Worst Case Nonzero-Error Interactive Communication
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Bibliographic record
Abstract
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In the interactive communication model, two parties <emphasis><formula formulatype="inline"><tex>$P_{\cal X}$</tex></formula></emphasis> and <emphasis><formula formulatype="inline"><tex>$P_{\cal Y}$</tex></formula></emphasis> possess respective private but correlated inputs <emphasis><formula formulatype="inline"> <tex>$x$</tex></formula></emphasis> and <emphasis><formula formulatype="inline"> <tex>$y$</tex></formula></emphasis>, and <emphasis><formula formulatype="inline"> <tex>$P_{\cal Y}$</tex></formula></emphasis> wants to learn <emphasis><formula formulatype="inline"><tex>$x$</tex></formula></emphasis> from <emphasis><formula formulatype="inline"><tex>$P_{\cal X}$</tex></formula></emphasis> while minimizing the communication required for the worst possible input pair <emphasis><formula formulatype="inline"><tex>$(x,y)$</tex></formula></emphasis>. Our contribution is the analysis of four nonzero-error models in this correlated data setting. In the private coin randomized model, both players are allowed to toss coins, and <emphasis><formula formulatype="inline"><tex>$P_Y$</tex></formula></emphasis> must learn <emphasis><formula formulatype="inline"><tex>$x$</tex></formula></emphasis> with high probability for every input pair. The second and third models are similar to the first one, but the players are allowed to use a common source of randomness and to solve several independent instances of the same problem simultaneously, respectively. In the fourth model, <emphasis><formula formulatype="inline"> <tex>$P_{\cal Y}$</tex></formula></emphasis> is allowed to answer incorrectly for a small fraction of the inputs. We show that one round of communication is nearly optimal for the private coin randomized model. We also prove that the last three models are equivalent and can be arbitrarily better than the original worst case deterministic model when interaction is not allowed. Finally, we show that the deterministic model and all the nonzero-error models are equivalent for a class of symmetric problems arising from several practical applications, although nonzero-error and randomization allow efficient one-way protocols. </para>
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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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.004 |
| Open science | 0.001 | 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