Measuring Shift-Invariance of Convolutional Neural Network with a Probability-Incorporated Metric

Abstract

In image classification tasks, convolutional neural networks (CNNs) have exhibited higher performance than many other methods. However, some recent studies have shown that CNNs are not shift-invariant, that is, even small spatial shifts in the image can drastically change the output distribution. This finding is non-intuitive because CNNs have long been believed to be shift-invariant. Therefore, we need to measure the shift-invariance of CNNs to better understand the performance of CNNs with respect to image classification. Previous research proposed the utilization of consistency as a metric for measuring shift-invariance. The consistency metric measures how often a CNN classifies the same top-1 class, given two different shifts on the same image. Herein, we identify two shortcomings of the consistency-based approach. First, consistency cannot perfectly capture the change in the output distribution of the CNN because it only considers the top-1 class from the distribution; therefore, other relevant information is lost. Second, the consistency metric is biased by the classification accuracy because the consistency value increases when the images are classified correctly; otherwise, it decreases. To overcome these shortcomings, this paper proposes the correctness-aware distribution distance (CADD). In CADD, we use the Jensen-Shannon (JS) divergence to measure the difference among the entire output distributions. Furthermore, the JS divergence on the correct and incorrect subsets that are split by the classification correctness is separately calculated and averaged. The experimental results demonstrate that the CADD is more stable and interpretable than the consistency-based approach.