Gradient issue with SVD in batch_rotprojs

[jinhong-ni]

Thanks for your re-implementation of MANO layer.

I'm trying to differentiate through MANO layer with rotation matrices mode for both root joint and other joints. I have a question regarding backward pass through SVD in batch_rotprojs function. As we are dealing with rotation matrices, the singular values will always be 1. However, as mentioned in https://pytorch.org/docs/stable/generated/torch.svd.html, the gradient will only be finite when the input does not have zero nor repeated singular values, which definitely contradict with our case here. So I'm wondering whether there is a workaround for this, or I have to stick with axis angles which have no such problems.

p.s., I'm considering differentiating through rotation matrices instead of axis angles, since according to some resources e.g. https://arxiv.org/pdf/2003.09572.pdf, using trigonometric functions tend to be more difficult to train since they are non-injective. As far as I know, converting axis angles involve trigonometry so I decide to skip the process if possible. Indeed, I've also tried training to regress axis angles which does not seem to converge.

Any suggestion would be appreciated! Thanks in advance.