Infinitely Many Coexisting Attractors and Scrolls in a Fractional-Order Discrete Neuron Map
Bibliographic record
Abstract
The neural network activation functions enable neural networks to have stronger fitting abilities and richer dynamical behaviors. In this paper, an improved fractional-order discrete tabu learning neuron (FODTLN) model map with a nonlinear periodic function as the activation function is proposed. The fixed points of the map are discussed. Then, the rich and complex dynamical behaviors of the map under different parameters and order conditions are investigated by using some common nonlinear dynamical analysis methods combined with the fractional-order approximate entropy method. Furthermore, it is found that fractional-order differential operators affect the generation of multiscrolls, and the model has infinitely many coexisting attractors obtained by changing the initial conditions. Interestingly, attractor growth and state transition are found. Finally, the map is implemented on the DSP hardware platforms to verify the realizability. The results show that the map exhibits complex and interesting dynamical behaviors. It provides a fundamental theory for the research of artificial neural networks.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".