{
  "schema_version": 1,
  "title": "Reproduction: On the Sharp Input-Output Analysis of Nonlinear Systems under Adversarial Attacks",
  "emoji": "🛡",
  "space_id": "snaykey/repro-nonlinear-sysid",
  "paper": {
    "openreview_id": "xrUgA8PrNN"
  },
  "tags": [
    "icml2026-repro",
    "paper-xrUgA8PrNN"
  ],
  "updated_at": "2026-07-31T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: On the Sharp Input-Output Analysis of Nonlinear Systems under Adversarial Attacks",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "claim-1-theorem-3-1-error-bound",
        "title": "The paper analyzes an ℓ1-norm (least-absolute-deviation) estimator and proves it achieves an estimation error bound of Θ(ρ^τ), where ρ is the system's contraction factor and τ is the input memory length (Theorem 3.1).",
        "file": "pages/claim-1-theorem-3-1-error-bound/page.md",
        "children": []
      },
      {
        "slug": "claim-2-assumption-2-8-attack-prob",
        "title": "Theorem 3.1's guarantee requires the adversarial attack probability to satisfy p < 1/(2τ), which ensures the probability (1-p)^τ of an attack-free observation window exceeds one half (Assumption 2.8, Remark 2.9).",
        "file": "pages/claim-2-assumption-2-8-attack-prob/page.md",
        "children": []
      },
      {
        "slug": "claim-3-theorem-3-4-lower-bound",
        "title": "A matching lower bound of order Θ(ρ^τ L r/λ) is established, proving the upper bound of Theorem 3.1 is order-optimal and that no estimator can improve on this rate under probabilistic adversarial attacks (Theorem 3.4).",
        "file": "pages/claim-3-theorem-3-4-lower-bound/page.md",
        "children": []
      },
      {
        "slug": "claim-4-section-3-2-exponential-decay",
        "title": "The estimation error is shown to decay exponentially with the input memory length τ through the contraction factor ρ ∈ (0,1) (Section 3.2).",
        "file": "pages/claim-4-section-3-2-exponential-decay/page.md",
        "children": []
      },
      {
        "slug": "claim-5-theorem-3-3-exact-recovery",
        "title": "Section 3.2 first derives sufficient conditions for exact recovery in the case without past-state effects (Theorem 3.3, Section 3.2.1), then extends the analysis to the general case with nonzero past-state terms (Section 3.2.2).",
        "file": "pages/claim-5-theorem-3-3-exact-recovery/page.md",
        "children": []
      },
      {
        "slug": "executive-summary",
        "title": "executive-summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}