A new approximating model for the time invariant nonlinear operators with fading memory
Bibliographic record
Abstract
The paper presents a construction theorem for a class of operators dense over the set of causal, time invariant fading memory operators. In this sense, it extends the classical results of S. Boyd and L.O. Chua that the Volterra series operators are universal approximators for this set of nonlinear operators often encountered in the theory of dynamical systems. This new representation is based on the remarkable property of the neural network ΣΠ functions to be a dense algebra in the set of continuous functions over compacta in Rn. More, this class of functions is known to allow effective approximations of non-analytical type non-linearities and, as a consequence, to avoid higher order terms else way present in a polynomial decomposition. It is expected that with a proper choice of the ΣΠ base functions this property transfers to the non-linear operator representation. Following this reasoning, we are able to prove the inclusion of the Volterra series in this richer set of nonlinear operators.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".