Emergence of Lie Symmetries in Functional Architectures Learned by CNNs.

In this paper we study the spontaneous development of symmetries in the early layers of a Convolutional Neural Network (CNN) during learning on natural images. Our architecture is built in such a way to mimic some properties of the early stages of biological visual systems. In particular, it contains a pre-filtering step ℓ defined in analogy with the Lateral Geniculate Nucleus (LGN).

LGN-CNN: A biologically inspired CNN architecture.

In this paper we introduce a biologically inspired Convolutional Neural Network (CNN) architecture called LGN-CNN that has a first convolutional layer composed of a single filter that mimics the role of the Lateral Geniculate Nucleus (LGN). The first layer of the neural network shows a rotational symmetric pattern justified by the structure of the net itself that turns up to be an approximation of a Laplacian of Gaussian (LoG). The latter function is in turn a good approximation of the receptive field profiles (RFPs) of the cells in the LGN.