A Method for Detecting Numerical Defects in Deep Learning Programs Based on Abstract Interpretation

To improve the efficiency of existing static analysis methods for detecting numerical bugs in deep learning programs, we propose a novel analysis approach. By utilizing abstract interpretation, we designed abstractions for tensors and 74 neural network operations on the Zonotope domain, and implemented a tool called NUMZ to detect numerical bugs in neural architectures. We conducted comparative experiments between NUMZ and the state-of-the-art tool RANUM on a benchmark consisting of 58 real-world neural network models with 34 numerical bugs. The results show that NUMZ achieved an accuracy of 96.5%, while RANUM only reached 48.2%. This demonstrates that the NUMZ method is significantly more accurate than existing approaches in detecting numerical errors in deep learning programs.