  Although Convolutional Neural Networks (CNNs) have achieved promising results
in image classification, they still are vulnerable to affine transformations
including rotation, translation, flip and shuffle. The drawback motivates us to
design a module which can alleviate the impact from different affine
transformations. Thus, in this work, we introduce a more robust substitute by
incorporating distribution learning techniques, focusing particularly on
learning the spatial distribution information of pixels in images. To rectify
the issue of non-differentiability of prior distribution learning methods that
rely on traditional histograms, we adopt the Kernel Density Estimation (KDE) to
formulate differentiable histograms. On this foundation, we present a novel
Differentiable Arithmetic Distribution Module (DADM), which is designed to
extract the intrinsic probability distributions from images. The proposed
approach is able to enhance the model's robustness to affine transformations
without sacrificing its feature extraction capabilities, thus bridging the gap
between traditional CNNs and distribution-based learning. We validate the
effectiveness of the proposed approach through ablation study and comparative
experiments with LeNet.
