Bibliographic record
Abstract
We develop an approach through geometric functional analysis to reconstruction of signals from few linear measurements and to error-correcting codes. An error-correcting code encodes an n-letter word x into an m-letter word y in such a way that x can be decoded correctly when any r letters of y are corrupted. We show that most linear orthogonal transformations Q : ℝn → ℝm form efficient and robust error-correcting codes over reals. The decoder (which corrects the corrupted components of y) is the metric projection onto the range of Q in the ℓ1-norm. This yields robust error-correcting codes over reals (and over alphabets of polynomial size), with a Gilbert-Varshamov type bound, and with quadratic time encoders and polynomial time decoders. An equivalent problem arises in signal processing: how to reconstruct a signal that belongs to a small class from few linear measurements? We prove that for most sets of Gaussian measurements, all signals of small support can be exactly reconstructed by the L1-norm minimization. This is an improvement of recent results of Donoho and of Candes and Tao. An equivalent problem in combinatorial geometry is the existence of “neighborly” symmetric polytopes, that is, polytopes with fixed number of facets and maximal number of lower-dimensional facets. We prove that most sections of a cube form such polytopes. Our work thus belongs to a common ground of coding theory, signal processing, combinatorial geometry, and geometric functional analysis. Our argument, which is based on concentration of measure and improving Lipschitzness by random projections, may be of independent interest in geometric functional analysis.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.023 | 0.006 |
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".