I've just read the source code and it seems that the differentiation of 
Cholesky decomposition and solving triangular systems is directly supported 
and more efficient than I thought. Also, I didn't realize that solvers 
could solve for many b at once, so no inversion needed.

On Monday, November 7, 2016 at 12:36:01 PM UTC+1, Kiuhnm Mnhuik wrote:
>
> Hi,
> I need to compute
>
>     y' inverse(XX') y
>
> for many y (say 10000), where X may be large but XX' is small (say 50x50 
> or 100x100).
> I need to do this symbolically because I need the gradient of that 
> expression wrt a parameter X depends on.
> Usually, I'd get L from the Cholesky decomposition, invert L, etc... I'd 
> invert L because I have many y, as I said.
> How should I do this in theano for maximum efficiency?
>

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