Comparing Sigmoid Transfer Functions for Neural Network Multistep Ahead Streamflow Forecasting
Bibliographic record
Abstract
One of the main problems of neural networks is the lack of consensus on how to best implement them. This work targets the question of the transfer function selection—a vital part of neural network providing nonlinear mapping potential. Three nonlinear transfer functions bounded by −1 and 1 are selected for testing, based on a literature review: the Elliott sigmoid, the bipolar sigmoid, and the tangent sigmoid. They are used to design multilayer perceptron neural networks for multistep ahead streamflow forecasting over five diverse watersheds and lead times from 1 to 5 days. All multilayer perceptrons have shown a good performance on the account of the four selected criteria, which confirms that the selected multilayer perceptron implementation procedure was adequate, namely, the data set length, the Kohonen network clustering method to create the training and testing sets, and the Levenberg-Marquardt back-propagation training procedure with Bayesian regularization. Specifically, results endorsed the tangent sigmoid as the most pertinent transfer function for streamflow forecasting, over the bipolar (logistic) and Elliott sigmoids, but the latter requires less computing time and as such may be a valuable option for operational hydrology. Also, results averaged over five lead times confirmed the universal approximation theorem that a linear transfer function is suitable for the output layer—a nonlinear transfer function in the output layer failed to improve performance values.
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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 | 0.005 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".