Modelling transpositional invariancy of melody recognition with an attractor neural network

Abstract

We present the attractor neural network (ANN) model that accounts for invariancy of melody recognition under transposition, modulated by msposition distance effect, while serving as a memory for tone sequences. Recognition is performed by an ANN with fast and slow synapies designed for storage and recognition of sequences of patterns where the recognition is defined as a completed set of transitions from one quasi-attractor to another. In our model, the sequence of ANN states evoked by the transposed melody is transformed into the sequence of perceptual templates of tones composing the original untransposed melody. A transposed tone first initiates a process of transposition-invariant recall of the original tone pattem. If this msposition-invariant recall was succesful. the recalled state serves for auto-associative retrieval of the colresponding paltem in a predetermined sequence. The tone patterns are combinations of panllel stripes of active neurons representing the active isofrequency bands in the auditory eonex which are orthogonal to the low-to-high frequency gradient. Such a representation allows for treating the problem of transposition-invariant recognition of the tone in the sequence as a translatiominvariant retrieval of its stripe representation. The translation-invariant retrieval of the tone pattern is accomplished by means of the modified algorithm of Dotsenko (1988 1. Phys. A: Moth Cen 21 L783-7) proposed for translation-, rotation- and size-invariant pattem recognition, which uses relaxation of neuronal firing thresholds lo guide the ANN evolution in the state space towards the desired memory attractor. The dynamics of neuronal relaxation is modified for storage and retrieval of low-activity patterns and Ihe original gradient optimization of threshold dynamics is replaced with optimization by simulated annealing. The proposed ANN model can be generalized for the transposition-invariant recognition of unhmonic sounds. for instance speech.