arXiv Artificial Intelligence

On the Expressive Power and Limitations of Multi-Layer SSMs

7 days ago 03.09.2026 07:00 👁 1 views
On the Expressive Power and Limitations of Multi-Layer SSMs

Quick summary

arXiv:2604.14501v2 Announce Type: replace-cross Abstract: We study how depth, finite precision, state dimension, and chain-of-thought (CoT) affect the expressive power of multi-layer state-space models (SSMs). For the explicit-table $K$-function-composition problem, a canonical benchmark for sequential information propagation, we prove that any $L$-layer SSM solving $(L+3)$-function composition must satisfy $d^2p=\Omega(N/L^3)$, where $d$ is the state dimension and $p$ is the per-scalar precision. Conversely, $K$-function composition is solved exactly by a $(K+1)$-layer generalized SSM with $d

Key takeaways

  • arXiv:2604.14501v2 Announce Type: replace-cross Abstract: We study how depth, finite precision, state dimension, and chain-of-thought (CoT) affect the expressive power of multi-layer state-space models (SSMs).
  • For the explicit-table $K$-function-composition problem, a canonical benchmark for sequential information propagation, we prove that any $L$-layer SSM solving $(L+3)$-function composition must satisfy $d^2p=\Omega(N/L^3)$, where $d$ is the state dimension and $p$ is the per-scalar precision.
  • Conversely, $K$-function composition is solved exactly by a $(K+1)$-layer generalized SSM with $d

Why it matters

The value of this work lies as much in how it was tested as in the claim itself. Sample design, baselines, uncertainty and replication help separate a laboratory result from real-world impact.

Kaynak sitede devamını oku: arXiv Artificial Intelligence ↗