Predicting Satisfiability at the Phase Transition
Bibliographic record
Abstract
Uniform random 3-SAT at the solubility phase transition is one of the most widely studied and empirically hardest distributions of SAT instances. For 20 years, this distribution has been used extensively for evaluating and comparing algorithms. In this work, we demonstrate that simple rules can predict the solubility of these instances with surprisingly high accuracy. Specifically, we show how classification accuracies of about 70% can be obtained based on cheaply (polynomial-time) computable features on a wide range of instance sizes. We argue in two ways that classification accuracy does not decrease with instance size: first, we show that our models' predictive accuracy remains roughly constant across a wide range of problem sizes; second, we show that a classifier trained on small instances is sufficient to achieve very accurate predictions across the entire range of instance sizes currently solvable by complete methods. Finally, we demonstrate that a simple decision tree based on only two features, and again trained only on the smallest instances, achieves predictive accuracies close to those of our most complex model. We conjecture that this two-feature model outperforms random guessing asymptotically; due to the model's extreme simplicity, we believe that this conjecture is a worthwhile direction for future theoretical work.
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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 | 0.002 | 0.015 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".