Journal: Frontiers in Computational Neuroscience

Article Title: Emergence of Lie Symmetries in Functional Architectures Learned by CNNs

doi: 10.3389/fncom.2021.694505

Figure Lengend Snippet: (A) The 7 × 7 even filter Ψ f , with orientation θ f = 13 8 ∙ . (B) Projection on the ( x, y ) plane of the connectivity kernel computed around the filter Ψ f displayed in (A) . The projection is obtained by maximizing the 3-D kernel of Equation (9) over the variable g , and the values are color-coded from white (low) to black (high). For better visualization, the kernel has been upsampled by a factor of 10 using the built-in Matlab function imresize . The vector field V and its integral curves forming the induced association field are shown in blue over the intensity values. (C) The association field induced by the kernel of even filters around Ψ f (blue), and its approximation using the integral curves defined in Equation (6) (red)—displayed over the kernel projection.

Article Snippet: The kernel was first resized by a factor of 10 using the built-in Matlab function imresize for better visualization, and then projected down on the spatial coordinates by taking the maximum over g . Note that around (0, 0) the field is aligned with the orientation of the starting filter Ψ f , while it starts to rotate when it moves away from the center – consistently with the typical shape of psychophysical association fields, see section 2.2.

Techniques: Plasmid Preparation