An Algorithm for Learning Orthonormal Matrix Codebooks for Adaptive Transform Coding
Bibliographic record
Abstract
<p>This paper proposes a novel data-driven approach to designing orthonormal transform matrix codebooks for adaptive transform coding of any non-stationary vector processes which can be considered locally stationary. Our algorithm, which belongs to the class of block-coordinate descent algorithms, relies on simple probability models such as Gaussian or Laplacian for transform coefficients to directly minimize with respect to the orthonormal transform matrix the mean square error (MSE) of scalar quantization and entropy coding of transform coefficients. A difficulty commonly encountered in such minimization problems is imposing the orthonormality constraint on the matrix solution. We get around this difficulty by mapping the constrained problem in Euclidean space to an unconstrained problem on the Stiefel manifold and leveraging known algorithms for unconstrained optimization on manifolds. While the basic design algorithm directly applies to non-separable transforms, an extension to separable transforms is also proposed. We present experimental results showing that adaptive coding with our transform codebook designs outperform the commonly used discrete cosine transform (DCT) in many regions of natural images and motion-compensated prediction error images of video frames. According to these results, the proposed codebook designs slightly outperform those found by a common alternative approach, the sparsity-based optimization. </p>
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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 | 0.001 | 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 | 0.001 | 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".