{
  "schema_version": 1,
  "title": "Reproduction: Global Convergence of Adaptive Sensing for Principal Eigenvector Estimation",
  "emoji": "🔬",
  "space_id": "snaykey/repro-adaptive-sensing-eigenvector",
  "paper": {
    "openreview_id": "XXYhEGXPPF",
    "arxiv_id": "2505.10882"
  },
  "tags": [
    "icml2026-repro",
    "paper-XXYhEGXPPF"
  ],
  "updated_at": "2026-07-22T18:00:00Z",
  "root": {
    "slug": "index",
    "title": "Reproduction: Global Convergence of Adaptive Sensing for Principal Eigenvector Estimation",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-theorem-1-convergence",
        "title": "Theorem 1 (informal) shows the adaptive sensing algorithm reaches constant-level alignment with the true eigenvector after O(λ₁λ₂d²/Δ²) iterations, after which the sine-squared alignment error decays as O(λ₁λ₂d²/(Δ²t)) (Theorem 1).",
        "file": "pages/claim-1-theorem-1-convergence/page.md",
        "children": []
      },
      {
        "slug": "claim-2-theorem-2-warmup",
        "title": "Theorem 2 (formal) specifies a warmup phase of t₀ = (4S+1)log(d/2) iterations after which the expected squared sine alignment satisfies E[1-(ūᵀu_{t₀})²] ≤ 0.5, followed by a distinct local convergence phase (Theorem 2).",
        "file": "pages/claim-2-theorem-2-warmup/page.md",
        "children": []
      },
      {
        "slug": "claim-3-minimax-rate",
        "title": "The paper's rate matches the minimax lower bound Ω(λ₁λ₂/Δ² · d/t) from Li et al. (2018) up to an extra factor of d, which is attributed to the cost of compressive (two-measurement) sampling (Section 3, Theorem 2).",
        "file": "pages/claim-3-minimax-rate/page.md",
        "children": []
      },
      {
        "slug": "claim-4-tracking-step-size",
        "title": "Section 5.1 ('Tracking a Moving Eigenvector') derives a closed-form optimal step size η̂ = √(V/S) and fixed point x* = V + √(VS) for the non-stationary tracking setting (Section 5.1).",
        "file": "pages/claim-4-tracking-step-size/page.md",
        "children": []
      },
      {
        "slug": "claim-5-figure-1-empirical",
        "title": "Figure 1 empirically validates the theoretical convergence rate of Algorithm 1 using d=10, Δ=1 across 20 trials, reporting 20th/80th percentile error bars (Figure 1).",
        "file": "pages/claim-5-figure-1-empirical/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}