Bibliographic record
Abstract
The present paper is an accessible digest, along with extensions, of previous work by the authors. We propose an unifying and versatile framework for a class of discrete time systems whose state is an element of a group, that we call linear observation systems on groups. Those systems strictly mimic linear systems in the sense that + is replaced with group multiplication , and linear maps by endomorphisms. Generalized linear observers on groups, which are the group counterpart of linear observers (and known as invariant observers on groups), are shown to share some important properties with linear observers, namely the fact the estimation error equation is autonomous. We then prove that, linear observation systems are in fact the only ones such that the error equation is autonomous, and relate them to group-affine systems we have previously introduced in continuous time. We also introduce a family of groups called SE_K(D), and leverage it to prove many non-linear discrete-time systems of navigation and robotics (including Simultaneous Localization And Mapping) are in fact linear observation systems on SE_K(D).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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 source (direct Gemma or distilled Codex), 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".