic computing (SC) designs, more accurate SC circuits with low area cost can be realized. However, if these basic SC circuits or blocks are cascaded in series to form a large complex system, correlation between stochastic numbers (SNs) from one block to the next would be lost; thus, inaccuracies are introduced. In this study, we propose correlating circuits to be used in building complex correlated SC systems. One of the circuits is the correlator that restores lost correlations between two SNs due to previous processing. In addition, a correlated SN generator is introduced to generate SN correlated to a specific SN. Experimental results show that our methods have improved the accuracy of stochastic computation and preserved the stochastic computing correlation without the need for conversion from SC to the conventional binary-encoded computing, and vice versa. Consequently, lower latency and lower area cost are achieved.

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Section: Related Workmentioning

confidence: 99%

Accurate and compact stochastic computations by exploiting correlation

Abdellatef¹,

Khalil-Hani²,

Shaikh-Husin³

2019

Turk J Elec Eng & Comp Sci

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“…Due to random fluctuation, stochastic operations often need to run for a very long time to produce highly accurate results. Recent progress in the idea of SC [17] [8], however, has revolutionized the paradigm and has changed the common belief on stochastic processing, that is, SC does not necessarily have to…”

Section: Introductionmentioning

confidence: 99%

“…If properly structured, random fluctuation can be removed and SC circuits can produce deterministic and completely accurate results. Najafi et al [17] have shown that by choosing relatively prime lengths for a specific class of stochastic streams-called unary streams, and repeating the streams up to the least common multiple of the stream lengths, a deterministic and completely accurate output can be produced by stochastic logic. Jenson and Riedel [8] further proposed two deterministic approaches of processing unary streams, rotation of streams and clock division.…”

Section: Introductionmentioning

confidence: 99%

“…While the unary stream-based deterministic approaches proposed in [17] and [8] are able to produce completely accurate results (i.e., results that are the same as the results of binary-radix computation), they suffer from a poor progressive precision property; The output converges to the expected correct value very slowly. This drawback can be a major limitation to wide use of these approaches in different applications.…”

Section: Introductionmentioning

confidence: 99%

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High Quality Down-Sampling for Deterministic Approaches to Stochastic Computing

Najafi

Lilja

2021

IEEE Trans. Emerg. Topics Comput.

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Deterministic approaches to stochastic computing (SC) have been recently proposed to remove the random fluctuation and correlation problems of SC and so produce completely accurate results with stochastic logic. For many applications of SC, such as image processing and neural networks, completely accurate computation is not required for all input data. Decision-making on some input data can be done in a much shorter time using only a good approximation of the input values. While the deterministic approaches to SC are appealing by generating completely accurate results, the cost of precise results makes them energy inefficient for the cases when slight inaccuracy is acceptable. In this work, we propose a high quality down-sampling method for previously proposed deterministic approaches to SC by generating pseudo-random-but accurate-stochastic bit streams. The result is a much better accuracy for a given number of input bits. Experimental results show that the processing time and the energy consumption of these deterministic methods are improved up to 61% and 41%, respectively, while allowing a mean absolute error (MAE) of 0.1%, and up to 500X and 334X improvement, respectively, for an MAE of 3.0%. The accuracy and the energy consumption are also improved compared to conventional random stream-based stochastic implementations.

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“…Najafi et al [16] use pulse-width modulation (PWM) to time-encode values for more efficient stochastic computing. To avoid these disadvantages, we need to use other proper sequences as input streams.…”

Section: Introductionmentioning

confidence: 99%

Random Error Reduction Scheme for Combinational Stochastic Circuit

Ye¹,

Hu²

2017

Mathematical Problems in Engineering

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In conventional stochastic computation, all the input streams are Bernoulli sequences (BSs), which may result in large random error. To reduce random error and improve computational accuracy, some other sequences have been reported as alternatives to BSs. However, these sequences only apply to the specific stochastic circuits, have difficulties in hardware generation, or have length constraints. To this end, new sequences without these disadvantages should be considered. This paper proposes the random error analysis method for stochastic computation based on autocorrelation sequence (AS), which is more general than the conventional one based on BS. The analysis results show that we can use the proper ASs as input streams of stochastic circuits to reduce random error. On the basis of that conclusion, we propose the random error reduction scheme based on maximal concentrated autocorrelation sequence (MCAS) and BS, both of which are ASs. MCAS and BS are applicable to any combinational stochastic circuit, are easily generated by hardware, and have no length constraints, which avoid the disadvantages of sequences in the previous work. Moreover, we apply the proposed random error reduction scheme into several typical stochastic circuits as case studies. The simulation results confirm the effectiveness of the proposed scheme.

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Time-Encoded Values for Highly Efficient Stochastic Circuits

Cited by 59 publications

References 28 publications

Accurate and compact stochastic computations by exploiting correlation

Accurate and compact stochastic computations by exploiting correlation

High Quality Down-Sampling for Deterministic Approaches to Stochastic Computing

Random Error Reduction Scheme for Combinational Stochastic Circuit

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