Why this work is in the frame
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Bibliographic record
Abstract
We consider the problem of compression for “easy ” Boolean functions: given the truth table of an n-variate Boolean function f computable by some unknown small circuit from a known class of circuits, find in deterministic time poly(2n) a circuit C (no restriction on the type of C) computing f so that the size of C is less than the trivial circuit size 2n/n. We get both positive and negative results. On the positive side, we show that several circuit classes for which lower bounds are proved by a method of random restrictions: • AC0, • (de Morgan) formulas, and • (read-once) branching programs, allow non-trivial compression for circuits up to the size for which lower bounds are known. On the negative side, we show that compressing functions from any class C ⊆ P/poly implies super-polynomial lower bounds against C for a function in NEXP; we also observe that compressing monotone functions of polynomial circuit complexity or functions computable by large-size AC0 circuits would also imply new superpolynomial circuit lower bounds. Finally, we apply the ideas used for compression to get zero-error randomized #SAT-algorithms for de Morgan and complete-basis formulas, as well as branching programs, on n variables of about quadratic size that run in expected time 2n/2n ϵ, for some ϵ> 0 (dependent on the size of the formula/branching program). ∗Research partially supported by an NSERC Discovery grant. †Research partially supported by an NSERC Discovery grant. 1
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| 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