Translation invariance in a network of oscillatory units

One of the important features of the human visual system is that it is able to recognize objects in a scale and translational invariant manner. However, achieving this desirable behavior through biologically realistic networks is a challenge. Neurons may be modeled as oscillatory dynamical units. It is possible for a network of these units to exhibit synchronized oscillations under the right conditions. The synchronization of neuronal firing patterns has been suggested as a possible solution the binding problem (where a biological mechanism is sought to explain how features that represent an object can be scattered across a network, and yet be unified). Networks consisting of such oscillatory units have been applied to solve the signal deconvolution or blind source separation problems. However, the use of the same network to achieve properties that the visual sytem exhibits, such as scale and translational invariance have not been fully explored. Some approaches investigated in the literature (Wallis 1996) involve the use of non-oscillatory elements that are arranged in a hierarchy of layers. The objects presented are allowed to move, and the network utilizes a trace learning rule, where a time averaged value of an output value is used to perform Hebbian learning with respect to the input value. This is a modification of the standard Hebbian learning rule, which typically uses instantaneous values of the input and output. In this paper we present a network of oscillatory amplitude-phase units connected in two layers. The types of connections include feedforward, feedback and lateral. The network consists of amplitude-phase units that can exhibit synchronized oscillations. We have previously shown that such a network can segment the components of each input object that most contribute to its classification. Learning is unsupervised and based on a Hebbian update, and the architecture is very simple. We extend the ability of this network to address the problem of translational invariance. We show that by a specific treatment of the phase values of the output layer, limited translational invariance is achieved. The scheme used in training is as follows. The network is presented with an input, which then moves. During the motion the amplitude and phase of the upper layer units is not reset, but continues with the past value before the introduction of the object in the new position. Only the input layer is changed instantaneously to reflect the moving object. This is a promising result as it uses the same framework of oscillatory units, and introduces motion to achieve translational invariance.