On Fractional Tikhonov Regularization: Application to the Adaptive Network-Based Fuzzy Inference System for Regression Problems
Bibliographic record
Abstract
In this article, we introduce a variant of the adaptive network-based fuzzy inference system (ANFIS). The proposed variant does not use backpropagation and grid partitioning, but the least-squares method with fractional Tikhonov regularization. The fractional regularization is a generalization of the standard regularization and is applied here to the learning process of the ANFIS scheme for the first time. This results in a simpler rule base, with a low number of rules, allowing to handle problems with many input variables with relatively low computational time while keeping high accuracy. We present new theoretical results on the fractional Tikhonov regularization. Such results are the basis for a formal discussion on how much the choice of a different architecture, resulting in a different matrix in the least-squares minimization, could affect the accuracy. We perform several numerical experiments on benchmark examples, first to assess the impact of the fractional regularization on the accuracy and then to compare our results against the most recent ones reported in the literature by other ANFIS-like or neuro-fuzzy systems. The numerical results show the good performance of the proposed approach.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| 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".