Computing vibrational energy levels by solving linear equations using a tensor method with an imposed rank
Bibliographic record
Abstract
Present day computers do not have enough memory to store the high-dimensional tensors required when using a direct product basis to compute vibrational energy levels of a polyatomic molecule with more than about five atoms. One way to deal with this problem is to represent tensors using a tensor format. In this paper, we use the canonical polyadic (CP) format. Energy levels are computed by building a basis from vectors obtained by solving linear equations. The method can be thought of as a CP realization of a block inverse iteration method with multiple shifts. The CP rank of the tensors is fixed, and the linear equations are solved with an method. There is no need for rank reduction and no need for orthogonalization, and tensors with a rank larger than the fixed rank used to solve the linear equations are never generated. The ideas are tested by computing vibrational energy levels of a 64-D bilinearly coupled model Hamiltonian and of acetonitrile (12-D).
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".