Reducing training data needs with minimal multilevel machine learning (M3L)
Bibliographic record
Abstract
Abstract For many machine learning applications in science, data acquisition, not training, is the bottleneck even when avoiding experiments and relying on computation and simulation. Correspondingly, and in order to reduce cost and carbon footprint, training data efficiency is key. We introduce minimal multilevel machine learning (M3L) which optimizes training data set sizes using a loss function at multiple levels of reference data in order to minimize a combination of prediction error with overall training data acquisition costs (as measured by computational wall-times). Numerical evidence has been obtained for calculated atomization energies and electron affinities of thousands of organic molecules at various levels of theory including HF, MP2, DLPNO-CCSD(T), DFHFCABS, PNOMP2F12, and PNOCCSD(T)F12, and treating them with basis sets TZ, cc-pVTZ, and AVTZ-F12. Our M3L benchmarks for reaching chemical accuracy in distinct chemical compound sub-spaces indicate substantial computational cost reductions by factors of ∼1.01, 1.1, 3.8, 13.8, and 25.8 when compared to heuristic sub-optimal multilevel machine learning (M2L) for the data sets QM7b, QM9 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi/> <mml:mrow> <mml:mi>LCCSD</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">T</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , Electrolyte Genome Project, QM9 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi/> <mml:mrow> <mml:mi>AE</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>CCSD</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">T</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> , and QM9 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi/> <mml:mrow> <mml:mi>EA</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>CCSD</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">T</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> , respectively. Furthermore, we use M2L to investigate the performance for 76 density functionals when used within multilevel learning and building on the following levels drawn from the hierarchy of Jacobs Ladder: LDA, GGA, mGGA, and hybrid functionals. Within M2L and the molecules considered, mGGAs do not provide any noticeable advantage over GGAs. Among the functionals considered and in combination with LDA, the three on average top performing GGA and Hybrid levels for atomization energies on QM9 using M3L correspond respectively to PW91, KT2, B97D, and τ -HCTH, B3LYP <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:math> (VWN5), and TPSSH.
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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 | 0.006 |
| 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 | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".