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%.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".