Why can we just have the generator output D directly instead of outputting L and reconstructing D?

[lkqnaruto]

Hi

Thank you for releasing the code and I really appreciate the hard work.

I wonder in Algorithm 1, Why can we just have the generator output D directly instead of outputting L and reconstructing D?

For example:

$\hat{D} = G(z)$
Symmetrize $\hat{D}$
Then Compute eigenvalues of $\frac{1}{2}J\hat{D}J $

[clonker]

1st of all wow, I had no idea you could embed maths into github markdown now, that's cool!

The rationale was that distance matrices form a cone so generating it directly would be quite difficult regarding sgd. Although I am not 100% on this anymore, it is just what worked at the time. I feel like you can probably do a lot better by your approach or a manifold-aware optimization which takes the cone curvature into account.
Do you have thoughts on this?