{
  "abstract": "An invertible graph aggregation preserves the complete feature table, but can increase the size of a classifier that reads one node at a time. For every even $N\\ge4$, we construct a labeled tree with $2N$ vertices and maximum degree three. A shared one-hidden-layer rectified linear unit (ReLU) classifier needs one hidden unit on the raw scalar features and exactly $N$ units after one lazy neighborhood mean. All aggregate values are distinct, and the mixing matrix has condition number at most 8. We determine the complete error curve for heads with a free affine term. The width separation persists under scalar perturbations. Under a specified bounded uniform-noise model with one nuisance coordinate, every one-unit aggregate head has expected error at least $1/12$, while a fixed $N$-unit head has zero error. Controlled fits compare trained heads with these explicit feasible scores. On Roman-empire and Tolokers, aggregation improves fitted prediction, and retaining raw features helps at the largest tested parameter budget. Training-only diagnostics include conditional output-layer optimality bounds for eight fixed runs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02274",
  "author_total": 3,
  "authors": [
    {
      "name": "Hiroyasu Usami"
    },
    {
      "name": "Masanori Tsukamoto"
    },
    {
      "name": "Kohei Hashiguchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18n5mc88r4s9h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02274",
  "fulltext_url": null,
  "id": "18n5mc88r4s9h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02274",
  "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",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02274",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/18n5mc88r4s9h.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:21Z",
      "native_id": "2611.02274",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02274"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Invertible Graph Aggregation Can Increase ReLU Readout Width",
  "title_text": "Invertible Graph Aggregation Can Increase ReLU Readout Width",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/18n5mc88r4s9h",
  "venue": "arXiv",
  "versions": []
}