# SoftmaxGRPO: Learning to Reason using Softmax Advantage Group Estimation

arXiv: https://arxiv.org/abs/2608.09271 · HTML: https://mlsanity.com/paper/2608.09271/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 41 of its 50 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (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)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [VL-Rethinker: Incentivizing Self-Reflection of Vision-Language Models with Reinforcement Learning](https://mlsanity.com/paper/2504.08837/) (2025)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [Iterative Reasoning Preference Optimization](https://mlsanity.com/paper/2404.19733/) (2024)
- [Crossing the Reward Bridge: Expanding RL with Verifiable Rewards Across Diverse Domains](https://mlsanity.com/paper/2503.23829/) (2025)
- [SoTA with Less: MCTS-Guided Sample Selection for Data-Efficient Visual Reasoning Self-Improvement](https://mlsanity.com/paper/2504.07934/) (2025)
- [General-Reasoner: Advancing LLM Reasoning Across All Domains](https://mlsanity.com/paper/2505.14652/) (2025)
- [OpenVLThinker: Complex Vision-Language Reasoning via Iterative SFT-RL Cycles](https://mlsanity.com/paper/2503.17352/) (2025)
- [MeetingBank: A Benchmark Dataset for Meeting Summarization](https://mlsanity.com/paper/2305.17529/) (2023)
- [Reward Augmented Maximum Likelihood for Neural Structured Prediction](https://mlsanity.com/paper/1609.00150/) (2016)
- [Reinforcing General Reasoning without Verifiers](https://mlsanity.com/paper/2505.21493/) (2025)
- [Rethinking the Trust Region in LLM Reinforcement Learning](https://mlsanity.com/paper/2602.04879/) (2026)

## Built on by (most cited first, 1 of 1)

- [Ascent Conditions for Length-Normalized Single-Rollout Policy Updates](https://mlsanity.com/paper/2610.14670/) (2026)

## Abstract (arXiv)

Group-based reinforcement learning objectives such as GRPO can allocate learning signal poorly across prompt difficulty: under binary rewards, group normalization induces a divergent weighting on easy prompts. We introduce Softmax Advantage Group Estimation (SoftmaxGRPO), a drop-in alternative that replaces z-score-normalized group advantages with temperature-scaled softmax advantages, keeping weights bounded regardless of prompt difficulty. For binary rewards, we derive the exact finite-group population objective and identify MaxRL as its low-temperature limit. For bounded scalar rewards, we show that the large-group update exactly optimizes a log-moment-generating-function objective, while a universal finite-group scalar objective cannot exist without additional assumptions on the reward distribution. Empirically, SoftmaxGRPO reallocates measured gradient budget away from near-solved prompts and consistently improves over GRPO under identical rewards. It reaches 51.8% on DeepMath with verifiable rewards and improves a 1.5B instruction-tuned model from 35.0% to 68.0% on Poetry using only lightweight text-similarity rewards.