5 problems

A Hopfield network is a neural network of $N$ neurons whose stored patterns are stable configurations of its dynamics. Linear capacity conjecture. The number of such patterns for a…

Let $F$ be a smooth function whose derivative satisfies $F'(x)>0$ for all $x>0$. Let $n\in\boldsymbol{N}$ be odd, let $m$ be a configuration in the model, and let $\xi^{(N)}(m)$ de…

Let $F$ be an activation function in a Hopfield model, and consider the regime in which the paper's results guarantee that mixed memories are fixed points of the retrieval dynamics…

Computational hardness conjecture. There is no algorithm with random initial conditions that can find such a ferromagnetic fixed point in a tractable amount of time.

A hypercomplex-valued Hopfield neural network uses neurons whose states and weights are hypercomplex numbers, while a corresponding real-valued model represents each hypercomplex n…