what

A mechanism to store vectors and allow retrieving them approximately

M = v_{0} k_{0}^{T} + v_{1} k_{1}^{T} + v_{2} k_{2}^{T} + ...

where

$M$ is the associative memory matrix, which is a running sum of dot products of pairs of unit vectors
$k_{i}$ and $v_{i}$ are unit vectors

how it works

In order to retrieve $v_{i}$ (approximately), multiply $M$ with $k_{i}$ . This works because:

$k_{i} k_{i} = 1$
$k_{i} k_{j} \approx 0 (i \neq = j)$ : because of random unit vectors in high dimension are nearly orthogonal Hence:

M \cdot k_{i} = v_{0} k_{0}^{T} k_{i} + v_{1} k_{1}^{T} k_{i} + v_{2} k_{2}^{T} k_{i} + \dots + v_{i} k_{i}^{T} k_{i} + \dots \approx v_{0} \cdot 0 + v_{1} \cdot 0 + v 2 \cdot 0 + \dots + v_{i} \cdot 1 + \dots \approx v_{i}