Error analysis of data mapping using 2-dimensional logarithmic number systems
Bibliographic record
Abstract
Multidimensional logarithmic number system (MDLNS) is a recently developed number representation that is very efficient for implementing the Inner Product Step Processor (IPSP). The MDLNS provides more degrees of freedom than the classical LNS by virtue of the orthogonal bases and ability to obtain reduction of hardware complexity from the use of multiple digits. This paper presents an analysis of errors introduced in data mapping from real numbers to 2-dimentional LNS (2-DLNS). Due to non-uniform error distribution, mapping space is divided by pre-assigned segments, where error performance can be uniquely characterized. Mapping errors are collected piece-wisely over all of the segments. In 1-digit 2-DLNS, error collection can be simplified by using pattern-matching scheme. Expressions for error variance are derived. It is shown that the use of a 2-DLNS representation results in significant lower error variance compared to floating-point number systems. The hardware complexity required with the error performance comparable to classic LNS can be significantly reduced due to smaller size of ROMs compared with LNS. The results of the error analysis have been verified by numerical simulations.
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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 | 0.002 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| 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) | 0.001 | 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".