IRS With Discrete Phase Shifts: When Is Quantization Optimal?
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Bibliographic record
Abstract
Intelligent reflective surfaces (IRS) with discrete phase shifts are considered. While no analytical solutions for globally-optimal discrete phase shifts are known, quantization of optimized continuous phase shifts is often used in the literature instead but the optimality of this strategy remains unknown. It is known to be not optimal in some special cases, but does there exist a broad class of cases for which this strategy is globally optimal? A partial answer to this question is provided here. In particular, scalar minimum-distance quantization of optimized continuous phase shifts is shown to be a globally-optimal strategy under discrete phase shifts if all quantization errors do not exceed 50% of their maximum possible value. Under mild additional conditions, it is the only strategy achieving global optimum. This is further extended to the scenarios where all quantization errors belong to an interval not exceeding half of the quantization step size, including, as special cases, the scenarios where all quantization errors are either positive or negative.
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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 | 0.001 | 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