Phase transitions and typical-case complexity: easy (hard) aspects of hard (easy) problems
Bibliographic record
Abstract
In this thesis, we study theoretically and empirically the typical-case hardness of randomly-generated instances of several algorithmic problems that are of interest in artificial intelligence research. For randomly-generated instances of constraint satisfaction problems (CSP), we identified a new class of algorithmically exploitable structures and proved that under certain instance distributions, random instances contain such structures with high probability (Chapter 4). In an effort to find a way to eliminate these structures from randomly-generated CSP instances, we established an interesting connection between the notion of constraint consistency in the literature and the resolution complexity of random CSP instances. By embedding a recursive structure called consistency core into random CSP models, we proposed a novel scheme to generate random CSP instances with theoretically guaranteed resolution complexity and empirically confirmed hardness (Chapter 5). Our proposal resolved the long-standing problem of generating hard random CSP instances with bounded domain size that has troubled the society for several years. While all of the results in Chapters 4 and 5 are aimed at backtracking search algorithms, we investigated in Chapter 6 the typical-case behavior of random instances in terms of the dynamic programming algorithms whose time and space complexities are exponential in the treewidth of the underlying structures. This type of algorithm has been widely used in the study of Bayesian network inference and CSPs. We established an improved lower bound on the threshold for a random graph to have a treewidth linear in the graph size. Similar techniques were then applied to random CSPs, random Bayesian networks, and fitness landscape models in computational biology and evolutionary computation.
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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 | 0.005 | 0.049 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 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 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".