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Pearlmutter (1994) and Mller (1993)
compute the product of a vector and the Hessian of
the error in
time.
Using Pearlmutter's notation,
we do the same with the Hessian of the output.
An operator is defined as follows:

(42) 
The Hessian of
the th output
of a feedforward net is computed
in 3 successive passes:
1. First backward pass ():

(43) 

(44) 

(45) 
2. First forward pass:

(46) 

(47) 
3. Second backward pass ():

(48) 

(49) 

(50) 
The elements of the vector
are
(see (41)).
Using the technique in
(Pearlmutter, 1994),
recurrent networks can be dealt with as well.
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Juergen Schmidhuber
20030213
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