Mixtures of Neural Operators Reduce Active Complexity in Operator Learning
Bibliographic record
Abstract
Operator-learning systems are not governed solely by total parameter count; for one query, the relevant bottleneck can be the model that must be loaded and evaluated. We study this distinction for classical neural operators on compact Sobolev subsets through a constructive comparison between routed mixtures of neural operators (MoNOs) and a fixed single-neural-operator construction. The comparison concerns expert-active complexity relative to that baseline, with total stored size and routing search accounted separately. A MoNO routes each input function through a tree to one expert. Our main theorem shows that every scalar uniformly continuous nonlinear operator with bounded output Sobolev radius on the approximation set admits a MoNO approximation whose active expert has smaller depth, width, and rank scaling than the analyzed single-neural-operator construction; for Lipschitz targets these expert quantities are bounded by $\mathcal{O}(\varepsilon^{-1})$. The theorem turns localization into an operator-level accounting of active expert size, routing depth, and number of experts. We also prove a quantitative universal approximation theorem for the underlying neural-operator architecture, with explicit dependence on compact-set diameter and modulus of continuity.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 | 0.020 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.008 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".