OMP-Net: Neural network unrolling of weighted Orthogonal Matching Pursuit
Bibliographic record
Abstract
In recent years, algorithm unrolling has emerged as a promising methodology in various signal-processing applications, intending to combine the strengths of iterative algorithms and deep learning. Despite its success, unrolling greedy sparse recovery algorithms, particularly Orthogonal Matching Pursuit (OMP), has yet to receive much attention. The primary challenge is the non-differentiable nature of the argsort operator, a key component in greedy algorithms, which hinders gradient backpropagation during training. To address this, we introduce ‘OMPNet’ by utilizing softsorting to approximate the argsort operator in a differentiable manner. Our numerical and theoretical analysis shows that under certain conditions, the approximation error is minimal, and the performance of the approximated OMP, which we call ‘Soft-OMP’, closely matches the original. We then incorporate Soft-OMP into the feedforward neural network’s layers, integrating learnable weight parameters to connect our approach to weighted sparse recovery. Our numerical results demonstrate that this network is trainable and can surpass the performance of the original OMP in certain scenarios.
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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".