How Long Does Infinite Width Last? Signal Propagation in Long-Range Linear Recurrences
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 $t$. We derive exact finite-width formulas for the hidden state signal energies in linear recurrences under complex Gaussian initialization. Using these formulas, we identify the joint depth--width scaling regimes that govern signal propagation: (i) a \emph{subc...
| Authors | Mariia Seleznova |
|---|---|
| Primary category | cs.LG |
| Published | 6 May 2026 |
| Last updated at source | 25 September 2026 |
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