{
  "abstract": "Recurrent Transformers reusing their weights rather than stacking $L$ distinct layers are becoming widely adopted due to their parameter efficiency [1,2,3]. However, the exact representational and dynamical differences between looped and stacked architectures remain uncharacterized. This paper presents a controlled study on the example of bViT model [1] applying one weight-tied block $L$ times. We train two models: bViT and standard ViT [4] on 12-lead electrocardiogram (ECG) classification tasks from the PTB-XL dataset under identical training protocols. Despite an $8.9\\times$ parameter reduction, bViT achieves accuracy parity with ViT. Geometric similarity metrics demonstrate that both architectures construct comparable latent representations in an equivalent canonical order. Crucially, their dynamics differ: bViT exhibits smaller step sizes and inter-patient sensitivity, as well as near-neutral behavior away from the data manifold, whereas ViT exhibits collapsing dimensionality of representations and out-of-distribution feature expansion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15498",
  "author_total": 5,
  "authors": [
    {
      "name": "Pawel Olszowiec"
    },
    {
      "name": "Michal Byra"
    },
    {
      "name": "Grzegorz Gruszczynski"
    },
    {
      "name": "Grzegorz Stefanski"
    },
    {
      "name": "Alberto Presta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2rhc4qmtbwv65.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15498",
  "fulltext_url": null,
  "id": "2rhc4qmtbwv65",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15498",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2705|ECG Monitoring and Analysis"
    ]
  ],
  "openalex": "W7213349633",
  "pdf_url": "https://arxiv.org/pdf/2609.15498",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2rhc4qmtbwv65.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2609.15498",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15498"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Same path, different walk: a mechanistic comparison of looped and stacked transformer encoders on 12-lead ECG",
  "title_text": "Same path, different walk: a mechanistic comparison of looped and stacked transformer encoders on 12-lead ECG",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/2rhc4qmtbwv65",
  "venue": "arXiv",
  "versions": []
}