  We discuss probabilistic neural networks with a fixed internal representation
as models for machine understanding. Here understanding is intended as mapping
data to an already existing representation which encodes an {\em a priori}
organisation of the feature space. We derive the internal representation by
requiring that it satisfies the principles of maximal relevance and of maximal
ignorance about how different features are combined. We show that, when hidden
units are binary variables, these two principles identify a unique model -- the
Hierarchical Feature Model (HFM) -- which is fully solvable and provides a
natural interpretation in terms of features. We argue that learning machines
with this architecture enjoy a number of interesting properties, like the
continuity of the representation with respect to changes in parameters and
data, the possibility to control the level of compression and the ability to
support functions that go beyond generalisation. We explore the behaviour of
the model with extensive numerical experiments and argue that models where the
internal representation is fixed reproduce a learning modality which is
qualitatively different from that of traditional models such as Restricted
Boltzmann Machines.
