# Don't Let Gains FADE: Breaking Down Policy Gradient Weights in RL

arXiv: https://arxiv.org/abs/2607.01490 · HTML: https://mlsanity.com/paper/2607.01490/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 60 of its 74 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 30 of 60)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [What Matters In On-Policy Reinforcement Learning? A Large-Scale Empirical Study](https://mlsanity.com/paper/2006.05990/) (2020)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)
- [RLEF: Grounding Code LLMs in Execution Feedback with Reinforcement Learning](https://mlsanity.com/paper/2410.02089/) (2024)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Implicit Under-Parameterization Inhibits Data-Efficient Deep Reinforcement Learning](https://mlsanity.com/paper/2010.14498/) (2020)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)
- [The Art of Scaling Reinforcement Learning Compute for LLMs](https://mlsanity.com/paper/2510.13786/) (2025)
- [CWM: An Open-Weights LLM for Research on Code Generation with World Models](https://mlsanity.com/paper/2510.02387/) (2025)
- [Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models](https://mlsanity.com/paper/2412.15287/) (2024)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems](https://mlsanity.com/paper/2505.15201/) (2025)

## Abstract (arXiv)

Reinforcement learning post-training dramatically improves LLM reasoning, but suffers from training instability and diversity collapse. Advantage functions offer an appealing fix: they reshape the training objective, reweight which rollouts drive learning, and are trivial to implement. Yet a proliferation of methods makes it unclear which advantage to use and when. We cut through the confusion with a unifying framework that decomposes any advantage into its positive and negative gradient mass along two orthogonal axes. On the sign axis, imbalanced updates collapse either entropy or weight geometry. On the difficulty axis, hard-problem focus sharpens signal but costs sample size. Both trade-offs shift during training: exploration favors balance and hard focus; exploitation favors suppression and medium focus. This motivates FADE (Focal Advantage with Dynamic Entropy), a self-adapting advantage that reads training dynamics to schedule the gradient weight automatically. FADE reaches peak pass@1 20k steps earlier than the best static baseline at the 7B scale and 2k steps earlier at the 32B , while achieving the best accuracy-diversity trade-off across all pass@k on LiveCodeBench and AIME.