How wrong could we be? A new way to solve underdetermined linear equations, illustrated via computed tomography
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
Too much reliance has been placed on calculating single images meeting possibly arbitrary optimization criteria.By generating a dispersion of multiple images consistent with the data, we may be able to learn how wrong we could be.Our problem is to generate a way of seeing a representative sample of all of the solutions in the hyperplane of solutions, which would be an array of images, each of which is a solution to the equations.To accomplish this, we suggest that our sampling is in a space of image basis functions, rather than directly in the hyperplane.As the number of basis functions is large, we design a selection criterion for choosing a subset that reasonably spans the space of images.First, we try a random sampling, which gives high frequency or sequency samples.Then we turn to more systematic sampling, based on the methods developed for one-pixel imaging.Some numerical experiments demonstrate that the use of basis functions as starting images for ART-like iterative algorithms may suffice to span the hyperplane of solutions, allowing choices between solutions other than simple optimization of arbitrary criteria such as minimum norm or maximum entropy, or deconvolution of the point spread function of the algorithm.
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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 | 0.001 |
| 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