Numerical analysis near singularities in RBF networks
Bibliographic record
Abstract
The existence of singularities often affects the learning dynamics in feedforward neural networks. In this paper, based on theoretical analysis results, we numerically analyze the learning dynamics of radial basis function (RBF) networks near singularities to understand to what extent singularities influence the learning dynamics. First, we show the explicit expression of the Fisher information matrix for RBF networks. Second, we demonstrate through numerical simulations that the singularities have a significant impact on the learning dynamics of RBF networks. Our results show that overlap singularities mainly have influence on the low dimensional RBF networks and elimination singularities have a more significant impact to the learning processes than overlap singularities in both low and high dimensional RBF networks, whereas the plateau phenomena are mainly caused by the elimination singularities. The results can also be the foundation to investigate the singular learning dynamics in deep feedforward neural networks.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.006 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".