Lower Bounds on Interactive Compressibility by Constant-Depth Circuits.
Bibliographic record
Abstract
We formulate a new connection between instance compressibility [HN10]), where the compressor uses circuits from a class C, and correlation with circuits in C. We use this connection to prove the first lower bounds on general probabilistic multi-round instance compression. We show that there is no probabilistic multi-round compression protocol for Parity in which the computationally bounded party uses a non-uniform AC 0-circuit and transmits at most n/(log(n)) ω(1) bits. This result is tight, and strengthens results of Dubrov and Ishai [DI06]. We also show that a similar lower bound holds for Majority. We also consider the question of round separation, i.e., whether for each r � 1, there are functions which can be compressed better with r rounds of compression than with r − 1 rounds. We answer this question affirmatively for compression using constant-depth polynomial-size circuits. Finally, we prove the first non-trivial lower bounds for 1-round compressibility of Parity by polynomial size ACC 0 [p] circuits where p is an odd prime.
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.
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 | 0.005 | 0.044 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.003 | 0.007 |
| Scholarly communication | 0.005 | 0.024 |
| Open science | 0.006 | 0.010 |
| Research integrity | 0.004 | 0.012 |
| Insufficient payload (model declined to judge) | 0.019 | 0.002 |
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".