Using expectation maximization to find likely assignments for solving CSP's
Why this work is in the frame
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Bibliographic record
Abstract
We present a new probabilistic framework for finding likely variable assignments in difficult constraint satisfaction problems. Finding such assignments is key to efficient search, but practical efforts have largely been limited to random guessing and heuristically designed weighting systems. In contrast, we derive a new version of Belief Propagation (BP) using the method of Expectation Maximization (EM). This allows us to differentiate between variables that are strongly biased toward particular values and those that are largely extraneous. Using EM also eliminates the threat of non-convergence associated with regular BP. Theoretically, the derivation exhibits appealing primal/dual semantics. Empirically, it produces an “EMBP”-based heuristic for solving constraint satisfaction problems, as illustrated with respect to the Quasigroup with Holes domain. EMBP outperforms existing techniques for guiding variable and value ordering during backtracking search on this problem. 1
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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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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