some queries about the SO3_diffusion_example.ipynb notebook

[sirius777coder]

HI,

It is excellent work to implement this series of so3 diffusion codes. I'm curious about one function in the SO3_diffusion_example.ipynb notebook below:

# Exponential map from tangent space at R0 to SO(3) 
def expmap(R0, tangent):
    skew_sym = torch.einsum('...ij,...ik->...jk', R0, tangent)
    return torch.einsum('...ij,...jk->...ik', R0, exp(skew_sym))

This function seems to do an exponential map from tangent space to SO(3). What is the meaning of the input "tangent" tensor? If it refers to a tangent vector of the R0 tangent space, why the shape of this vector in two dimensions is i and k?

[blt2114]

Hello. This does indeed compute the exponential map from the tangent space at R0 to SO(3). Tangent vectors of SO(3) are represented as 3x3 matrices and so have two dimensions. Does that answer the question?

[sirius777coder]

Great! Your assistance has been incredibly helpful.