Adaptive selection between individual and relational neuron splitting

Determine when a branch-and-bound procedure for relational neural-network verification should select individual neurons for splitting and when it should switch back to splitting relational neurons.

Background

SaBRe currently selects relational neurons exclusively when refining over-approximated bounds during branch-and-bound verification. The paper notes that allowing both individual and relational neurons as splitting candidates could potentially improve performance, but choosing between these two types of splits is unresolved. Although the dual formulation involves both individual and relational neurons and might provide a basis for the decision, the paper states that additional algorithmic design and comprehensive evaluation are needed.

References

As future work, we plan to investigate more refined splitting strategies to achieve tighter relational bounds and design neuron selection heuristic to further improve the efficiency and scalability of verification. Moreover, for problem splitting, our current approach selects relational neurons exclusively without considering individual neurons. While it is possible to consider both individual and relational neurons simultaneously, it introduces a non-trivial question about when we should select individual neurons and when we switch back to relational neurons. A possible solution could be based on our dual formulation, in which both individual and relational neurons are involved, however, more algorithmic details require more sophisticated design and comprehensive evaluation.

— Branch and Bound for Relational Verification of Neural Networks  (2608.13118 - Fukuda et al., 13 Aug 2026) in Section VI, “Conclusion and Future Work”