Neural network verification is often used as a core component within larger analysis procedures, which generate sequences of closely related verification queries over the same network. In existing neural network verifiers, each query is typically solved independently, and information learned during previous runs is discarded, leading to repeated exploration of the same infeasible regions of the search space. In this work, we aim to expedite verification by reducing this redundancy. We propose an incremental verification technique that reuses learned conflicts across related verification queries. The technique can be added on top of any branch-and-bound-based neural network verifier. During verification, the verifier records conflicts corresponding to learned infeasible combinations of activation phases, and retains them across runs. We formalize a refinement relation between verification queries and show that conflicts learned for a query remain valid under refinement, enabling sound conflict inheritance. Inherited conflicts are handled using a SAT solver to perform consistency checks and propagation, allowing infeasible subproblems to be detected and pruned early during search. We implement the proposed technique in the Marabou verifier and evaluate it on three verification tasks: local robustness radius determination, verification with input splitting, and minimal sufficient feature set extraction. Our experiments show that incremental conflict reuse reduces verification effort and yields speedups of up to 1.9× over a non-incremental baseline.
Figures & tables
Figure 1: Branch-and-bound search tree over ReLU phase decisions.
Method
Time (s)
Solved
Propagations
Conflicts
Non-incremental
315.6
160
–
–
Incremental
233.5
185
8.2
107.4
Speedup
1.35 ×
–
–
–
Table 1: Robustness radius evaluation on MNIST.
Figure 2: Incremental vs. non-incremental for robustness radius determination.
Method
Time (s)
Solved
Propagations
Conflicts
Non-incremental
84.1
489
–
–
Incremental
43.9
491
1.7
7.9
Speedup
1.92 ×
–
–
–
Table 2: Evaluation of iterative input splitting for Lyapunov certificate verification.
Figure 3: Incremental vs. non-incremental for input splitting.
Figure 4: Minimal sufficient feature set visualizations for GTSRB inputs. Pixels not included in the explanation are shown in gray.
Method
Explanation Size
Propagations
Conflicts
Non-incremental
848.52
–
–
Incremental
844.21
2.30
92.14
Table 3: Minimal sufficient feature set extraction on GTSRB.
Figure 5: Incremental vs. non-incremental explanation size over time.
State-of-the-art neural network verifiers use the branch-and-bound procedure as their core solving mechanism. We introduce an inprocessing framework for neural network verification driven by the lookahead procedure. Under this framework, lookahead derives new lemmas over the phases of unstable ReLUs, which are collected into an implication graph that is used to prune the search space and vivify boolean cuts. We instantiate the framework in two state-of-the-art verifiers, Marabou and α-β-CROWN, and demonstrate that it improves performance in both, proving up to 34% more instances unsatisfiable.
In this work, we investigate the effect of lookahead branching strategies in neural network verification. We present a general recipe to integrate lookahead into any branch-and-bound verifier and demonstrate how one of the current state-of-the-art branching heuristics, FSB, can be viewed as a special instantiation of the lookahead branching strategy. We also describe how, in addition to improving the quality of branching decisions, lookahead can generate additional lemmas that accelerate verification. We instantiate the method in two representative branch-and-bound-based verifiers (Marabou and α-β-CROWN), and demonstrate that lookahead leads to consistent speedups in verification time and up to 57% more solved instances. Code is available at https://github.com/ai-ar-research/lookahead-branching.
Liam Davis, Duo Zhou, Huan Zhang +3
Amherst College · University of Illinois Urbana-Champaign · Hebrew University of Jerusalem +1
Neural network verification has become a key tool for providing formal guarantees on the behaviour of neural networks. However, many verification problems remain computationally intractable in the worst case: even for common adversarial robustness specifications, verification is NP-complete. Here, we explore the application of solver-level warmstarting for neural network verification to exploit information from previous solutions. We study the effect on running time as several properties are modified, including perturbation radii, input data and the networks themselves, using a pipeline that is generalisable and potentially adaptable to state-of-the-art verifiers. Our results show that warmstarting can significantly reduce verification time in most cases. Moreover, warmstarting enables the successful verification of instances that could not be solved from scratch within the given time limit.
Annelot Bosman, Minghao Liu, Marta Kwiatkowska +2
Leiden Institute of Advanced Computer Science, Leiden · University of Oxford, United Kingdom · Chair for AI Methodology, RWTH Aachen University, Germany +1