{
  "abstract": "Selective state space models (SSMs) have recently emerged as a compelling alternative to transformers, combining competitive performance with substantially improved inference efficiency. At each SSM layer, a sequence of hidden states are propagated by a recurrence, mixing information of different tokens. Despite using a different mechanism, this mixing plays a role analogous to attention in transformers. In fact, recent works have shown that the two architectures may be closer than they first appear, as this recurrence admits a formulation akin to linear attention. In transformers, attention is known to drive the tokens to cluster, i.e., to reach consensus, collapsing in the limit to a single direction. Thus, we ask: does the recurrence at the core of SSMs drive the tokens to consensus, as attention does in transformers? To answer this question, we take a dynamical systems perspective on SSMs, modeling the evolution of tokens across layers as an ordinary differential equation. By exploiting input-to-state stability arguments, we establish local exponential stability of the consensus equilibria and characterize their domain of attraction for time-varying weight matrices, a setting not addressed by previous results. We thereby show that the resemblance between SSMs and transformers does run deeper: the recurrence at the core of SSMs aggregates tokens just as attention does. Numerical experiments on a pretrained Mamba-2 model point to the output gate as the component that regulates the extent of this consensus, preventing the tokens from reaching it in full.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17997",
  "author_total": 3,
  "authors": [
    {
      "name": "João Pedro Silvestre"
    },
    {
      "name": "Álvaro Rodríguez Abella"
    },
    {
      "name": "Paulo Tabuada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01aq8b193nj28.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17997",
  "fulltext_url": null,
  "id": "01aq8b193nj28",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17997",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Topic Modeling"
    ]
  ],
  "openalex": "W7213528995",
  "pdf_url": "https://arxiv.org/pdf/2609.17997",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01aq8b193nj28.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.17997",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17997"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The Attention Within: Consensus Dynamics in Selective State Space Models",
  "title_text": "The Attention Within: Consensus Dynamics in Selective State Space Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/01aq8b193nj28",
  "venue": "arXiv",
  "versions": []
}