Robust Symmetry Detection via Riemannian Langevin Dynamics
Why this work is in the frame
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Bibliographic record
Abstract
Symmetries are ubiquitous across all kinds of objects, whether in nature or in man-made creations. While these symmetries may seem intuitive to the human eye, detecting them with a machine is nontrivial due to the vast search space. Classical geometry-based methods work by aggregating "votes" for each symmetry but struggle with noise. In contrast, learning-based methods may be more robust to noise, but often overlook partial symmetries due to the scarcity of annotated data. In this work, we address this challenge by proposing a novel symmetry detection method that marries classical symmetry detection techniques with recent advances in generative modeling. Specifically, we apply Langevin dynamics to a redefined symmetry space to enhance robustness against noise. We provide empirical results on a variety of shapes that suggest our method is not only robust to noise, but can also identify both partial and global symmetries. Moreover, we demonstrate the utility of our detected symmetries in various downstream tasks, such as compression and symmetrization of noisy shapes.
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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 | 0.001 | 0.000 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.000 | 0.001 |
| 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