  Despite deep learning's transformative impact on various domains, the
reliability of Deep Neural Networks (DNNs) is still a pressing concern due to
their complexity and data dependency. Traditional software fault localization
techniques, such as Spectrum-based Fault Localization (SBFL), have been adapted
to DNNs with limited success. Existing methods like DeepFault utilize SBFL
measures but fail to account for fault propagation across neural pathways,
leading to suboptimal fault detection. Addressing this gap, we propose the
NP-SBFL method, leveraging Layer-wise Relevance Propagation (LRP) to identify
and verify critical neural pathways. Our innovative multi-stage gradient ascent
(MGA) technique, an extension of gradient ascent (GA), activates neurons
sequentially, enhancing fault detection efficacy. We evaluated the
effectiveness of our method, i.e. NP-SBFL-MGA, on two commonly used datasets,
MNIST and CIFAR-10, two baselines DeepFault and NP- SBFL-GA, and three
suspicious neuron measures, Tarantula, Ochiai, and Barinel. The empirical
results showed that NP-SBFL-MGA is statistically more effective than the
baselines at identifying suspicious paths and synthesizing adversarial inputs.
Particularly, Tarantula on NP-SBFL-MGA had the highest fault detection rate at
96.75%, surpassing DeepFault on Ochiai (89.90%) and NP-SBFL-GA on Ochiai
(60.61%). Our approach also yielded results comparable to those of the
baselines in synthesizing naturalness inputs, and we found a positive
correlation between the coverage of critical paths and the number of failed
tests in DNN fault localization.
