Emergence of Lie symmetries in functional architectures learned by CNNs
This work provides insights into how artificial neural networks can mimic biological visual system development, which is incremental as it builds on known models.
The study investigated the spontaneous emergence of symmetries in early layers of a CNN trained on natural images, finding that learned filters and connectivity kernels approximate biological models like Laplacian of Gaussian and Gabor functions, with orientation selectivity and association fields aligning with group-based models of V1 connectivity.
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 the early stages of biological visual systems. In particular, it contains a pre-filtering step $\ell^0$ defined in analogy with the Lateral Geniculate Nucleus (LGN). Moreover, the first convolutional layer is equipped with lateral connections defined as a propagation driven by a learned connectivity kernel, in analogy with the horizontal connectivity of the primary visual cortex (V1). The layer $\ell^0$ shows a rotational symmetric pattern well approximated by a Laplacian of Gaussian (LoG), which is a well-known model of the receptive profiles of LGN cells. The convolutional filters in the first layer can be approximated by Gabor functions, in agreement with well-established models for the profiles of simple cells in V1. We study the learned lateral connectivity kernel of this layer, showing the emergence of orientation selectivity w.r.t. the learned filters. We also examine the association fields induced by the learned kernel, and show qualitative and quantitative comparisons with known group-based models of V1 horizontal connectivity. These geometric properties arise spontaneously during the training of the CNN architecture, analogously to the emergence of symmetries in visual systems thanks to brain plasticity driven by external stimuli.