Optimal Filtering and the Separation Principle on Very Large Networks: a Graphon Q-noise Analysis
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Bibliographic record
Abstract
Estimation of stochastic systems on very large networks is intractable computationally. Graphon theory provides limit objects for infinite sequences of graphs by mapping adjacency matrices to the unit square, enabling the modelling of dynamical systems on arbitrarily large graphs via functional analytic methods. In previous work (Dunyak and Caines, 2022, 2023, 2024), Q-noise was used to extend stochastic systems on large graphs to stochastic systems in Hilbert spaces on graphons; in this paper the linear system state estimation problem on large networks and their graphon limits are analysed, and a Separation Principle of control and estimation is introduced. Convergence of finite network linear system state estimates, together with the corresponding Kalman filter systems to their graph limit counterparts, is established. A computational example of this convergence is illustrated on a standard graphon example.
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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 | 0.000 | 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 it