Query-to-Communication Lifting Using Low-Discrepancy Gadgets
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Bibliographic record
Abstract
Lifting theorems are theorems that relate the query complexity of a function\n$f:\\{0,1\\}^{n}\\to\\{0,1\\}$ to the communication complexity of the composed\nfunction $f \\circ g^{n}$, for some "gadget"\n$g:\\{0,1\\}^{b}\\times\\{0,1\\}^{b}\\to\\{0,1\\}$. Such theorems allow transferring\nlower bounds from query complexity to the communication complexity, and have\nseen numerous applications in the recent years. In addition, such theorems can\nbe viewed as a strong generalization of a direct-sum theorem for the gadget\n$g$.\n We prove a new lifting theorem that works for all gadgets $g$ that have\nlogarithmic length and exponentially-small discrepancy, for both deterministic\nand randomized communication complexity. Thus, we significantly increase the\nrange of gadgets for which such lifting theorems hold.\n Our result has two main motivations: First, allowing a larger variety of\ngadgets may support more applications. In particular, our work is the first to\nprove a randomized lifting theorem for logarithmic-size gadgets, thus improving\nsome applications of the theorem. Second, our result can be seen as a strong\ngeneralization of a direct-sum theorem for functions with low discrepancy.\n
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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