Optimal causal quantization of Markov Sources with distortion constraints
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Bibliographic record
Abstract
For Markov sources, the structure of optimal causal encoders minimizing the total communication rate subject to a mean-square distortion constraint is studied. The class of sources considered lives in a continuous alphabet, and the encoder is allowed to be variable-rate. Both the finite-horizon and the infinite-horizon problems are considered. In the finite-horizon case, the problem is non-convex, whereas in the infinite-horizon case the problem can be convexified under certain assumptions. For a finite horizon problem, the optimal deterministic causal encoder for a kth-order Markov source uses only the most recent k source symbols and the information available at the receiver, whereas the optimal causal coder for a memoryless source is memoryless. For the infinite-horizon problem, a convex-analytic approach is adopted. Randomized stationary quantizers are suboptimal in the absence of common randomness between the encoder and the decoder. If there is common randomness, the optimal quantizer requires the randomization of at most two deterministic quantizers. In the absence of common randomness, the optimal quantizer is non-stationary and a recurrence-based time-sharing of two deterministic quantizers is optimal. A linear source driven by Gaussian noise is considered. If the process is stable, innovation coding is almost optimal at high-rates, whereas if the source is unstable, then even a high-rate time-invariant innovation coding scheme leads to an unstable estimation process.
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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