Least squares solution for error correction on the real field using quantized DFT codes
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Bibliographic record
Abstract
Least squares (LS) methods are frequently used in many statistical problems, including the solution of overdetermined linear systems. We analyze the effect of using the LS solution in the decoding of quantized discrete Fourier transform (DFT) codes. We show how the LS solution can improve detection, localization, and calculation of errors in the real field, and come close to the quantization error level under the mean squared error (MSE) fidelity criterion. Assuming perfect localization, the LS estimation substantially decreases the MSE between the transmitted and reconstructed sequences, regardless of the magnitude of channel error to quantization noise ratio. Furthermore, when quantization noise is comparable to or larger than channel errors, where error localization is usually very poor, the LS solution still brings down the estimation error, resulting a reconstruction error at the level of quantization error.
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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