Control Over Noisy Forward and Reverse Channels
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Bibliographic record
Abstract
We consider the problem of remotely controlling a continuous-time linear time-invariant system driven by Brownian motion process, when communication takes place over noisy memoryless discrete- or continuous-alphabet channels. What makes this class of remote control problems different from most of the previously studied models is the presence of noise in both the forward channel (connecting sensors to the controller) and the reverse channel (connecting the controller to the plant). For stability of the closed-loop system, we look for the existence of an invariant distribution for the state, for which we show that it is necessary that the entire control space and the state space be encoded, and that the reverse channel be at least as reliable as the forward channel. We obtain necessary conditions and sufficient conditions on the channels and the controllers for stabilizability. Using properties of the underlying sampled Markov chain, we show that under variable-length coding and some realistic channel conditions, stability can be achieved over discrete-alphabet channels even if the entire state and control spaces are to be encoded and the number of bits that can be transmitted per unit time is strictly bounded. For control over continuous-alphabet channels, however, a variable rate scheme is not necessary. We also show that memoryless policies are rate-efficient for Gaussian channels.
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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 | 0.000 |
| 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 it