{
  "schema_version": 1,
  "title": "Repro: Dual Quaternion SE(3) Synchronization with Recovery Guarantees",
  "emoji": "🧭",
  "space_id": "snaykey/repro-effective-model-pruning",
  "paper": {
    "openreview_id": "nbkYuKIcXr"
  },
  "tags": [
    "icml2026-repro",
    "paper-nbkYuKIcXr"
  ],
  "updated_at": "2026-07-26T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Repro: Dual Quaternion SE(3) Synchronization with Recovery Guarantees",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-linear-contraction-rate",
        "title": "Theorem 3.2 proves DQGPM achieves linear error contraction at rate (1/10)^k for the standard (rotation) part when noise satisfies ||Delta||_{op,st} <= n/350 and ||Delta||_{op,I} <= n/300, providing the first finite-iteration recovery guarantee for SE(3) synchronization (Section 3, Theorem 3.2).",
        "file": "pages/claim-1-linear-contraction-rate/page.md",
        "children": []
      },
      {
        "slug": "claim-2-synthetic-rotation-error",
        "title": "In synthetic benchmarks with n=100 nodes at observation rate p=0.05, DQGPM attains rotation error 0.034 +/- 0.051 versus 0.056 +/- 0.632 for eigendecomposition (EIG); at p=0.30 both methods converge to near-zero error (0.0005 vs 0.001) (Table 2).",
        "file": "pages/claim-2-synthetic-rotation-error/page.md",
        "children": []
      },
      {
        "slug": "claim-3-runtime",
        "title": "DQGPM runs in 0.007-0.011 seconds on average across synthetic settings, faster than the eigendecomposition baseline's 0.011-0.019 seconds (Table 3).",
        "file": "pages/claim-3-runtime/page.md",
        "children": []
      },
      {
        "slug": "claim-4-stanford-registration",
        "title": "On Stanford point-set registration datasets, DQGPM achieves rotation errors of about 0.019-0.025 radians and translation errors under 0.002m, substantially outperforming semidefinite relaxation (SDR), which exceeds 3 radians of rotation error on sparse graphs (Table 4).",
        "file": "pages/claim-4-stanford-registration/page.md",
        "children": []
      },
      {
        "slug": "claim-5-error-decay-noise-floor",
        "title": "Figure 1 shows DQGPM's error decays linearly over iterations before plateauing at a noise floor matching the theoretical bound predicted by Theorem 3.2 (Figure 1).",
        "file": "pages/claim-5-error-decay-noise-floor/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}