Computing vibrational energy levels using a canonical polyadic tensor method with a fixed rank and a contraction tree
Bibliographic record
Abstract
In this paper, we use the previously introduced Canonical Polyadic (CP)-Multiple Shift Block Inverse Iteration (MSBII) eigensolver [S. D. Kallullathil and T. Carrington, J. Chem. Phys. 155, 234105 (2021)] in conjunction with a contraction tree to compute vibrational spectra. The CP-MSBII eigensolver uses the CP format. The memory cost scales linearly with the number of coordinates. A tensor in CP format represents a wavefunction constrained to be a sum of products (SOP). An SOP wavefunction can be made more accurate by increasing the number of terms, the rank. When the required rank is large, the runtime of a calculation in CP format is long, although the memory cost is small. To make the method more efficient, we break the full problem into pieces using a contraction tree. The required rank for each of the sub-problems is small. To demonstrate the effectiveness of the ideas, we computed vibrational energy levels of acetonitrile (12-D) and ethylene oxide (15-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 | 0.000 | 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) | 0.003 | 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".