Detecting numerical bugs in neural network architectures

Detecting bugs in deep learning software at the architecture level provides additional benefits that detecting bugs at the model level does not provide. This paper makes the first attempt to conduct static analysis for detecting numerical bugs at the architecture level. We propose a static analysis approach for detecting numerical bugs in neural architectures based on abstract interpretation. Our approach mainly comprises two kinds of abstraction techniques, i.e., one for tensors and one for numerical values. Moreover, to scale up while maintaining adequate detection precision, we propose two abstraction techniques: tensor partitioning and (elementwise) affine relation analysis to abstract tensors and numerical values, respectively. We realize the combination scheme of tensor partitioning and affine relation analysis (together with interval analysis) as DEBAR, and evaluate it on two datasets: neural architectures with known bugs (collected from existing studies) and real-world neural architectures. The evaluation results show that DEBAR outperforms other tensor and numerical abstraction techniques on accuracy without losing scalability. DEBAR successfully detects all known numerical bugs with no false positives within 1.7-2.3 seconds per architecture. On the real-world architectures, DEBAR reports 529 warnings within 2.6-135.4 seconds per architecture, where 299 warnings are true positives.