Graph-Structured Rubrics: Compiling Rubrics into Typed Evaluation Graphs for LLM Judges

Rubric-based evaluators commonly treat rubrics as prompt context or flat criteria: they specify what to judge but leave criterion composition implicit, even when natural-language rules state it. We introduce Graph-Structured Rubrics (GSR), which compiles a rubric into a response-independent typed evaluation graph before observing responses. Criterion nodes elicit judgments; transformation, reduction, and gating operators compose them through named ports; and a task-specific output mapping, termed Readout, converts the unique sink into a score or preference. Compilation rejects malformed or type-incompatible graphs. Pointwise evaluation judges rubric dimensions separately before graph aggregation; pairwise evaluation reuses the graph with one judgment for each candidate under every criterion. Under GPT-OSS-120B, GSR improves exact score agreement by 0.62--6.75 percentage points over Prometheus-style scoring on four pointwise datasets and achieves the numerically highest end-to-end pairwise accuracy on two preference benchmarks under native tie and abstention policies.