Associative Memory using Dictionary Learning and Expander Decoding

TL;DR

This paper introduces a neural associative memory that efficiently learns a large dataset representation and robustly recalls messages from noisy inputs, using dictionary learning and expander decoding techniques.

Contribution

It proposes a novel neural associative memory framework capable of storing exponentially large datasets with high error correction, combining dictionary learning and expander code decoding.

Findings

Stores $ ext{exp}(n)$ messages with $O(n)$ nodes.

Corrects $ ext{Omega}(n / ext{polylog} n)$ adversarial errors.

Maps learning and recall to dictionary learning and expander decoding.

Abstract

An associative memory is a framework of content-addressable memory that stores a collection of message vectors (or a dataset) over a neural network while enabling a neurally feasible mechanism to recover any message in the dataset from its noisy version. Designing an associative memory requires addressing two main tasks: 1) learning phase: given a dataset, learn a concise representation of the dataset in the form of a graphical model (or a neural network), 2) recall phase: given a noisy version of a message vector from the dataset, output the correct message vector via a neurally feasible algorithm over the network learnt during the learning phase. This paper studies the problem of designing a class of neural associative memories which learns a network representation for a large dataset that ensures correction against a large number of adversarial errors during the recall phase. Specifically, the associative memories designed in this paper can store dataset containing $\exp(n)$ $n$-length message vectors over a network with $O(n)$ nodes and can tolerate $\Omega(\frac{n}{{\rm polylog} n})$ adversarial errors. This paper carries out this memory design by mapping the learning phase and recall phase to the tasks of dictionary learning with a square dictionary and iterative error correction in an expander code, respectively.