Generalized convolutional many-body distribution functional representations
Bibliographic record
Abstract
Modern machine learning (ML) models of chemical and materials systems with billions of parameters require vast training datasets and considerable computational efforts. Lightweight kernel or decision tree-based methods, however, can be rapidly trained, leading to a considerably lower carbon footprint. We introduce generalized convolutional many-body distribution functionals (cMBDF) as highly compute and data-efficient atomic representations for accurate kernels that excel in low-data regimes. Generalizing the MBDF framework, cMBDF encodes local chemical environments in a compact fashion using translationally and rotationally invariant functionals of smooth atomic densities weighted by interaction potentials. The functional values can be efficiently evaluated by expressing them in terms of convolutions which are calculated via fast Fourier transforms and stored on predefined grids. In the generalized form, each atomic environment is described using a set of functionals uniformly defined by three integers; many-body, derivative, weighting orders. Irrespective of size/composition, cMBDF atomic vectors remain compact and constant in size for a fixed choice of these orders controlling the structural and compositional resolution. While being up to two orders of magnitude more compact than other popular representations, cMBDF is shown to be more accurate for the learning of various quantum properties such as energies, dipole moments, homo-lumo gaps, heat capacity, polarizability, optimal exact-exchange admixtures, and basis-set scaling factors. Applicability for organic and inorganic chemistry is tested as represented by the QM7b, QM9, and VQM24 datasets. Due to its compactness, model training and testing times are reduced from 23 h to 8 min, implying a corresponding reduction in carbon footprint.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| 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".