SymCL: Riemannian Contrastive Learning on the Symmetric Positive Definite Manifold for Visual Classification
Bibliographic record
Abstract
Symmetric Positive Definite (SPD) matric has been proven to be an effective feature descriptor in the realm of artificial intelligence, as it can encode spatiotemporal statistical information of data on a curved Riemannian manifold, i.e., SPD manifold. Although existing Riemannian neural networks have demonstrated superiority in many scientific fields, the inherent reliance on labels within supervised learning renders them susceptible to label errors. Besides, it is insufficient to depend solely on labels to learn effective feature distributions in some complicated data scenarios. Drawing inspiration from the considerable achievements of contrastive learning (CL) across diverse tasks, we extend the conventional CL paradigm to the context of SPD manifolds, which we denote SymCL, paving the way for a novel approach in SPD matrix-based visual classification. Furthermore, we inject a Riemannian triplet loss-based Riemannian metric learning (RML) into the designed SPD manifold CL framework for the sake of improving the discrimination of the learned geometric representations. Extensive experimental results on four datasets verify the effectiveness of the proposed algorithm.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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".