logbook.json

{
  "schema_version": 1,
  "title": "Reproduction: Full-Batch GD Outperforms One-Pass SGD in Single-Index Learning",
  "emoji": "📉",
  "space_id": "snaykey/repro-fullbatch-gd-singleindex",
  "paper": {
    "openreview_id": "QItZDBVCT0"
  },
  "tags": [
    "icml2026-repro",
    "paper-QItZDBVCT0"
  ],
  "updated_at": "2026-08-01T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Full-Batch GD Outperforms One-Pass SGD in Single-Index Learning",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "claim-1-theorem-3-1-quadratic-no-advantage",
        "title": "For quadratic activation σ(z) = z², when the sample size n = o(d log d), spherical gradient flow fails to achieve weak recovery, showing full-batch updates offer no statistical advantage over one-pass SGD in this regime (Theorem 3.1).",
        "file": "pages/claim-1-theorem-3-1-quadratic-no-advantage/page.md",
        "children": []
      },
      {
        "slug": "claim-2-theorem-3-2-separation",
        "title": "With a truncated quadratic activation, full-batch spherical gradient flow achieves weak recovery with only n ≳ d samples, compared to the n ≳ d log d samples required by one-pass SGD, establishing a sample complexity separation (Theorem 3.2).",
        "file": "pages/claim-2-theorem-3-2-separation/page.md",
        "children": []
      },
      {
        "slug": "claim-3-theorem-4-1-strong-recovery",
        "title": "Using the truncated activation on squared loss with small initialization (r₀ = d^-15), full-batch gradient descent achieves strong recovery in T ≳ log d gradient steps given n ≥ CM⁴d samples (Theorem 4.1).",
        "file": "pages/claim-3-theorem-4-1-strong-recovery/page.md",
        "children": []
      },
      {
        "slug": "claim-4-section-4-two-phase",
        "title": "The trajectory of full-batch gradient descent decomposes into an initial angle-reduction phase lasting O(log d/η) steps followed by geometric convergence during a refinement phase (Section 4).",
        "file": "pages/claim-4-section-4-two-phase/page.md",
        "children": []
      },
      {
        "slug": "claim-5-theorem-3-2-lower-bound",
        "title": "Full-batch methods with truncated activation match the information-theoretic sample lower bound of n ≳ d, removing the extra log d factor that is unavoidable for one-pass SGD under quadratic activation (Theorem 3.2).",
        "file": "pages/claim-5-theorem-3-2-lower-bound/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": []
      }
    ]
  }
}