{
  "schema_version": 1,
  "title": "Repro: Theoretical Challenges in Learning for Branch-and-Cut",
  "emoji": "🌳",
  "space_id": "snaykey/repro-projected-ssgd",
  "paper": {
    "openreview_id": "gqKLmdooqZ"
  },
  "tags": [
    "icml2026-repro",
    "paper-gqKLmdooqZ"
  ],
  "updated_at": "2026-07-30T10:20:03+00:00",
  "root": {
    "slug": "index",
    "title": "Repro: Theoretical Challenges in Learning for Branch-and-Cut",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "claim-1",
        "title": "Selecting cuts by LP bound improvement, a common supervision signal for learned cut selection, can produce branch-and-cut trees that are 2^Omega(n) times larger than trees produced by selecting cuts via a simpler efficacy proxy score (Theorem 3.1, Section 3).",
        "file": "pages/claim-1/page.md",
        "children": []
      },
      {
        "slug": "claim-2",
        "title": "Arbitrarily small perturbations (epsilon) to the right-hand sides of cuts can change the minimum achievable branch-and-cut tree size from a single node to 2^Omega(n) nodes (Theorem 3.3, Section 3).",
        "file": "pages/claim-2/page.md",
        "children": []
      },
      {
        "slug": "claim-3",
        "title": "A learned branching policy whose per-node scores differ from strong branching by at most an arbitrarily small epsilon for any epsilon>0 can still produce a search tree of at least 2^(n+1)-1 nodes, versus at most 2n+1 nodes for strong branching itself (Theorem 4.1, Section 4).",
        "file": "pages/claim-3/page.md",
        "children": []
      },
      {
        "slug": "claim-4",
        "title": "Merely k deviations from the strong branching trajectory can inflate the resulting tree size by a factor of 2^Omega(k) (Theorem 4.4, Section 4).",
        "file": "pages/claim-4/page.md",
        "children": []
      },
      {
        "slug": "claim-5",
        "title": "Even branching policies that assign identical scores to candidate variables can produce exponentially different tree sizes depending solely on the tie-breaking rule used (Proposition 2).",
        "file": "pages/claim-5/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}