Guaranteed-Safe Approximate Reachability via State Dependency-Based Decomposition
Why this work is in the frame
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Bibliographic record
Abstract
Hamilton Jacobi (HJ) Reachability is a formal verification tool widely used in robotic safety analysis. Given a target set as unsafe states, a dynamical system is guaranteed not to enter the target under the worst-case disturbance if it avoids the Backward Reachable Tube (BRT). However, computing BRTs suffers from exponential computational time and space complexity with respect to the state dimension. Previously, system decomposition and projection techniques have been investigated, but the trade off between applicability to a wider class of dynamics and degree of conservatism has been challenging. In this paper, we propose a State Dependency Graph to represent the system dynamics, and decompose the full system where only dependent states are included in each subsystem, and "missing" states are treated as bounded disturbance. Thus for a large variety of dynamics in robotics, BRTs can be quickly approximated in lower-dimensional chained subsystems with the guaranteed-safety property preserved. We demonstrate our method with numerical experiments on the 4D Quadruple Integrator, and the 6D Bicycle, an important car model that was formerly intractable.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.002 |
| 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