Study of Sparsity Emanating from NKPD and its Utilization to Enhance NKPD based Adaptive Algorithms
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Bibliographic record
Abstract
Recently, the nearest Kronecker product (NKP) decomposition has become popular in several adaptive filtering (AF) applications owing to its fast convergence and tracking ability. In this paper, we study the nature of the smaller weight vectors resulting from NKP decomposition (NKPD) of a wide range of acoustic impulse responses (IRs). The study shows that the smaller weight vectors resulting from NKPD exhibit moderate to high degree of sparsity. To exploit this knowledge in AF problems, we propose a class of proportionate update based NKP normalized least-mean-square (NKP-NLMS) type algorithms: namely, the improved proportionate NKP-NLMS (NKP-IPNLMS) algorithm which uses the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{1}$</tex> -norm of the smaller weight vectors and the NKP- IPNLMS <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$-\ell_{0}$</tex> which uses an approximation of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{0}$</tex> -norm. Further, we propose a new approximation of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{0}$</tex> -norm with reduced computational complexity, using which we also propose the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{NKP}-\text{IPNLMS}-\ell_{0}-2$</tex> algorithm. Next, we present a comparison of computational complexity of the proposed algorithms. Simulation results show the improved performance achieved by the proposed algorithms, showing the advantage of exploiting sparsity in the smaller weight vectors in NKPD based adaptive algorithms.
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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 it