An FPGA-Based Singular Value Decomposition Processor
Bibliographic record
Abstract
A two-sided rotation Jacobi SVD algorithm is used to compute the SVD and is implemented on a two million gate FPGA. A mesh-connected array structure is proposed based on Brent, Luk, and Van Loan's idea of an expandable square systolic array of simple 2x2 processors to compute the SVD of a large matrix, so as to shorten the iteration time and thus increase the implementation speed. The array consists of an n/2xn/2 array of 2x2 processor elements to compute the SVD of an nxn matrix. The trigonometric functions and the vector multiplication in the algorithm are tailored to the use of CORDIC (coordinate rotation digital computer) algorithms for hardware-efficient solutions. Two SVD processors, the basic SVD processor and the extended SVD processor, were developed. The algorithms to decompose the matrix were first evaluated in Matlab and then the processors were implemented using the Virtex-II FPGA from Xilinx as the target device. The basic SVD processor utilizes the proposed mesh-connected array structure and CORDIC algorithm. The implementation concentrates on utilizing the features of the FPGA to speed up operations and reduce the area required. In order to compute a large SVD without increasing the size of the FPGA, the extended SVD processor was developed to reuse the SVD array of the basic SVD processor. These two processors were successfully implemented on the FPGA device. Speed data and comparisons are presented
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.012 | 0.005 |
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".