Solver-Hard Is Not Model-Hard: A Hardness-Controlled Diagnostic for LLM Constraint Reasoning
LLM constraint reasoners are often evaluated near the random-SAT phase transition, confounding density and solver hardness. We test instance-level transfer while near-matching clause density. At aligned size bins, with near-matched density and matched maximum clause width, we compare proof-hard expander-Tseitin and proof-easy ladder-Tseitin formulas, pigeonhole anchors, and density-mismatched controls. Theory separates their resolution hardness; a solver-specific Glucose mean-conflict proxy differs by up to $51\times$, and five other solvers preserve the direction. Across three included models (243 instances each; a fourth is excluded for abstention), the near-matched-density accuracy gap...
| Authors | Lucky Verma |
|---|---|
| Primary category | cs.LG |
| Published | 19 July 2026 |
| Last updated at source | 19 July 2026 |
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