Manifold Geometry with Fast Automatic Derivatives and Coordinate Frame\n Semantics Checking in C++
Bibliographic record
Abstract
Computer vision and robotics problems often require representation and\nestimation of poses on the SE(3) manifold. Developers of algorithms that must\nrun in real time face several time-consuming programming tasks, including\nderiving and computing analytic derivatives and avoiding mathematical errors\nwhen handling poses in multiple coordinate frames. To support rapid and\nerror-free development, we present wave_geometry, a C++ manifold geometry\nlibrary with two key contributions: expression template-based automatic\ndifferentiation and compile-time enforcement of coordinate frame semantics. We\ncontrast the library with existing open source packages and show that it can\nevaluate Jacobians in forward and reverse mode with little to no runtime\noverhead compared to hand-coded derivatives. The library is available at\nhttps://github.com/wavelab/wave_geometry .\n
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 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 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".