Efficiently Approximable Real-Valued Functions
Bibliographic record
Abstract
We consider a class, denoted APP, of real-valued functions f : f0; 1g n ! [0; 1] such that f can be approximated, to within any ffl ? 0, by a probabilistic Turing machine running in time poly(n; 1=ffl). We argue that APP can be viewed as a generalization of BPP, and show that APP contains a natural complete problem: computing the acceptance probability of a given Boolean circuit; in contrast, no complete problems are known for BPP. We observe that all known complexity-theoretic assumptions under which BPP is easy (i.e., can be efficiently derandomized) imply that APP is easy; on the other hand, we show that BPP may be easy while APP is not, by constructing an appropriate oracle. 1 Introduction The complexity class BPP is traditionally considered a class of languages that can be efficiently decided with the help of randomness. While it does contain some natural problems, the "semantic" nature of its definition (on every input, a BPP machine must have either at least 3=4 or at...
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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 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".