Two level decomposition based matrix multiplication for FPGAs
Bibliographic record
Abstract
In this paper, we present an efficient design approach for the implementation of large size matrix multiplication with wide bit size elements targeting FPGAs. The proposed technique first partitions the input matrices into smaller dimensions, and then segment the word-width of the elements into smaller sections. The segmentation is driven by the architecture of the targeted FPGA platform. A highly optimized scalar signed multiplier has been developed, and used as a basic block to construct a 2 by 2 matrix multiplier on Xilinx' and Altera's FPGAs. The result of the implementations showed that our method has outperformed the techniques utilized by commercial tools, ISE and Quartus, and the balanced word-width decomposition approach to realize the matrix multiplications proposed in. Compared to these approaches we achieved delay reduction range from 7.1% to 28% and area saving range from 6.7% to 32%.
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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 | 0.000 | 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".