How Long Does Infinite Width Last? Signal Propagation in Long-Range Linear Recurrences

ArXi:2605.05113v1 Announce Type: new We study signal propagation in linear recurrent models at finite width. While existing signal propagation theory relies predominantly on the infinite-width limit, it remains unclear for how long that approximation remains accurate when recurrent depth $t$ grows jointly with width $n$. This question is especially relevant for modern recurrent sequence models, whose natural operating regime involves long input sequences, i.e., large $t