RAIL-CLIPPER Branch-and-Bound Scales Verification of Nonlinear Neural Feedback Systems
The paper presents RAIL and CLIPPER to scale combinatorial verification of nonlinear neural feedback systems by joint branch-and-bound on closed-loop abstractions. It improves bound tightness and runtime over pure propagation or pure combinatorial baselines on standard control benchmarks. The approach enables verification of larger controllers while preserving cross-timestep correlations.
The arXiv paper 2609.16298 introduces RAIL as an interface layer and CLIPPER as a branch-and-bound procedure that operates on abstractions of nonlinear neural feedback loops. Prior combinatorial solvers hit exponential blowup on networks above a few dozen neurons; propagative methods such as CROWN-style LiRPA lose correlation across time steps. The new construction preserves symbolic relations by refining enclosures and splitting ReLU activations in the same search tree.
Benchmarks in the submission show runtime reductions on cart-pole and quadrotor models with 50-200 neuron controllers, where baseline tools time out or return vacuous bounds. The method records tighter interval bounds at each branch because polyhedral sets are propagated through both plant dynamics and network layers without resetting correlations at each time step.
Operationally this shifts verification from offline certification of small controllers to online or design-time checking of autonomy stacks that combine learned policies with nonlinear plants. The framework requires the dynamics to admit polyhedral outer approximations; systems with non-Lipschitz or hybrid resets remain outside its current scope.
Next steps include integration with existing LiRPA libraries and extension to stochastic or partially observed dynamics, as stated in the authors' future-work paragraph.
Akinwande et al.: CLIPPER will certify controllers with 500+ neurons on standard quadrotor dynamics within 30 minutes on commodity hardware by Q3 2027.
Sources (2)
- [1]Primary Source(https://arxiv.org/abs/2609.16298)
- [2]Supporting Source(https://arxiv.org/abs/2302.02829)