  Supervised learning has long been attributed to several feed-forward neural
circuits within the brain, with attention being paid to the cerebellar granular
layer. The focus of this study is to evaluate the input activity representation
of these feed-forward neural networks. The activity of cerebellar granule cells
is conveyed by parallel fibers and translated into Purkinje cell activity; the
sole output of the cerebellar cortex. The learning process at this
parallel-fiber-to-Purkinje-cell connection makes each Purkinje cell sensitive
to a set of specific cerebellar states, determined by the granule-cell activity
during a certain time window. A Purkinje cell becomes sensitive to each neural
input state and, consequently, the network operates as a function able to
generate a desired output for each provided input by means of supervised
learning. However, not all sets of Purkinje cell responses can be assigned to
any set of input states due to the network's own limitations (inherent to the
network neurobiological substrate), that is, not all input-output mapping can
be learned. A limiting factor is the representation of the input states through
granule-cell activity. The quality of this representation will determine the
capacity of the network to learn a varied set of outputs. In this study we
present an algorithm for evaluating quantitatively the level of
compatibility/interference amongst a set of given cerebellar states according
to their representation (granule-cell activation patterns) without the need for
actually conducting simulations and network training. The algorithm input
consists of a real-number matrix that codifies the activity level of every
considered granule-cell in each state. The capability of this representation to
generate a varied set of outputs is evaluated geometrically, thus resulting in
a real number that assesses the goodness of the representation
