Universality of Linear Recurrences Followed by Non-linear Projections: Finite-Width Guarantees and Benefits of Complex Eigenvalues

arXiv:2307.11888v2 Announce Type: replace
Abstract: Deep neural networks based on linear complex-valued RNNs interleaved with position-wise MLPs are gaining traction as competitive approaches to sequence modeling. Examples of such architectures include state-space models (SSMs) like S4, LRU, and Mamba: recently proposed models that achieve promising performance on text, genetics, and other data that require long-range reasoning. Despite experimental evidence highlighting these architectures' effectiveness and computational efficiency, their expressive power remains relatively unexplored, especially in connection to specific choices crucial in …

abstract architectures arxiv benefits cs.lg cs.ne examples linear mamba modeling networks neural networks non-linear space state type wise