# Compute as Teacher: Turning Inference Compute Into Reference-Free Supervision

arXiv: https://arxiv.org/abs/2509.14234 · HTML: https://mlsanity.com/paper/2509.14234/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 50 references that are in the map.
- First posted on arXiv 17 Sep 2025.

## Builds on (most cited first, 30 of 39)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [HealthBench: Evaluating Large Language Models Towards Improved Human Health](https://mlsanity.com/paper/2505.08775/) (2025)
- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [RLPR: Extrapolating RLVR to General Domains without Verifiers](https://mlsanity.com/paper/2506.18254/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)

## Built on by (most cited first, 18 of 18)

- [Expanding the Capabilities of Reinforcement Learning via Text Feedback](https://mlsanity.com/paper/2602.02482/) (2026)
- [Reward and Guidance through Rubrics: Promoting Exploration to Improve Multi-Domain Reasoning](https://mlsanity.com/paper/2511.12344/) (2025)
- [InfiMed-ORBIT: Aligning LLMs on Open-Ended Complex Tasks via Rubric-Based Incremental Training](https://mlsanity.com/paper/2510.15859/) (2025)
- [SPINE: Token-Selective Test-Time Reinforcement Learning with Entropy-Band Regularization](https://mlsanity.com/paper/2511.17938/) (2025)
- [Learning to Pose Problems: Reasoning-Driven and Solver-Adaptive Data Synthesis](https://mlsanity.com/paper/2511.09907/) (2025)
- [Likelihood-Based Reward Designs for General LLM Reasoning](https://mlsanity.com/paper/2602.03979/) (2026)
- [Making, not Taking, the Best of N](https://mlsanity.com/paper/2510.00931/) (2025)
- [Conversation for Non-verifiable Learning: Self-Evolving LLMs through Meta-Evaluation](https://mlsanity.com/paper/2601.21464/) (2026)
- [Foundational Automatic Evaluators: Scaling Multi-Task Generative Evaluator Training for Reasoning-Centric Domains](https://mlsanity.com/paper/2510.17793/) (2025)
- [On the Generalization Gap in Self-Evolving Language Model Reasoning](https://mlsanity.com/paper/2606.01075/) (2026)
- [From Holistic Evaluation to Structured Criteria: Rubrics Across the Evolving LLM Landscape](https://mlsanity.com/paper/2606.08625/) (2026)
- [AutoOR: Scalably Post-training LLMs to Autoformulate Operations Research Problems](https://mlsanity.com/paper/2604.16804/) (2026)
- [Soft-SVeRL: Self-Verified Reinforcement Learning with Soft Rewards](https://mlsanity.com/paper/2605.28561/) (2026)
- [RREDCoT: Segment-Level Reward Redistribution for Reasoning Models](https://mlsanity.com/paper/2606.06475/) (2026)
- [Continual Self-Improvement with Lightweight Experiential Latent Memories](https://mlsanity.com/paper/2606.17803/) (2026)
- [Decoupled Physical Modeling and Execution for Physics Reasoning](https://mlsanity.com/paper/2608.22126/) (2026)
- [Learning to Optimize through Solver-Grounded Self-Play](https://mlsanity.com/paper/2609.34205/) (2026)
- [Binarization Flattens the Score Space](https://mlsanity.com/paper/2609.35797/) (2026)

## Abstract (arXiv)

Where do learning signals come from when there is no ground truth in post-training? We show that inference compute itself can serve as supervision. By generating parallel rollouts and converting them into reference estimates, models can learn without human labels-critically, even in non-verifiable domains like healthcare guidance where no programmatic checker exists. We call this framework Compute as Teacher (CaT) and it turns inference-time compute from parallel rollouts into supervision for RL training. The framework has two components: (1) reference estimation which aggregates rollouts into a pseudo-reference answer, and (2) reward derivation which converts that pseudo-reference into RL rewards. For (1), we explore a simple method we call synthesis, but the framework admits any aggregator. For (2), we introduce self-proposed rubrics for non-verifiable domains. These are binary, auditable criteria generated from the pseudo-reference and scored by an LLM judge. On HealthBench, models trained with CaT match or exceed inference-time aggregation quality while using 9x less test-time compute. Here, CaT also competes with learning from expert physician annotations, yielding up to +30% relative improvement over the initial policy. The framework extends naturally to verifiable rewards, matching the best existing baselines on MATH-500 in test-time RL and demonstrating 'drop-in' versatility across both types of domains.