Bibliographic record
Abstract
Quadratic programs (QP), minimizations of quadratic objectives subject to linear inequality and equality constraints, are at the heart of algorithms across scientific domains. Applications include fundamental tasks in geometry processing, simulation, engineering, animation and finance where the accurate, reliable, efficient, and scalable solution of QP problems is critical. However, available QP algorithms generally provide either accuracy or scalability - but not both. Some algorithms reliably solve QP problems to high accuracy but work only for smaller-scale QP problems due to their reliance on dense matrix methods. Alternately, many other QP solvers scale well via sparse, efficient algorithms but cannot reliably deliver solutions at requested accuracies. Towards addressing the need for accurate and efficient QP solvers at scale, we develop NASOQ, a new, full-space QP algorithm that provides accurate, efficient, and scalable solutions for QP problems. To enable NASOQ we construct a new row modification method and fast implementation of LDL factorization for indefinite systems. Together they enable efficient updates and accurate solutions of the iteratively modified KKT systems required for accurate QP solves. While QP methods have been previously tested on large synthetic benchmarks, to test and compare NASOQ's suitability for real-world applications we collect here a new benchmark set comprising a wide range of graphics-related QPs across physical simulation, animation, and geometry processing tasks. We combine these problems with numerous pre-existing stress-test QP benchmarks to form, to our knowledge, the largest-scale test set of application-based QP problems currently available. Building off of our base NASOQ solver we then develop and test two NASOQ variants against best, state-of-the-art available QP libraries - both commercial and open-source. Our two NASOQ-based methods each solve respectively 98.8% and 99.5% of problems across a range of requested accuracies from 10 -3 to 10 -9 with average speedups ranging from 1.7× to 24.8× over fastest competing methods.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.047 | 0.013 |
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".