ebekkers / gsplinets Goto Github PK

Hi. First of all thank you for the great work and open sourcing the code!
I had a question regarding the theoretical aspect embedded in the code. So from what I see from the code, it seems like the B spline basis is formulated based on the arguments (xx_basis_scale, xx_basis_size, etc) which are combined to form the kernel (as it is the whole idea of the model).

My question is how does the model learn to become equivariant over the group being considered? The initialization of the weights of the coefficients is xavier_initializer which is a normal distribution with mean 0.

I see that lines such as

        return (1/self.H.det(h))*Kernel( self.H.left_action_on_Rn( self.H.inv(h), self.xx_grid ) )

        return (1/self.H.det(h))*Kernel( self.H.left_action_on_Rn( h_inv, self.xx_grid ), self.H.prod(h_inv, self.input_h_grid.grid) )

aims to transform the original kernel for group convolution on the inputs of (xx_grid and/or input_h_grid).

So how does this lead to the kernel being able to satisfy the constraints stated in the paper (thm1 and corollary)?

Once again, thank you for the work and looking forward for the reply!

Hey, Great work. I really interested in this topic. But do you have any plan to release a PyTorch version, which I think will help to get more attention.

Best.