A Low-Power and High-Accuracy Approximate Adder for Logarithmic Number System
Bibliographic record
Abstract
The Logarithmic Number System (LNS) exploits the non-uniform distribution of data in convolutional neural networks (CNNs), so it leads to a high accuracy for image classification. An LNS provides an easier way to implement complex operations such as multiplication and division. However, addition and subtraction in the LNS require huge hardware resources due to the involved nonlinear operations. To mitigate this problem, we design a low-power approximate logarithmic adder with high-accuracy. Initially, a compact piecewise linear approximation (CPLA) algorithm is proposed to approximately compute the binary exponentiation and logarithm. Implemented by using simple circuits, the CPLA algorithm results in higher accuracy than the classical Mitchell’s algorithm. Consequently, three approximate logarithmic adders are devised, denoted as LA_CPLA1, LA_CPLA2, and LA_CPLA3. Compared with the logarithmic adder design based on lookup tables, the proposed LA_CPLA3 with a configuration of (e, f, n) = (7, 6, 3) achieves 35.05% and 39.80% reductions in area and power dissipation respectively, with a 0.01% mean relative error distance (MRED). We define (e, f) as the bit width of the logarithmic adder, where e and f are the bit widths of the integer and fractional parts, respectively. n is the approximate LSBs in the proposed LA_CPLAs processed by using OR gates. Compared with the multiply and accumulate (MAC) unit in a conventional system using fixed-point numbers, the MAC in the LNS using the proposed LA_CPLAs achieve a lower power by 5.96% to 32.02%, and a smaller area by 6.48% to 32.40%. To assess the efficiency of the proposed approximate adders, they are applied to the implementations of two image processing and CNN applications. The simulation results show that LA_CPLAs result in marginal accuracy loss compared to the corresponding accurate implementations.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".