AI RESEARCH
Optimal Decay Spectra for Linear Recurrences
arXiv CS.CL
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ArXi:2604.07658v1 Announce Type: cross Linear recurrent models offer linear-time sequence processing but often suffer from suboptimal long-range memory. We trace this to the decay spectrum: for $N$ channels, random initialization collapses the minimum spectral gap to $O(N^{-2})$, yielding sub-exponential error $\exp(-\Omega(N/\log N))$; linear spacing avoids collapse but degrades to $\exp(-O(N/\sqrt{T}))$, practically algebraic over long contexts. We