Evaluating Kolmogorov–Arnold Networks for Scientific Discovery: A Simple Yet Effective Approach
Why this work is in the frame
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Bibliographic record
Abstract
Kolmogorov–Arnold Network (KAN) is an emerging interpretable neural network compared to fully black-box MLPs. Recently, emerging works focus on comprehensive and fair comparisons between KAN and MLP in various tasks. However, these works didn't focus on the strongest advantage of KAN: generating symbolic outputs. The ability of KAN to provide scientific insights or even discover new science is under-examined. In this work, we propose several novel metrics to measure how well a KAN performs on symbolic function fitting: R^2-Mean, weighted R^2-complexity loss, and ranking metrics. We also propose a metric to determine mathematical complexity of a target function and evaluate KAN with several functions of different mathematical complexity. Additionally, we also tried inputs with different ranges to find the effect of normalization.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.005 | 0.029 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it