When Expert Experience Can Be Quantified: How Rubrics Become Data Assets for LLM Inference Training

Introduction

Reliable inference is a core challenge for large language models (LLMs) on complex tasks such as mathematics, code, medicine, and finance. The author argues that supervising only the final answer is insufficient because correct answers can be produced by flawed reasoning, and incorrect answers hide diverse failure modes.

Chapter 1 – Process Supervision

The article defines two complementary supervision methods:

Formal verification (hard rules) : Translate natural‑language problems and proofs into a machine‑checkable formal language (e.g., Lean). Successful compilation guarantees that every reasoning step follows the formal system.

Rubrics (soft rules) : Decompose expert judgment into structured, scoreable criteria that can be used for fine‑grained, explainable evaluation of the reasoning process.

Example: the inequality a + b ≥ 2√(ab) is proved in natural language with three steps, then expressed in Lean so the compiler can verify each step.

Chapter 2 – Formal Verification

The verification pipeline consists of two steps:

Convert the natural‑language problem into a Formal Statement .

Convert the model‑generated reasoning into a Formal Proof and compile it. Passing compilation yields a strong reward signal.

Experiments with the Goedel‑32B model achieved 39.27% validity and 34.17% accuracy, surpassing the 1‑trillion‑parameter Qwen3‑Max on formal translation, demonstrating that even small models can learn precise formal expression when trained with this signal. Limitations include scarce high‑quality verified data (≈10 k usable examples after filtering 50 k), strong dependence on correct translation, and coarse binary feedback.

Chapter 3 – Rubrics for Multi‑Dimensional Process Evaluation

Rubrics turn implicit expert standards into explicit, hierarchical scoring items. The CRAFT (Criteria‑Rubrics Adaptive Fine‑Tuning) pipeline builds Rubrics data through an expert‑in‑the‑loop workflow:

Standard definition : Experts select representative queries, define primary and secondary evaluation dimensions (e.g., content accuracy, calculation correctness, fidelity).

Rubrics iteration : A Rubrics‑generation model proposes detailed Rubrics for each query; a small set of human‑rated answers and a judge model are used to detect inconsistencies, after which experts refine the Rubrics.

Data consolidation : Stabilized Rubrics are used to automatically generate large‑scale SFT, RL, and benchmark datasets.

Rubrics enable three downstream training usages:

Rubric‑based RL : Rewards are computed by aggregating dimension‑wise scores (logic consistency, calculation accuracy, etc.) rather than a single scalar.

SFT data construction : Rubrics guide high‑quality answer generation, reject‑sampling, and can be injected into chain‑of‑thought prompts.

Alternating RL‑SFT framework : During RL rollouts, Rubrics diagnose persistent low‑scoring dimensions; the system pauses RL, obtains expert‑corrected responses, performs targeted online SFT on the weak dimensions, then resumes RL.

Experimental results show that Rubrics improve both math (MATH, AIME) and medical (HealthBench) tasks. On math benchmarks, Rubric‑driven RL outperforms ordinary RL, and the alternating RL‑SFT pipeline yields a further large accuracy boost. On medical QA, models trained with CRAFT‑produced Rubrics achieve higher data efficiency and better performance than baselines that use the original dataset Rubrics.

Chapter 4 – Future Outlook

The authors plan to open‑source the CRAFT pipeline, annotation interface, Rubrics datasets, and the post‑training methods, aiming to extend the approach to higher‑value domains such as finance, clinical decision support, and multi‑step agent tasks.