  The prevailing approach to embedding prior knowledge within convolutional
layers typically includes the design of steerable kernels or their modulation
using designated kernel banks. In this study, we introduce the Analytic
Convolutional Layer (ACL), an innovative model-driven convolutional layer,
which is a mosaic of analytical convolution kernels (ACKs) and traditional
convolution kernels. ACKs are characterized by mathematical functions governed
by analytic kernel parameters (AKPs) learned in training process. Learnable
AKPs permit the adaptive update of incorporated knowledge to align with the
features representation of data. Our extensive experiments demonstrate that the
ACLs not only have a remarkable capacity for feature representation with a
reduced number of parameters but also attain increased reliability through the
analytical formulation of ACKs. Furthermore, ACLs offer a means for neural
network interpretation, thereby paving the way for the intrinsic
interpretability of neural network. The source code will be published in
company with the paper.
