Legendre polynomial-based quantized neural network repairing

Quantized neural networks (QNNs) are increasingly deployed in safety-critical domains, but quantization often exacerbates their susceptibility to adversarial perturbations. We propose Legendre Polynomial-based Quantized Neural Network Repairing, a novel framework that formulates verification and repair as a mixed-integer linear programming problem. By approximating nonlinear activations with Legendre polynomials, the method exploits their orthogonality, rapid convergence, and strong approximation properties to achieve efficient constraint encoding with provable error bounds. Leveraging the Gurobi solver, our approach enables automated detection and correction of quantization-induced vulnerabilities without access to the original training data. Experiments on standard QNN benchmarks demonstrate that the method improves both robustness and scalability over existing techniques, while ensuring formal safety guarantees.