---
title: "Diagonal Equivalence in State Space Models: Characterization, Retrieval Rank, and Selective Extensions"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.03101v1"
permalink: "https://feed.astralor.com/items/itm_71ae21e8e2349414081cfcf5"
published: "2026-11-02T13:17:42.000Z"
score: 60
channel: "tech"
tags: ["RAG","Diagonal Equivalence","State Space Models","Characterization","Retrieval Rank","Selective Extensions","SSMs","With"]
---

# Diagonal Equivalence in State Space Models: Characterization, Retrieval Rank, and Selective Extensions

## At a glance

We classify real and complex state-space models (SSMs) with linear transitions, distinguishing fixed-basis diagonal equivalence from input-output equivalence and tracking coefficient-conditioning windows under coordinat…

## Key points

- We classify real and complex state-space models (SSMs) with linear transitions, distinguishing fixed-basis diagonal equivalence from input-output equivalence and tracking coefficient-conditioning windows under coordinat…
- We characterize diagonal equivalence through commuting transition families whose members are diagonalizable over the chosen field.
- With time-shared token-local matrix maps, we identify this class's state-mediated kernels with unnormalized scalar-mode linear attention with multiplicative masks.

## Full text

We classify real and complex state-space models (SSMs) with linear transitions, distinguishing fixed-basis diagonal equivalence from input-output equivalence and tracking coefficient-conditioning windows under coordinate changes. We characterize diagonal equivalence through commuting transition families whose members are diagonalizable over the chosen field. With time-shared token-local matrix maps, we identify this class's state-mediated kernels with unnormalized scalar-mode linear attention with multiplicative masks. Mamba 3's multiple-input, multiple-output (MIMO) construction lifts one value per local interface; SSD-MIMO routes independent values for local retrieval rank above one. HybridMamba combines Mamba 1's per-coordinate decay, Mamba 2-style heads and Mamba 3's complex rotations and two-endpoint writes, mixing real and rotating state blocks with different decay laws. They recover Mamba 1-3 single-input, single-output (SISO) configurations as exact special cases. On five large H100 bfloat16 workloads, our fused GPU kernels improve geometric-mean training time over official Mamba 1/3 in matched SISO recoveries, with Mamba 2 near parity at SSM-core scope. Memory tradeoffs depend on the baseline and metric: saved-for-backward versus peak allocation. In small-model multi-token recall experiments, both designs outperform Mamba 1-3 on the hardest tier; higher routing ranks perform best in gated or phase-diverse configurations. In single-seed language models with about 500M parameters, both improve on Mamba 1/2 in test loss at 2B tokens, but the routing gains do not translate into lower language-model loss. Our best configurations approach Mamba 3 SISO through 10B tokens while remaining behind it and Mamba 3 MIMO in language-model loss.

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