PROFILE_MODE a suggestion message says you should compile the function in a
different mode like for e.g. FAST_RUN_NOGC. When you try to compile in this
mode, you get an error saying there is no such mode .. though there actually
is.

tensor.as_tensor_variable on inputs of x, but I should do that only if they
where numpy.ndarrays (maybe other types) .. because they could be random
states case in which tensor.as_tensor_variable fails.

instead of int .. not sure why but I don't see anything wrong with that

found out this is not the right way of doing it, and there is a much
better(tested) way, namely specify_shape

of scan to be in a certain form, which is not true anymore if constant
folding replaces them by a constant.

node in a graph.

madness of elemwise operation introduced by infershape of subtensor and by
scan and makes plots of computational graphs readable and possibly faster.

check if they still use as little memory as needed in FAST_RUN.

gradients.

the key ( in this case the right key .. for scan to figure things out).

optimizer to use a limited amount of memory instead of forcing scan to do
that. This way you can compute gradients through reduce, foldl and flodr as
well.

there is one or not.