The Communication Complexity of Correlation
Bibliographic record
Abstract
LetXandYbe finite nonempty sets and(X,Y) a pair of random variables taking values inX?Y. We consider communication protocols between two parties,AliceandBob, for generatingXandY.Aliceis provided anx?Xgenerated according to the distribution ofX, and is required to send a message toBobin order to enable him to generatey?Y, whose distribution is the same as that ofY|X=x. Both parties have access to a shared random string generated in advance. LetT[X:Y] be the minimum (over all protocols) of the expected number of bitsAliceneeds to transmit to achieve this. We show that I[X:Y] ? T[X:Y] ? I [X:Y] + 2 log2(I[X:Y]+ O(1). We also consider the worst case communication required for this problem, where we seek to minimize the average number of bitsAlicemust transmit for the worst casex?X. We show that the communication required in this case is related to the capacityC(E) of the channelE, derived from(X,Y) , that mapsx?Xto the distribution ofY|X=x. We also show that the required communicationT(E) satisfiesC(E) ?T(E) ?C(E) + 2 log2(C(E)+1) +O(1). Using the first result, we derive a direct-sum theorem in communication complexity that substantially improves the previous such result shown by Jain, Radhakrishnan, and Sen [In Proc. 30th International Colloquium of Automata, Languages and Programming (ICALP), ser. Lecture Notes in Computer Science, vol. 2719. 2003, pp. 300-315]. These results are obtained by employing a rejection sampling procedure that relates the relative entropy between two distributions to the communication complexity of generating one distribution from the other.
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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 | 0.011 | 0.108 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.002 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.004 | 0.006 |
| Scholarly communication | 0.010 | 0.019 |
| Open science | 0.004 | 0.008 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.016 | 0.003 |
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".