Figure 2: A visual representation of the training stimuli used to train the networks. Each
square represents one stimulus unit, and the area filled in black is proportional to the
activation of the unit, so that a white square means minimum activation and a completely
filled one full activation.
to the training stimuli. A more detailed presentation of the stimuli and targets we
have used is given in the next section.
Prior to training each network has to be given some initial set of connections
on which the chosen learning procedure will act, and this will affect to some ex-
tent its response properties. That this effect exists is both trivial and important,
for the initial state of the network has a natural counterpart in the animal’s state
before training. This latter state is the result of both genetic and individual his-
tory factors, which are of course able to affect behaviour (see e.g. Peterson, 1962;
Mason & Reidinger, 1983, for examples relevant to stimulus control). What the
initial connections should be to model a real situation is not well understood, and
we resort simply on setting weights at random in the interval [-0.1, 0.1], with uni-
form distribution. With these settings the data emerging from the simulations will
be best compared with experiments in which no strong pre-existing bias affected
generalization performance. On the other hand we can be sure that the observed
features, for instance the shape of gradients, are truly due to the training procedure
and not to the initial connection values.
3 Training and Testing
This section illustrates what stimuli we have used to train the networks, and what
tests have been devised to investigate their generalization abilities, relating both
of these steps to actual experimental situations; we consider the training first.
3.1 Training Stimuli
To start, we focus for simplicity on just two stimuli (i.e. a single discrimination
task), noted s+ and s- (see figure 2). The positive stimulus differs from the neg-
ative one in its central region, that we call for short the ‘signal’. The activation
of the input units increases towards the centre of the signal. This models the fact
that a given stimulus usually activates the receptor cells to different extents, there
being cells that are most active, some that are mildly active, and some that are
unaffected. The networks are trained to have a high output to s+ and a low one