Input driven optimization of echo state network parameters for prediction on chaotic time series
Bibliographic record
Abstract
Echo State Networks (ESNs) have emerged as powerful tools for time series prediction, yet their performance heavily depends on reservoir structure, which traditionally relies on random weights independent of input data characteristics. This paper presents a theoretical framework and optimization approach for ESN reservoir design, demonstrating that reservoir weights should be adapted based on input data properties, and that both topology and weights significantly influence prediction accuracy. Building on theoretical insights about input-dependent reservoir behavior, we propose two complementary methods: a supervised approach that directly optimizes reservoir weights through gradient descent, and a semi-supervised technique that combines small-world and scale-free network properties with hyperparameter optimization. Our extensive experiments across multiple datasets, including synthetic chaotic systems (Mackey-Glass and NARMA time series) and real-world climate data, demonstrate that the proposed methods consistently outperform traditional ESNs by achieving substantially lower prediction errors. Most notably, our analysis reveals that edge connectivity parameters play a crucial role, second only to reservoir size in determining network performance. These findings provide important practical guidelines for ESN design and open new directions for automated reservoir optimization based on input data characteristics.
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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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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".