Research on the interpretability of surface defect detection transfer learning tasks based on information bottleneck theory

With the development of deep learning, many researches have been devoted to the explanatory nature of Neural Networks (NNs), among which the Information Bottleneck (IB) theory based on information theory has received the most attention. Previous IB work has focused on small MLP or several-layer CNN networks, and a small number of datasets, and the applicability of its conclusions in popular image classification models cannot be verified, especially lacking in transfer learning. To address the above issues, we experiment on an industrial surface defects classification task to investigate IB and performance variations in ResNet transfer learning. The local densities of feature parameters in ResNet transfer learning are calculated by adaptive bins and K-nearest neighbour method. The mutual information of input image information-model parameters and model parameters-output information is calculated, and it is found that there are two stages of fitting and compression of CNN features in transfer learning. The IB representation method <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>D</mml:mi> <mml:mi>I</mml:mi> <mml:mi>B</mml:mi> </mml:math> is proposed, and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>M</mml:mi> <mml:mi>a</mml:mi> <mml:mi>x</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>D</mml:mi> <mml:mi>I</mml:mi> <mml:mi>B</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> value is found to be positively correlated with the CNN model performance, which provides an innovative idea to explain the transfer learning performance of the model from the IB perspective. Evaluating 81 transfer learning tasks with the derived IP conclusions captures 22.2% poor models for re-optimization. To our knowledge, we are the first study to analyze IB in transfer learning and generalize to the understanding of common CNN image classification models.