Factual recall in linear associative memories: sharp asymptotics and mechanistic insights

ArXi:2605.10795v1 Announce Type: cross Large language models nstrate remarkable ability in factual recall, yet the fundamental limits of storing and retrieving input--output associations with neural networks remain unclear. We study these limits in a minimal setting: a linear associative memory that maps $p$ input embeddings in $\mathbb{R}^d$ to their corresponding~$d$-dimensional targets via a single layer, requiring each mapped input to be well separated from all other targets.