What are the differences between local and global computations in the context of neural networks? We would like to make the distinction between two kinds of local computations in systems consisting of a large number of connected units:

`Local in space' is meant to say that changes of a unit's weight vector should depend solely on activation information from the unit itself and from connected units. The update complexity for a unit's weight vector at a given time should be only proportional to the dimensionality of the weight vector. This implies that for a completely recurrent network the weight update complexity at a given time is where is the number of units.

`Local in time' is meant to say that weight changes should
take place continually, and that changes should depend only
on information about units and weights from a fixed recent time
interval.
This contrasts to weight changes that take place
only after externally defined episode boundaries, which require
additional *a priori* knowledge and in some cases high peaks of
computation time. The expression `local in
time' corresponds to the notion of `on-line' learning.

As far as we can judge today, biological systems use completely local computations to accomplish complex spatio-temporal credit assignment tasks. However, the local learning rules proposed so far (like Hebb's rule) make sense only if there are no `hidden units'.

In this paper (which is based on [Schmidhuber, 1989]) we want to demonstrate that local credit assignment with `hidden units' is no contradiction by itself, by giving a constructive example: We propose a method local in both space and time which is designed to deal with `hidden units' and with units whose past activations are `hidden in time'.

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