Practical message-passing framework for large-scale combinatorial optimization
Bibliographic record
Abstract
Graphical Model (GM) has provided a popular framework for big data analytics because it often lends itself to distributed and parallel processing by utilizing graph-based ‘local’ structures. It models correlated random variables where in particular, the max-product Belief Propagation (BP) is the most popular heuristic to compute the most-likely assignment in GMs. In the past years, it has been proven that BP can solve a few classes of combinatorial optimization problems under certain conditions. Motivated by this, we explore the prospect of using BP to solve generic combinatorial optimization problems. The challenge is that, in practice, BP may converge very slowly and even if it does converge, the BP decision often violates the constraints of the original problem. This paper proposes a generic framework that enables us to apply BP-based algorithms to compute an approximate feasible solution for an arbitrary combinatorial optimization task. The main novel ingredients include (a) careful initialization of BP messages, (b) hybrid damping on BP updates, and (c) post-processing using BP beliefs. Utilizing the framework, we develop parallel algorithms for several large-scale combinatorial optimization problems including maximum weight matching, vertex cover and independent set. We demonstrate that our framework delivers high approximation ratio, speeds up the process by parallelization, and allows large-scale processing involving billions of variables.
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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 | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 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".