Toward Energy-Efficient Stochastic Circuits Using Parallel Sobol Sequences
Bibliographic record
Abstract
Stochastic computing (SC) often requires long stochastic sequences and, thus, a long latency to achieve accurate computation. The long latency leads to an inferior performance and low energy efficiency compared with most conventional binary designs. In this paper, a type of low-discrepancy sequences, the Sobol sequence, is considered for use in SC. Compared to the use of pseudorandom sequences generated by linear feedback shift registers (LFSRs), the use of Sobol sequences improves the accuracy of stochastic computation with a reduced sequence length. The inherent feature in Sobol sequence generators enables the parallel implementation of random number generators with an improved performance and hardware efficiency. In particular, the underlying theory is formulated and circuit design is proposed for an arbitrary level of parallelization in a power of 2. In addition, different strategies are implemented for parallelizing combinational and sequential stochastic circuits. The hardware efficiency of the parallel stochastic circuits is measured by energy per operation (EPO), throughput per area (TPA), and runtime. At a similar accuracy, the 8× parallel stochastic circuits using Sobol sequences consume approximately 1% of the EPO of the conventional LFSR-based nonparallelized circuits. Meanwhile, an average of 70 (up to 89) times improvements in TPA and less than 1% runtime are achieved. A sorting network is implemented for a median filter (MF) as an application. For a similar image processing quality, a higher energy efficiency is obtained for an 8× parallelized stochastic MF compared with its binary counterpart.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".