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"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": []
}
]
}
} |