RITE: Investigating and Mitigating Rubric Drift in LLM-Based Grading

Large language models are increasingly used to grade open-ended student responses, yet construct-irrelevant variation can change their judgments. We call this failure rubric drift: grading changes despite fixed questions, rubrics, and rubric-relevant evidence. We introduce EduR²Bench, with 1,060 verified rubric-equivalence groups and 3,297 variants across four STEM subjects, and Criterion Flip Rate (CFR), a label-free drift diagnostic. Rubric drift is widespread across open-weight, frontier, and specialized graders and is distinct from grading accuracy. Our central finding is supervision-induced invariance (SII): correctness supervision on original responses reduces CFR on unsupervised equivalent variants from 26.3% to 11.7%, accompanied by contraction of upper-middle-layer representation gaps. However, SII is limited by supervision coverage, label reliability, and transformation-family transfer. These boundaries motivate Rubric-Invariant Training via Equivalence (RITE), which combines correctness grounding with equivalence supervision. Using labels only on original responses, RITE reduces CFR to 5.2% while preserving grading quality and retains substantial benefit on a held-out transformation family and unseen human-written rewrites. Together, our results characterize when rubric invariance emerges from supervision and how to strengthen it explicitly.