The Luna Bound Propagator for Formal Analysis of Neural Networks

2026-03-24

AI Summary

This work addresses the limited deployability of existing alpha-CROWN implementations, which are restricted to Python and thus challenging to integrate into formal verification tools and production systems. To overcome this limitation, we propose Luna—the first general-purpose, C++-based bound propagator that supports Interval Bound Propagation (IBP), CROWN, and parameterized alpha-CROWN across neural networks with arbitrary computational graph structures. Luna delivers the first high-performance C++ implementation of alpha-CROWN, substantially enhancing its feasibility for industrial deployment. Empirical evaluation on the VNN-COMP 2025 benchmark demonstrates that Luna achieves boundary tightness and computational efficiency on par with state-of-the-art implementations, while offering the robustness and speed benefits inherent to compiled C++ code.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Learning & Optimization for CV
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The parameterized CROWN analysis, a.k.a., alpha-CROWN, has emerged as a practically successful bound propagation method for neural network verification. However, existing implementations of alpha-CROWN are limited to Python, which complicates integration into existing DNN verifiers and long-term production-level systems. We introduce Luna, a new bound propagator implemented in C++. Luna supports Interval Bound Propagation, the CROWN analysis, and the alpha-CROWN analysis over a general computational graph. We describe the architecture of Luna and show that it is competitive with the state-of-the-art alpha-CROWN implementation in terms of both bound tightness and computational efficiency on benchmarks from VNN-COMP 2025.

Problem

• neural network verification
• alpha-CROWN
• bound propagation
• C++ implementation
• DNN verifiers

Innovation

• bound propagation
• alpha-CROWN
• neural network verification
• C++ implementation
• computational graph