Homology-Rank-Informed Geometry Score for Configuration Space Reconstruction
Bibliographic record
Abstract
Accurately reconstructing datasets holds paramount significance in the field of machine learning. In path planning problems, the ability to precisely reconstruct the configuration space (CS) is pivotal for distinguishing between collision-free states and states in collisions. Collision states can be visualized as voids within the CS of a robot. In this paper, we introduce a novel approach to assess the fidelity of the reconstructed distribution of collision-free states by adapting the concept of homology rank of manifolds with a geometry score tailored to the unique characteristics of CS. This scoring mechanism effectively quantifies the degree to which the reconstructed CS faithfully represents the collision-free space and facilitates the identification of collision states. To validate our proposed methodology, extensive simulations were conducted across a range of case studies. The results demonstrate the capability of our approach to measure the resemblance between the original dataset and its regenerated counterpart with an acceptable accuracy.
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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".