BREAKING THE COHERENCE BARRIER: A NEW THEORY FOR COMPRESSED SENSING
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
This paper presents a framework for compressed sensing that bridges a gap between existing theory and the current use of compressed sensing in many real-world applications. In doing so, it also introduces a new sampling method that yields substantially improved recovery over existing techniques. In many applications of compressed sensing, including medical imaging, the standard principles of incoherence and sparsity are lacking. Whilst compressed sensing is often used successfully in such applications, it is done largely without mathematical explanation. The framework introduced in this paper provides such a justification. It does so by replacing these standard principles with three more general concepts: asymptotic sparsity, asymptotic incoherence and multilevel random subsampling. Moreover, not only does this work provide such a theoretical justification, it explains several key phenomena witnessed in practice. In particular, and unlike the standard theory, this work demonstrates the dependence of optimal sampling strategies on both the incoherence structure of the sampling operator and on the structure of the signal to be recovered. Another key consequence of this framework is the introduction of a new structured sampling method that exploits these phenomena to achieve significant improvements over current state-of-the-art techniques.
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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