Improved mnist model (baseline for icosahedral CNNs)

Added a larger model to the MNIST experiment. Per default the old model is used but the new model can be selected via command line parameter. This model was used as competitive baseline for the icosahedral CNN (https://arxiv.org/pdf/1902.04615.pdf)

The new model is deeper and operates on more resolutions / bandwidths. A further important improvement is the choice of grids on S^2 and SO(3) which is inspired by regular GCNNs, specifically SFCNNs (https://arxiv.org/abs/1711.07289) and the grid used on the Icosahedral CNN. Examplary parameters are: so3_near_identity_grid(n_alpha=6, max_beta=np.pi/16, n_beta=1, max_gamma=2*np.pi, n_gamma=6) In contrast to the default grid we use max_gamma=2*np.pi which ensures that the kernel will be equally spaced over the whole fiber SO(2) of the bundle SO(3)->S^2. The choice n_gamma=n_alpha is in analogy to regular GCNNs. n_beta=1 makes results in a small kernel with one central point and one ring around (analog to the kernel of the icosahedral CNN and a 3x3 kernel which often used in conv2d). The size of the kernel is growing with decreasing bandwidth by choosing max_beta=16, max_beta=8, max_beta=4, ... in consecutive layers. Again, this corresponds to icosahedral CNNs and best practices in conv2d networks.

jonkhler / s2cnn

Improved mnist model (baseline for icosahedral CNNs) #35