A Simple Supervised Hashing Algorithm Using Projected Gradient and Oppositional Weights
Bibliographic record
Abstract
Learning to hash is generating similarity-preserving binary representations of images, which is, among others, an efficient way for fast image retrieval. Two-step hashing has become a common approach because it simplifies the learning by separating binary code inference from hash function training. However, the binary code inference typically leads to an intractable optimization problem with binary constraints. Different relaxation methods, which are generally based on complicated optimization techniques, have been proposed to address this challenge. In this paper, a simple relaxation scheme based on the projected gradient is proposed. To this end in each iteration, we try to update the optimization variable as if there is no binary constraint and then project the updated solution to the feasible set. We formulate the projection step as fining closet binary matrix to the updated matrix and take advantage of the closed-form solution for the projection step to complete our learning algorithm. Inspired by opposition-based learning, pairwise opposite weights between data points are incorporated to impose a stronger penalty on data instances with higher misclassification probability in the proposed objective function. We show that this simple learning algorithm leads to binary codes that achieve competitive results on both CIFAR-10 and NUS-WIDE datasets compared to state-of-the-art benchmarks.
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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 | 0.001 |
| 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".