## Exponential Pattern Retrieval Capacity with Non-Binary Associative Memory

**Speaker: **
Amir Hesam Salavati
, ALGO - EPFL

### abstract

In this talk, we address the problem of neural association for a network of non-binary neurons. Here, the task is to recall a previously memorized pattern from its noisy version using a network of neurons whose states assume values from a finite number of non-negative integer levels. Prior works in this area consider storing a finite number of purely random patterns, and have shown that the pattern retrieval capacities (maximum number of patterns that can be memorized) scale only linearly with the number of neurons in the network. In our formulation of the problem, we consider storing patterns from a suitably chosen set of patterns, that are obtained by enforcing a set of simple constraints on the coordinates. Such patterns may be generated from purely random information symbols by simple neural operations. In coding theoretical parlance, the problem corresponds to designing a decoding algorithm that is simple enough to be implemented by artificial neurons.

Two simple neural update algorithms are presented, and it is shown that the proposed mechanisms result in a pattern retrieval capacity that is exponential in terms of the network size. Furthermore, using analytical results and simulations, we show that the suggested methods can tolerate a fair amount of errors in the input.

Full presentation