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If with a specific application
we want to make use of the representational capacity of real-valued codes
and if we are satisfied with decorrelated (instead of independent)
representational units,
then we might remove the -Term
from (4) by setting . In this case, we want to minimize
Note that with real-valued units the invertibility criterion
theoretically can be achieved with a single unit. In that
case, the independence criterion would force all other units
to take on constant values in response to all input
patterns. In noisy environments, however, it may turn out to
be advantageous to code the input into more than one
representational unit. This has already been noted by Linsker (1988) in
the context of his Infomax principle.
Juergen Schmidhuber
2003-02-13
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