Catalytic Branching Programs from Groups and General Protocols
Bibliographic record
Abstract
CCCatalytic branching programs (catalytic bps) compute the same n -bit Boolean function f at multiple entry points that need to be remembered at the exit nodes of the branching program (bp). When a doubly exponential number of entry points is allowed, linear amortized catalytic bp size is known to be achievable for any f . Here a method is introduced that produces a catalytic bp out of a reversible bp and a deterministic dag-like communication protocol. In a multiplicity range as low as linear, approximating a threshold is shown possible at linear amortized cost. In the same low range, computing Maj and Mod are shown possible at a cost that beats the brute force repetition of the best known bp for these functions by a polylog factor. In the exponential range, the method yields O ( n log n ) amortized cost for any symmetric function.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.012 | 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 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".