{
  "schema_version": 1,
  "title": "Reproduction: Nonlinear Autoencoders Learn Structure Invisible to PCA",
  "emoji": "🧬",
  "space_id": "snaykey/repro-solvable-nonlinear-ae",
  "paper": {
    "openreview_id": "wm3ABfhE7P"
  },
  "tags": [
    "icml2026-repro",
    "paper-wm3ABfhE7P"
  ],
  "updated_at": "2026-08-01T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Nonlinear Autoencoders Learn Structure Invisible to PCA",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "claim-1-two-latent-factors",
        "title": "The spiked cumulant model introduces two latent factors, one recoverable by PCA from the covariance and one appearing only in higher-order moments and invisible to PCA (Section 3).",
        "file": "pages/claim-1-two-latent-factors/page.md",
        "children": []
      },
      {
        "slug": "claim-2-nonlinear-ae-both-spikes",
        "title": "For correlation exponent 2 ≤ k* < ∞, a minimal nonlinear autoencoder x̂ = (w/√d) σ(wᵀx/√d) with tied encoder-decoder weights provably recovers both latent spikes while PCA and linear autoencoders recover only the covariance-visible one (Section 2, Result 3.1).",
        "file": "pages/claim-2-nonlinear-ae-both-spikes/page.md",
        "children": []
      },
      {
        "slug": "claim-3-amp-weak-recovery",
        "title": "Approximate Message Passing weakly recovers both spikes once the sample-to-dimension ratio α exceeds a threshold α_weak^AMP determined by the moments of the coupling coefficients (Result 3.2).",
        "file": "pages/claim-3-amp-weak-recovery/page.md",
        "children": []
      },
      {
        "slug": "claim-4-spherical-gradient-flow",
        "title": "Under conditions C2 < 0 and C3 ≠ 0, spherical gradient flow on the nonlinear autoencoder achieves weak recovery of the hidden spike in logarithmic time Θ(log d) (Theorem 4.2).",
        "file": "pages/claim-4-spherical-gradient-flow/page.md",
        "children": []
      },
      {
        "slug": "claim-5-testloss-misalign",
        "title": "Linear autoencoders achieve lower reconstruction (test) loss than nonlinear autoencoders yet fail to recover the hidden spike, demonstrating that self-supervised test loss misaligns with representation quality (Figure 2).",
        "file": "pages/claim-5-testloss-misalign/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": []
      }
    ]
  }
}