How to decide the bandwidth?

Firstly, thank you for the great work!

As the paper mentioned The maximum frequency b is known as the bandwidth, and is related to the resolution of the spatial grid (Kostelec and Rockmore, 2007).

I notice that the bandwidth is set to 30 when you generate the new MNIST dataset. For each S2Convolution and SO3Convolution, the bandwidth is different.

I wonder how to decide the parameter bandwidth when we use S2Convolution or SO3Convolution? Is it also a super parameter (empirical value) or need to be calculated meticulously?

Why you set bandwidth = 30 when you generate the new MNIST dataset?

Thank you!

[tscohen]

Ultimately it is a hyperparameter, similar to the spatial resolution in a planar CNN. In a planar CNN this is purely determined by by the stride of the convolutions and the pooling, but in spherical CNNs you have more flexibility: you can in principle choose the resolution freely in each layer.

There are currently no good “best practices” for spherical CNN architecture design, and this includes the bandwidth/resolution, but there are a couple of considerations that would factor into the decision:

• Higher resolution means you can represent more small details
• Higher resolution means higher computational cost
• If you reduce the resolution too quickly, you would ignore units in the input, just like when you use 2D convolution with a stride that is larger than the filter size.
• If the task is classification, you would typically start with a high resolution and gradually decrease it. The final layer can have very low resolution, and each unit has a receptive field that covers the whole input.
• If the task is e.g. segmentation, you could try a U-net like architecture.

We choose bandwidth=30 because it’s not too large, but still allows us to represent MNIST digits without losing too much detail. MNIST images are 28x28, but we project them only on the top of the sphere, so using a spherical grid with 2*b=60 samples per dimension, we can represent it fairly accurately.

[Jiankai-Sun]

Great thanks to your quick reply! Your work is so fascinating!