# Compress the Easy, Explore the Hard: Difficulty-Aware Entropy Regularization for Efficient LLM Reasoning

arXiv: https://arxiv.org/abs/2602.22642 · HTML: https://mlsanity.com/paper/2602.22642/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 26 of its 28 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 26 of 26)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [TokenSkip: Controllable Chain-of-Thought Compression in LLMs](https://mlsanity.com/paper/2502.12067/) (2025)
- [Thinkless: LLM Learns When to Think](https://mlsanity.com/paper/2505.13379/) (2025)
- [Chain of Thoughtlessness? An Analysis of CoT in Planning](https://mlsanity.com/paper/2405.04776/) (2024)
- [TreeRL: LLM Reinforcement Learning with On-Policy Tree Search](https://mlsanity.com/paper/2506.11902/) (2025)
- [Stepwise Perplexity-Guided Refinement for Efficient Chain-of-Thought Reasoning in Large Language Models](https://mlsanity.com/paper/2502.13260/) (2025)
- [EDGE-GRPO: Entropy-Driven GRPO with Guided Error Correction for Advantage Diversity](https://mlsanity.com/paper/2507.21848/) (2025)
- [ThinkSwitcher: When to Think Hard, When to Think Fast](https://mlsanity.com/paper/2505.14183/) (2025)
- [ConCISE: Confidence-guided Compression in Step-by-step Efficient Reasoning](https://mlsanity.com/paper/2505.04881/) (2025)
- [Direct Evaluation of Chain-of-Thought in Multi-hop Reasoning with Knowledge Graphs](https://mlsanity.com/paper/2402.11199/) (2024)
- [Rethinking Entropy Regularization in Large Reasoning Models](https://mlsanity.com/paper/2509.25133/) (2025)
- [Self-prompted Chain-of-Thought on Large Language Models for Open-domain Multi-hop Reasoning](https://mlsanity.com/paper/2310.13552/) (2023)
- [CURE: Critical-Token-Guided Re-Concatenation for Entropy-Collapse Prevention](https://mlsanity.com/paper/2508.11016/) (2025)
- [Aware First, Think Less: Dynamic Boundary Self-Awareness Drives Extreme Reasoning Efficiency in Large Language Models](https://mlsanity.com/paper/2508.11582/) (2025)
- [Reasoning Efficiently Through Adaptive Chain-of-Thought Compression: A Self-Optimizing Framework](https://mlsanity.com/paper/2509.14093/) (2025)
- [Representation-Level Counterfactual Calibration for Debiased Zero-Shot Recognition](https://mlsanity.com/paper/2510.26466/) (2025)

## Built on by (most cited first, 4 of 4)

- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [ExpThink: Experience-Guided Reinforcement Learning for Adaptive Chain-of-Thought Compression](https://mlsanity.com/paper/2605.07501/) (2026)
- [Implicit Compression Regularization: Concise Reasoning via Internal Shorter Distributions in RL Post-Training](https://mlsanity.com/paper/2605.07316/) (2026)
- [Is Next-Chunk Reasoning RL Really Better than SFT? Revisiting Training Strategies under no-CoT Data](https://mlsanity.com/paper/2608.23256/) (2026)

## Abstract (arXiv)

Chain-of-Thought (CoT) has substantially empowered Large Language Models (LLMs) to tackle complex reasoning tasks, yet the verbose nature of explicit reasoning steps incurs prohibitive inference latency and computational costs, limiting real-world deployment. While existing compression methods - ranging from self-training to Reinforcement Learning (RL) with length constraints - attempt to mitigate this, they often sacrifice reasoning capability for brevity. We identify a critical failure mode in these approaches: explicitly optimizing for shorter trajectories triggers rapid entropy collapse, which prematurely shrinks the exploration space and stifles the discovery of valid reasoning paths, particularly for challenging questions requiring extensive deduction. To address this issue, we propose Compress responses for Easy questions and Explore Hard ones (CEEH), a difficulty-aware approach to RL-based efficient reasoning. CEEH dynamically assesses instance difficulty to apply selective entropy regularization: it preserves a diverse search space for currently hard questions to ensure robustness, while permitting aggressive compression on easier instances where the reasoning path is well-established. In addition, we introduce a dynamic optimal-length penalty anchored to the historically shortest correct response, which effectively counteracts entropy-induced length inflation and stabilizes the reward signal. Across six reasoning benchmarks, CEEH consistently reduces response length while maintaining accuracy comparable to the base model, and improves Pass@k relative to length-only optimization.