Photonics-Based Cholesky Decomposition
Bibliographic record
Abstract
Matrix decomposition approaches are the techniques that partition a complex matrix into its constituents in order to reduce the computational complexity of different matrix calculations. Among different decomposition techniques, Cholesky decomposition [1] , in which a Hermitian positive semi-definite matrix is decomposed into the product between a lower triangular matrix and its conjugate transpose, has been employed in different applications [2] . In particular, Cholesky decomposition has been widely used to compute the inverse of large matrices [3] , because of the advantages it offers terms of the computational complexity and memory requirements [4] . While matrix decomposition reduces the computational complexity, the hardware in which the decomposition is performed affects the overall efficiency and the time required to decompose the matrix. Photonics-based computation has been proposed as a promising approach that offers low-computational cost for ultra-fast data processing [5] . In this paper, a photonic computing architecture is proposed to improve the time and power efficiency of Cholesky decomposition. This is specifically attractive for wireless communication systems, where computational resources are limited and the data needs to be processed on the fly. The proposed architecture is based on Broadcast-and-Weight (B&W) protocol [6] , in which a bank of microring modulators and wavelength division multiplexing scheme are utilized to implement dot product in an optical platform. In the proposed architecture, a feedback control procedure is designed to set the weights by applying voltages to microring resonators.
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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 | 0.001 | 0.001 |
| 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 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.003 |
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".