Why is interpolation necessary?

[shaform]

interpolates = X + (alpha*differences)
= X + U[0, 1] (X_p - X)
= X + U[0, 1](X + 0.5*std * U[0,1] - X)
= X + U[0, 1] * 0.5 std * U[0, 1]
= X + 0.5 * std * U[0, 1]^2
~= X_p

so it appears that X_p can be directly used instead of interpolates.

And the paper actually used X_p instead of interpolates.

[kodalinaveen3]

Yes! We will be releasing updated version of our paper next week. The first draft was done in haste, while shooting for a conference deadline