Centrosymmetric constrained Convolutional Neural Networks

Complex signals can be viewed as compositions of numerous sine waves with different frequencies and amplitudes. As the fundamental unit of perceiving image features, traditional Convolutional Neural Networks (CNNs) typically employ convolutional kernels without direct constraints. However, human perception of the world is inherently structured, relevant studies have indicated that considering the potential underlying correlation structures among data features or variables holds significant value, with particular emphasis on symmetric transformations in representation learning gaining attention in the field of neuroscience. Inspired by the process of human visual concept perception and classic image feature detection operators, when the convolution kernels have a similar scale to the objects, they produce larger responses. This paper introduces constraints on model parameters using centrosymmetric convolutional kernels. Under the influence of nonlinear combinations and local connections in neural networks, these kernels can diversely represent or perceive local image features. Experimental comparisons are conducted, and it is observed that the approach proposed in this paper not only enhances the convergence and accuracy of model, but also reduces the model solution space, resulting in an interpretable perception of local concepts. Furthermore, comparative experiments with classic deep CNNs have demonstrated comparable performance.