{
  "schema_version": "1.0",
  "title": "Reproduction: On the Effect of Misspecifying the Embedding Dimension in Low-rank Network Models",
  "emoji": "🕸️",
  "space_id": "snaykey/repro-embedding-dim-misspec",
  "paper": {
    "arxiv_id": "2601.06014",
    "openreview_id": "wIMGGV9l1i"
  },
  "tags": [
    "icml2026-repro",
    "paper-wIMGGV9l1i"
  ],
  "updated_at": "2026-07-29T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: On the Effect of Misspecifying the Embedding Dimension in Low-rank Network Models",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "children": []
      },
      {
        "slug": "claim-1-theorem-3-1-delocalization",
        "title": "Under the random dot product graph (RDPG) model where P = rho_n * X X^T for latent positions X in R^(n x r), Theorem 3.1 shows trailing eigenvectors associated with zero eigenvalues delocalize, with maximum entry magnitude bounded by r^2 (log n)^(4+6*gamma) / sqrt(n) (Theorem 3.1).",
        "children": []
      },
      {
        "slug": "claim-2-theorem-3-2-overspecification",
        "title": "Theorem 3.2 shows that when the embedding dimension is over-specified (k>0 extra dimensions), consistent estimation of the latent positions still holds but only at the slower rate n^(-1/4), compared to the n^(-1/2) rate achieved under correct specification (Theorem 3.2).",
        "children": []
      },
      {
        "slug": "claim-3-theorem-3-2-underspecification",
        "title": "Theorem 3.2 also shows that when the embedding dimension is under-specified (k<0), there is a fundamental lower bound on estimation error of order sqrt(|k| * rho_n), which need not vanish as the network size grows, proving inconsistency (Theorem 3.2).",
        "children": []
      },
      {
        "slug": "claim-4-section-3-two-to-inf-bound",
        "title": "Under correct specification, the adjacency spectral embedding satisfies ||X_hat_{1:r} W - rho_n^{1/2} X_{1:r}||_{2,infty} <~ phi_n, typically achieving the n^{-1/2} rate; over-specification adds an error term of order sqrt(sigma^2 k) * r^2 (log n)^(5+6*gamma) / n^{1/4} (Section 3).",
        "children": []
      },
      {
        "slug": "claim-5-section-3-1-conjecture-1",
        "title": "Section 3.1 states Conjecture 1, extending the over-/under-specification results from weighted networks to binary networks under relaxed variance conditions (Section 3.1, Conjecture 1).",
        "children": []
      },
      {
        "slug": "claim-6-section-4-simulations",
        "title": "Section 4 presents simulation experiments across multiple noise distributions confirming the theoretical over- and under-specification rates (Section 4).",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "children": []
      }
    ]
  },
  "revision": 1
}