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Supervised learning has long been attributed to several feed-forward neuralcircuits within the brain, with attention being paid to the cerebellar granularlayer. The focus of this study is to evaluate the input activity representationof these feed-forward neural networks. The activity of cerebellar granule cellsis conveyed by parallel fibers and translated into Purkinje cell activity; thesole output of the cerebellar cortex. The learning process at thisparallel-fiber-to-Purkinje-cell connection makes each Purkinje cell sensitiveto a set of specific cerebellar states, determined by the granule-cell activityduring a certain time window. A Purkinje cell becomes sensitive to each neuralinput state and, consequently, the network operates as a function able togenerate a desired output for each provided input by means of supervisedlearning. However, not all sets of Purkinje cell responses can be assigned toany set of input states due to the network's own limitations (inherent to thenetwork neurobiological substrate), that is, not all input-output mapping canbe learned. A limiting factor is the representation of the input states throughgranule-cell activity. The quality of this representation will determine thecapacity of the network to learn a varied set of outputs. In this study wepresent an algorithm for evaluating quantitatively the level ofcompatibility/interference amongst a set of given cerebellar states accordingto their representation (granule-cell activation patterns) without the need foractually conducting simulations and network training. The algorithm inputconsists of a real-number matrix that codifies the activity level of everyconsidered granule-cell in each state. The capability of this representation togenerate a varied set of outputs is evaluated geometrically, thus resulting ina real number that assesses the goodness of the representation

A Metric for Evaluating Neural Input Representation in Supervised Learning Networks