ICML 2025

LEVIS: Large Exact Verifiable Input Spaces for Neural Networks
Mohamad Chehade * 1 2 Wenting Li * 2 Brian W. Bell 2 Russell Bent 2 Saif R. Kazi 2 Hao Zhu 1
Abstract
The robustness of neural networks is crucial in
safety-critical applications, where identifying a re-
liable input space is essential for effective model
selection, robustness evaluation, and the devel-
opment of reliable control strategies. Most ex-
isting robustness verification methods assess the
worst-case output under the assumption that the
input space is known. However, precisely identi-
fying a verifiable input space C, where no adver-
sarial examples exist, is challenging due to the
possible high dimensionality, discontinuity, and
non-convex nature of the input space. To address
this challenge, we propose a novel framework,
LEVIS, consisting of LEVIS-α and LEVIS-β.
LEVIS-α identifies a single, large verifiable
ball that intersects at least two boundaries of a
bounded region C. In contrast, LEVIS-β sys-
tematically captures the entirety of the verifiable
space by integrating multiple verifiable balls. Our
contributions are fourfold: (1) We introduce a ver-
ification framework, LEVIS, incorporating two
optimization techniques for computing nearest
and directional adversarial points based on mixed-
integer programming (MIP). (2) To enhance scal-
ability, we integrate complementarity-constrained
(CC) optimization with a reduced MIP formula-
tion, achieving up to a 6-fold reduction in runtime
while approximating the verifiable region in a
principled manner. (3) We provide a theoretical
analysis characterizing the properties of the veri-
fiable balls obtained through LEVIS-α. (4) We
validate our approach across diverse applications,
including electrical power flow regression and
*Equal contribution
1Chandra Department of Electrical
and Computer Engineering,
The University of Texas at
Austin, Austin, TX, USA
2Los Alamos National Labora-
tory,
Los Alamos,
NM, USA. Correspondence to:
Mo-
hamad Chehade <c...