An information‐theoretic approach to basis‐set fitting of electron densities and other non‐negative functions
Bibliographic record
Abstract
The numerical ill-conditioning associated with approximating an electron density with a convex sum of Gaussian or Slater-type functions is overcome by using the (extended) Kullback-Leibler divergence to measure the deviation between the target and approximate density. The optimized densities are non-negative and normalized, and they are accurate enough to be used in applications related to molecular similarity, the topology of the electron density, and numerical molecular integration. This robust, efficient, and general approach can be used to fit any non-negative normalized functions (e.g., the kinetic energy density and molecular electron density) to a convex sum of non-negative basis functions. We present a fixed-point iteration method for optimizing the Kullback-Leibler divergence and compare it to conventional gradient-based optimization methods. These algorithms are released through the free and open-source BFit package, which also includes a L2-norm squared optimization routine applicable to any square-integrable scalar function.
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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 | 0.004 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| 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".