Spatio-temporal patterns in CNNs for classification: the winnerless competition principle

Researches in neurophysiology have shown that neurons belonging to olfactory system in the insect brain as well as in vertebrate nervous system respond to external stimuli with complex spike sequences. These can be regarded as the result of a transformation of spatial inputs into spatio-temporal patterns. From this biological evidence, dynamical systems able to represent this dynamics in term of stimulus-dependent closed orbits have been studied. Under consideration, in particular, there have been neural networks called "winnerless competition" networks: the trajectories of such systems pass near heteroclinic orbits connecting saddle points or limit cycles. The sequence of saddles which forms the trajectory varies, as a function either of the connection strength between the neurons or of some additive terms which represent the stimuli. In this way the system has an intrinsic capability of distinguish among different stimuli and can be used as a classifier. In this work we investigate how a winnerless competition network can be created by using a single layer CNN and how the trajectory is modified by the incoming stimuli. Then we propose a compact rule to code the different trajectories in order to extract from the spatio-temporal patterns a simple code which labels the class associated with the current stimulus