{
  "schema_version": 1,
  "title": "Rotary Position Encodings for Graphs (WIRE)",
  "emoji": "🌊",
  "space_id": "snaykey/repro-wire",
  "paper": {
    "arxiv_id": "2509.22259",
    "openreview_id": "trn64znfNx"
  },
  "tags": [
    "icml2026-repro",
    "paper-trn64znfNx"
  ],
  "updated_at": "2026-07-21T17:22:51+00:00",
  "root": {
    "slug": "index",
    "title": "Rotary Position Encodings for Graphs (WIRE)",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-wire-algorithm",
        "title": "WIRE applies rotary position encodings to graphs by using Laplacian spectral coordinates to define graph-dependent rotation angles (Figure 1, Section 3).",
        "file": "pages/claim-1-wire-algorithm/page.md",
        "children": []
      },
      {
        "slug": "claim-2-equivariance",
        "title": "The WIRE transformation is equivariant to node-order permutations up to sign flips and rotations in degenerate eigenspaces (Lemma 1).",
        "file": "pages/claim-2-equivariance/page.md",
        "children": []
      },
      {
        "slug": "claim-3-rope-special-case",
        "title": "Regular RoPE is recovered as a special case of WIRE on grid graphs with appropriate learnable frequencies (Theorem 2, Figure 2).",
        "file": "pages/claim-3-rope-special-case/page.md",
        "children": []
      },
      {
        "slug": "claim-4-effective-resistance",
        "title": "WIRE asymptotically depends on graph effective resistance under the paper's spectral-feature assumptions (Theorem 3).",
        "file": "pages/claim-4-effective-resistance/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      },
      {
        "slug": "claim-5-empirical-tables",
        "title": "Experiments report WIRE improvements on synthetic monochromatic-subgraph and shortest-path tasks, point-cloud transformers, and efficient graph transformer benchmarks (Table 1, Table 2, Table 3, Table 4).",
        "file": "pages/claim-5-empirical-tables/page.md",
        "children": []
      }
    ]
  },
  "agent_view_tokens": 2954,
  "revision": "1784654571781165900"
}