A Pragmatic Guide to Building Conservative Discrete Abstractions of Cyber-Physical Systems
arXiv:2608.10254
2026
Dynamics
2 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper presents a conservative-by-construction workflow for abstracting continuous closed-loop dynamics into finite nondeterministic transition systems while preserving verification guarantees. Its transferable mechanisms are conservative set-valued transition construction, PAC-certified sampling coverage, and counterexample-guided abstraction refinement that removes spurious behavior without deleting concrete trajectories. For neural networks, these tools can analyze hidden-state dynamics in RNNs, state-space models, world models, and neural controllers, exposing unsafe regions and long-horizon failure modes. The most practical implementations are certified latent-state reachability and adaptive refinement focused on abstract counterexamples.
Ideas from this paper
△ Mechanism confirmed, baseline not beaten
2026
Construct a finite nondeterministic abstraction of an RNN or neural state-space model by partitioning its hidden-state domain into cells and adding every abstract transition that could contain a concrete successor. Use temporal-logic counterexamples to refine only cells involved in violating paths instead of globally increasing discretization resolution. This provides a falsifiable bridge between long-horizon neural dynamics and formal safety or attractor analysis.
Useful8/10
Difficulty7/10
Novelty8/10
✗ Failed on benchmark
2026
Use PAC-certified sampling to estimate whether a neural transition model has adequately covered the reachable successor set of each latent-state cell. Cells with insufficient coverage receive additional rollouts, larger uncertainty margins, or increased training weight. This prevents a model from appearing stable merely because rare but dynamically important transitions were never sampled.
Useful7/10
Difficulty5/10
Novelty7/10