Equations 6 and 7 show that we
could compute the expected description length if we knew how to
evaluate the expectations of the functions *f*_{i}.

Let be a function whose expectation
value we would like to compute. As before, we shall approximate *f*_{i}
with its second order Taylor's series expansion. However, we are not
going to expand *f*_{i} with respect to the discretised parameters
of the network but the direct parameters of the
function *f*_{i}. The expansion is thus computed about the expectation
values .

Taking expectation from both sides of equation 8 yields

Here we have denoted the variance of by *v*_{j}: . The first order terms disappear because
. We have also assumed that for all , either and are uncorrelated or
, which removes the second order
cross terms.