Fig. 6: Manifold geometry.
From: Separability and geometry of object manifolds in deep neural networks
a Mean manifold dimension for point-cloud manifolds of AlexNet and VGG-16 (top, full line: full-class manifolds, dashed line: top 10% manifolds) and smooth 2-d manifolds for the same deep networks (bottom, full line: translation manifolds, dashed line: shear manifolds). AlexNet top 10% manifolds results already appeared as “after training” results from Fig. 3f. Values of point-cloud top 10% manifolds are showed against a secondary y-axis (color-coded by the markers edge) to improve visibility. b Mean manifold radius for point-cloud manifolds of AlexNet and VGG-16 (top, full line: full-class manifolds, dashed line: top 10% manifolds) and smooth 2-d manifolds for the same deep networks (bottom, full line: translation manifolds, dashed line: shear manifolds). AlexNet top 10% manifolds results already appeared as “after training” results from Fig. 3g. Line and markers indicate mean value over different choices of objects; surrounding shaded areas indicate 95% confidence interval. The x-axis labels provides abbreviation of the layer types. Marker shape represents layer type (circle—pixel layer, square—convolution layer, right-triangle—max-pooling layer, hexagon—fully connected layer, down-triangle—local normalization layer). Features in linear layers are extracted after a ReLU nonlinearity. Color (blue—AlexNet, green—VGG-16) changes from dark to light along the network.
