Dense memory with high order neural networks

AbstractGeneral high order neural networks [LD…] (models which are multinomial as opposed to linear in gain functions) offer high storage capacity [PPH] and fast convergence [GM] at the expense combinatorial growth of connections. This paper presents a specific high order neural network design which can store using n neurons any number M,1≤M≤2n, of any of the binomial n-strings; in a schematic representation the model requires only 5n+M(1+2n) edges. Each stored n-string represents a memory as a constant attractor trajectory of an n-dimensional differential equation dynamical system, a memory model neural network. With sufficiently high gains, the only stable attractors are the memories. Thus the memory model amounts to a solution of a version of the fundamental memory problem posed in [LMP] and elsewhere. The memory model can be used in error-correcting decoding of any binary string code and can accept noisy nonbinary signals