THE ALGORITHM

Let
denote the inputs of the training set.
We approximate by , where
is defined like in the previous
section (replacing by ).
For simplicity, in what follows, we will abbreviate
by .
Starting with a random initial weight vector,
flat minimum search (FMS)
tries to find a that not only has low
but also defines a box with maximal
box volume and, consequently, minimal
.
Note the relationship to MDL: is the number of bits required
to describe the weights, whereas
the number of bits needed to describe the ,
given
(with
),
can be bounded by fixing (see appendix A.1).
In the next section we derive the following algorithm.
We use gradient descent to minimize
,
where
, and

It can be shown that by using Pearlmutter's and Mller's efficient second order method, the gradient of can be computed in time (see details in A.3).

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