From Support Propagation to Belief Propagation in Constraint Programming
Why this work is in the frame
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Bibliographic record
Abstract
The distinctive driving force of constraint programming to solve combinatorial problems has been a privileged access to problem structure through the high-level models it uses. From that exposed structure in the form of so-called global constraints, powerful inference algorithms have shared information between constraints by propagating it through shared variables’ domains, traditionally by removing unsupported values. This paper investigates a richer propagation medium made possible by recent work on counting solutions inside constraints. Beliefs about individual variable-value assignments are exchanged between contraints and iteratively adjusted. It generalizes standard support propagation and aims to converge to the true marginal distributions of the solutions over individual variables. Its advantage over standard belief propagation is that the higher-level models featuring large-arity (global) constraints do not tend to create as many cycles, which are known to be problematic for convergence. The necessary architectural changes to a constraint programming solver are described and an empirical study of the proposal is conducted on its implementation. We find that it provides close approximations to the true marginals and that it significantly improves search guidance.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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