5 problems

Let $n$ be the vocabulary size and $d$ the embedding dimension, with $n,d\to\infty$. Top-1 retrieval requires the memory load $n/d^2$ to lie below the critical threshold obtained b…

The original problem uses a fixed collection of output embeddings, whereas the decoupled problem resamples the output embeddings independently across retrieval constraints. Equal-c…

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…

The model is obtained by formally sending the polynomial interaction order $n$ to infinity; the preceding discussion concerns interaction functions and the model's storage capacity…