Optimal Abstractions for Verifying Properties of Kolmogorov-Arnold Networks (KANs)
This work addresses the problem of ensuring reliability in KANs for researchers and practitioners in AI safety, though it is incremental as it builds on existing verification methods for neural networks.
The paper tackles the challenge of verifying properties of Kolmogorov-Arnold Networks (KANs) by developing a systematic framework that creates optimal piecewise affine abstractions, enabling efficient encoding as Mixed Integer Linear Programs and achieving superior verification results across benchmarks.
We present a novel approach for verifying properties of Kolmogorov-Arnold Networks (KANs), a class of neural networks characterized by nonlinear, univariate activation functions typically implemented as piecewise polynomial splines or Gaussian processes. Our method creates mathematical ``abstractions'' by replacing each KAN unit with a piecewise affine (PWA) function, providing both local and global error estimates between the original network and its approximation. These abstractions enable property verification by encoding the problem as a Mixed Integer Linear Program (MILP), determining whether outputs satisfy specified properties when inputs belong to a given set. A critical challenge lies in balancing the number of pieces in the PWA approximation: too many pieces add binary variables that make verification computationally intractable, while too few pieces create excessive error margins that yield uninformative bounds. Our key contribution is a systematic framework that exploits KAN structure to find optimal abstractions. By combining dynamic programming at the unit level with a knapsack optimization across the network, we minimize the total number of pieces while guaranteeing specified error bounds. This approach determines the optimal approximation strategy for each unit while maintaining overall accuracy requirements. Empirical evaluation across multiple KAN benchmarks demonstrates that the upfront analysis costs of our method are justified by superior verification results.