Stochastic stabilization of a noisy linear system with a fixed-rate adaptive quantizer
Bibliographic record
Abstract
Zooming type adaptive quantizers have been introduced in the networked control literature as efficient coders for stabilizing open-loop unstable noise-free systems connected over noiseless channels with arbitrary initial conditions. Such quantizers can be regarded as a special class of the Goodman-Gersho adaptive quantizers. In this paper, we provide a stochastic stability result for such quantizers when the system is driven by an additive noise process. Conditions leading to stability are evaluated when the system is driven by noise with non-compact support for its probability measure. It is shown that zooming quantizers are efficient and almost achieve the fundamental lower bound of the logarithm of the absolute value of an unstable eigenvalue. In particular, such quantizers are asymptotically optimal when the unstable pole of the linear system is large for a weak form of stability.
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| 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".