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3.2 Network Characteristics 27

lize a form of recurrent network dynamic operating on a continuous
attractor manifold.

Hetero-association and Auto-association: The ability to evaluate the given
input and recall the desired output is also called association. Hetero-
association is the common (one-way) input to output mapping (func-
tion mapping). The capability of auto-association allows to infer dif-
ferent kinds of desired outputs on the basis of an incomplete pat-
tern. This enables the learning of more general relations in contrast
to function mapping.

Local versus Global Representation: For a network with local represen-
tation, the output of a certain input is produced only by a localized
part of the network (which is pin-pointed by the notion of a “grand-
mother cell”). Using global representation, the network output is as-
sembled of information distributed over the entire network. A global
representation is more robust against single neuron failures. Here, as a
result the network performance degrades gracefully, like the biological
brain usually does. The local representation of knowledge is easier
to interpret and not endangered by the so-called “catastrophic inter-
ference”, see “on-line learning” below.

Batch versus Incremental Learning: Calculating the network weight up-
dates under consideration of all training examples at once is called
“batch-mode” learning. For a linear network, the solution of this
learning task can be shown to be equivalent to finding the pseudo-
inverse of a matrix, that is formed by the training data. In contrast,
incremental learning is an iterative weight update that is often based
on some gradient descent for an “error function”. For good conver-
gence this often requires the presentation of the training examples
in a stochastic sequence. Iterative learning is usually more efficient,
particularly w.r.t. memory requirements.

Off-line versus On-line Learning and Interferences: Off-line learning al-
lows easier control of the training procedure and validity of the data
(identification of outliers). On-line, incremental learning is very im-
portant, since it provides the ability to dynamically adapt to new or
changing situations. But it generally bears the danger of undesired
“interferences” (“after-learning” or “life-long learning”).