This reference presents PT-LiRPA, a novel neural network verification framework that combines Linear Relaxation-based Perturbation Analysis (LiRPA) with statistical sampling. By utilizing Extreme Value Theory to estimate tight intermediate reachable sets, the method significantly reduces the over-approximation errors typical of formal verification tools. PT-LiRPA provides probabilistic guarantees on verification soundness while maintaining low computational costs. Extensive experiments demonstrate that this approach tightens output bounds and outperforms state-of-the-art verifiers on complex benchmarks, offering robust certification in scenarios where traditional deterministic methods fail.