Modulation of Activation Function in Triangular Recurrent Neural Networks for Time Series Modeling
Bibliographic record
Abstract
This paper introduces a novel method to dynamically vary the activation function slopes in recently developed upper and lower triangular recurrent neural networks (ULTRNN) to enhance their modeling capability. The ULTRNN employs a pair of triangular feedback weight matrices with block diagonal elements whose eigenvalues are constrained to lie on or close to the unit circle in the complex z-plane to maintain network and training stability. The activation function slopes of the ULTRNN state variables are dynamically varied by a second modulating network. The inputs to the modulating network are the state variables of the principal ULTRNNs and their inputs. The modulating network is trained simultaneously with the principal ULTRNN to compute the activation function slope for the latter's each state variable at each time step. Such dynamic variation of the activation function slopes selectively enhances the contribution of certain states while suppressing that of the others. A larger slope results in a longer time contribution of the corresponding state and helps model long-term dependencies. Conversely, a smaller slope results in a shorter time contribution and may be used to model controlled "forgetting". The proposed modulation technique enhances the ULTRNN's ability to effectively incorporate short-term memory and long-term dependencies. Simulation results show that with activation function modulation the ULTRNNs are able to autonomously replicate the outputs of sample chaotic dynamic system with good accuracy. This capability can be highly effective in modeling or characterizing the inherent process that generates the time series.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 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".