GREAT: Grassmannian Recursive Algorithm for Tracking and Online System Identification
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Bibliographic record
Abstract
This paper introduces an online approach for identifying time-varying subspaces defined by linear dynamical systems. The approach of representing linear systems by non-parametric subspace models has received significant interest in the field of data-driven control recently. This system representation enables us to provide rigorous guarantees for linear time-varying systems, which are difficult to obtain for parametric system models. The proposed method leverages optimization on the Grassmann manifold leading to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Grassmannian Recursive Algorithm for Tracking</i> (GREAT). We view subspaces as points on the Grassmann manifold and adapt the estimate based on online data by performing optimization on the manifold. At each time step, a single measurement from the current subspace corrupted by a bounded error is available. The subspace estimate is updated online using Grassmannian gradient descent on a cost function incorporating a window of the most recent data. Under suitable assumptions on the signal-to-noise ratio of the online data and the subspace's rate of change, we establish theoretical guarantees for the resulting algorithm. More specifically, we prove an exponential convergence rate and provide an uncertainty quantification of the estimates in terms of an upper bound on their distance to the true subspace. The applicability of the proposed algorithm is demonstrated by means of numerical examples.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 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 it