Subtractive random forests
Bibliographic record
Abstract
Motivated by online recommendation systems, we study a family of random forests.The vertices of the forest are labeled by integers.Each non-positive integer i 0 is the root of a tree.Vertices labeled by positive integers n 1 are attached sequentially such that the parent of vertex n is n -Z n , where the Z n are i.i.d.random variables taking values in Z + .We study several characteristics of the resulting random forest.In particular, we establish bounds for the expected tree sizes, the number of trees in the forest, the number of leaves, the maximum degree, and the height of the forest.We show that for all distributions of the Z n , the forest contains at most one infinite tree, almost surely.If EZ n < , then there is a unique infinite tree and the total size of the remaining trees is finite, with finite expected value if EZ 2 n < .If EZ n = then almost surely all trees are finite.
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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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 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".