Lookup Table Refactoring: Towards Efficient Logarithmic Number System Addition for Large Language Models
Bibliographic record
Abstract
Compared to integer quantization, logarithmic quantization aligns more effectively with the long-tailed distribution of data in large language models (LLMs), resulting in lower quantization errors. Moreover, the logarithmic number system (LNS) employs a fixed-point adder to perform multiplication, indicating a potential reduction in computational complexity for LLM accelerators that require extensive multiply-accumulate (MAC) operations. However, a key bottleneck is that LNS addition requires complex nonlinear functions, which are typically approximated using lookup tables (LUTs). This study aims to reduce the hardware resources needed for LUTs in LNS addition while maintaining high precision. Specifically, we investigate the specific nature of addition operations within LLMs; the relationship between the hardware parameters of the LUT and the computing errors is then mathematically derived. Based on these insights, we propose LUT refactoring to optimize the LUT for enhanced efficiency in LNS addition. With 10.93% and 19.78% reductions in area-delay product (ADP) and power-delay product (PDP), respectively, LUT refactoring results in an accuracy improvement of up to 33.5% in LLM benchmarks compared to the naive design. When compared to integer quantization, our method achieves higher accuracy while reducing area by 18.27% and power by 42.61%.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".