{
  "schema_version": 1,
  "title": "Reproduction: Positive Distribution Shift as a Framework for Understanding Tractable Learning",
  "emoji": "🔄",
  "space_id": "snaykey/repro-positive-distribution-shift",
  "paper": {
    "openreview_id": "DkLQ40hTlt"
  },
  "tags": [
    "icml2026-repro",
    "paper-DkLQ40hTlt"
  ],
  "updated_at": "2026-07-31T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Positive Distribution Shift as a Framework for Understanding Tractable Learning",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "claim-1-theorem-4-3-parity-tractable",
        "title": "Noisy parities are D-DS-PAC learnable by an explicit efficient algorithm using m(epsilon) = O(d^2 log^2(d)/epsilon / (1-2eta)^2) samples, despite being conjectured computationally hard under the standard PAC model (Theorem 4.3).",
        "file": "pages/claim-1-theorem-4-3-parity-tractable/page.md",
        "children": []
      },
      {
        "slug": "claim-2-theorem-4-5-parity-stylized-sgd",
        "title": "Noisy parities are also D-DS-PAC learnable using a stylized layerwise SGD procedure on a 2-layer neural network with L1 regularization and sparsity-dependent initialization (Theorem 4.5).",
        "file": "pages/claim-2-theorem-4-5-parity-stylized-sgd/page.md",
        "children": []
      },
      {
        "slug": "claim-3-theorems-4-6-4-8-juntas",
        "title": "Noisy k-juntas are D-DS-PAC learnable via a Correlational Statistical Query algorithm using O(d^k + 2^k) queries, and are R-DS-PAC learnable via stylized layerwise SGD with a covariance loss using m = O~(d log(1/epsilon) / epsilon^2) samples (Theorems 4.6 and 4.8).",
        "file": "pages/claim-3-theorems-4-6-4-8-juntas/page.md",
        "children": []
      },
      {
        "slug": "claim-4-theorem-3-2-circuit-fpds",
        "title": "Any polynomial-size circuit with label noise is universally f-PDS learnable by SGD on specially constructed networks with polynomial sample complexity and runtime, though this construction requires designing the training distribution around the target function (Theorem 3.2).",
        "file": "pages/claim-4-theorem-3-2-circuit-fpds/page.md",
        "children": []
      },
      {
        "slug": "claim-5-theorems-5-2-5-3-membership-queries",
        "title": "The paper establishes a hierarchy of learnability notions showing D-DS-PAC learning implies non-adaptive membership query (NA-MQ) learning, and NA-MQ learners can be converted into R-DS-PAC learners with sample complexity m(epsilon) = O(m0(epsilon/2) * (log m0(epsilon/2) + log(1/epsilon))) (Theorems 5.2 and 5.3).",
        "file": "pages/claim-5-theorems-5-2-5-3-membership-queries/page.md",
        "children": []
      },
      {
        "slug": "claim-6-computational-not-statistical",
        "title": "The benefit of positive distribution shift for tractable learning is argued to be primarily computational rather than statistical, since PDS can enable polynomial-time algorithms without reducing information-theoretic sample complexity (Section 4, Abstract).",
        "file": "pages/claim-6-computational-not-statistical/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": []
      }
    ]
  }
}