# ETS: Energy-Guided Test-Time Scaling for Training-Free RL Alignment

arXiv: https://arxiv.org/abs/2601.21484 · HTML: https://mlsanity.com/paper/2601.21484/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 45 of its 84 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 30 of 45)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding](https://mlsanity.com/paper/2505.22618/) (2025)
- [EAGLE-3: Scaling up Inference Acceleration of Large Language Models via Training-Time Test](https://mlsanity.com/paper/2503.01840/) (2025)
- [LLaDA 1.5: Variance-Reduced Preference Optimization for Large Language Diffusion Models](https://mlsanity.com/paper/2505.19223/) (2025)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [A Survey on Efficient Inference for Large Language Models](https://mlsanity.com/paper/2404.14294/) (2024)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control](https://mlsanity.com/paper/2402.15194/) (2024)
- [LLM Post-Training: A Deep Dive into Reasoning Large Language Models](https://mlsanity.com/paper/2502.21321/) (2025)
- [Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning](https://mlsanity.com/paper/2507.00432/) (2025)
- [LongCat-Image Technical Report](https://mlsanity.com/paper/2512.07584/) (2025)
- [Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models](https://mlsanity.com/paper/2412.15287/) (2024)

## Built on by (most cited first, 5 of 5)

- [Your "Pro" LLM Subscription May Actually Be "Free": Exposing Fingerprint Spoofing Risks in LLM Inference Services](https://mlsanity.com/paper/2606.16100/) (2026)
- [HTAM: Hierarchical Transition-Attended Memory for Operator Optimization](https://mlsanity.com/paper/2605.29734/) (2026)
- [Turning Off-Policy Tokens On-Policy: A Plug-in Approach for Improving LLM Alignment](https://mlsanity.com/paper/2607.04728/) (2026)
- [SpecFit: Not All Draft Tokens Cost the Same in Offloaded MoE Inference](https://mlsanity.com/paper/2610.15417/) (2026)
- [MERIT: Multimodal Evidence Reasoning over Image Tables](https://mlsanity.com/paper/2610.17937/) (2026)

## Abstract (arXiv)

Reinforcement Learning (RL) post-training alignment for language models is effective, but also costly and unstable in practice, owing to its complicated training process. To address this, we propose a training-free inference method to sample directly from the optimal RL policy. The transition probability applied to Masked Language Modeling (MLM) consists of a reference policy model and an energy term. Based on this, our algorithm, Energy-Guided Test-Time Scaling (ETS), estimates the key energy term via online Monte Carlo, with a provable convergence rate. Moreover, to ensure practical efficiency, ETS leverages modern acceleration frameworks alongside tailored importance sampling estimators, substantially reducing inference latency while provably preserving sampling quality. Experiments on MLM (including autoregressive models and diffusion language models) across reasoning, coding, and science benchmarks show that our ETS consistently improves generation quality, validating its effectiveness and design. The code is available at https://github.com/sheriyuo/ETS.