{
  "schema_version": 1,
  "title": "Repro: Deep Networks Learn to Parse Context-Free Languages from Local Statistics",
  "emoji": "🎯",
  "space_id": "snaykey/repro-learn-to-parse",
  "paper": {
    "arxiv_id": "2602.06065",
    "openreview_id": "mJgkPAFdiK"
  },
  "tags": [
    "icml2026-repro",
    "paper-mJgkPAFdiK"
  ],
  "updated_at": "2026-07-24T13:14:27+00:00",
  "root": {
    "slug": "index",
    "title": "Repro: Deep Networks Learn to Parse Context-Free Languages from Local Statistics",
    "file": "pages/index.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": []
      },
      {
        "slug": "claim-1-varying-tree-rhm-model",
        "title": "Introduces the Varying-tree Random Hierarchy Model, a tunable class of uniform-depth PCFGs with m2 binary and m3 ternary production rules per symbol scaling asymptotically as m2=f2*v and m3=f3*v^2 in vocabulary size v (Section 2).",
        "file": "pages/claim-1-varying-tree-rhm-model/page.md",
        "children": []
      },
      {
        "slug": "claim-2-phase-transition-fc",
        "title": "Identifies a phase transition at critical ambiguity parameter f_c = 3/8, below which sentences are globally unambiguous (unique parse/class label) and above which multiple valid parse trees exist, driven by spurious nonterminals in the inside algorithm (Section 3, Figure 3).",
        "file": "pages/claim-2-phase-transition-fc/page.md",
        "children": []
      },
      {
        "slug": "claim-3-closed-form-pstar-formula",
        "title": "Derives a closed-form sample complexity formula P* = O((p2^2/2)^(1-L) · v · m3 · m2^(L-1)) for learning the grammar via root-to-substring covariance clustering (Section 4, Equation 8).",
        "file": "pages/claim-3-closed-form-pstar-formula/page.md",
        "children": []
      },
      {
        "slug": "claim-4-pstar-v2-cnn-collapse",
        "title": "Confirms P* ~ v^2 scaling (with f=1/v) for CNNs via test-loss collapse when training set size is rescaled by the theoretical P* (Section 5.1, Figure 1).",
        "file": "pages/claim-4-pstar-v2-cnn-collapse/page.md",
        "children": []
      },
      {
        "slug": "claim-5-pstar-v5-scaling",
        "title": "Shows P* ~ v^5 scaling for f=1/4 and depth L=3 as vocabulary size v increases, validated against CNN training curves (Section 5.1, Figure 7a).",
        "file": "pages/claim-5-pstar-v5-scaling/page.md",
        "children": []
      },
      {
        "slug": "claim-6-scaling-across-architectures",
        "title": "Demonstrates the same P* ~ v^2 sample-complexity scaling law holds across CNNs, an Inside Neural Network (INN), and an encoder-only Transformer, with INN having the best prefactor due to task-aligned architecture (Section 5.2, Figure 8).",
        "file": "pages/claim-6-scaling-across-architectures/page.md",
        "children": []
      }
    ]
  },
  "agent_view_tokens": 4217,
  "revision": "1784898867605368900"
}