Treasure Trove at Banacha. Set Patterns in Descriptive Proximity Spaces
Bibliographic record
Abstract
This paper introduces descriptive set patterns that originated from our visits with Zdzisław Pawlak and Andrzej Skowron at Banacha and environs in Warsaw. This paper also celebrates the generosity and caring manner of Andrzej Skowron, who made our visits to Warsaw memorable events. The inspiration for the recent discovery of descriptive set patterns can be traced back to our meetings at Banacha. Descriptive set patterns are collections of near sets that arise rather naturally in the context of an extension of Solomon Leader's uniform topology, which serves as a base topology for compact Hausdorff spaces that are proximity spaces. The particular form of proximity space (called EF-proximity) reported here is an extension of the proximity space introduced by V. Efremovič during the first half of the 1930s. Proximally continuous functions introduced by Yu.V. Smirnov in 1952 lead to pattern generation of comparable set patterns. Set patterns themselves were first considered by T. Pavlidis in 1968 and led to U. Grenander's introduction of pattern generators during the 1990s. This article considers descriptive set patterns in EF-proximity spaces and their application in digital image classification. Images belong to the same class, provided each image in the class contains set patterns that resemble each other. Image classification then reduces to determining if a set pattern in a test image is near a set pattern in a query image.
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How this classification was reachedexpand
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 | 0.003 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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 teacher head, 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".