# SofT-GRPO: Surpassing Discrete-Token LLM Reinforcement Learning via Gumbel-Reparameterized Soft-Thinking Policy Optimization

arXiv: https://arxiv.org/abs/2511.06411 · HTML: https://mlsanity.com/paper/2511.06411/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 44 of its 55 references that are in the map.
- First posted on arXiv 9 Nov 2025.

## Placed in

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

## Builds on (most cited first, 30 of 44)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [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)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://mlsanity.com/paper/2502.21074/) (2025)
- [Compressed Chain of Thought: Efficient Reasoning Through Dense Representations](https://mlsanity.com/paper/2412.13171/) (2024)
- [Soft Thinking: Unlocking the Reasoning Potential of LLMs in Continuous Concept Space](https://mlsanity.com/paper/2505.15778/) (2025)
- [LightThinker: Thinking Step-by-Step Compression](https://mlsanity.com/paper/2502.15589/) (2025)
- [Efficient Reasoning Models: A Survey](https://mlsanity.com/paper/2504.10903/) (2025)
- [Token Assorted: Mixing Latent and Text Tokens for Improved Language Model Reasoning](https://mlsanity.com/paper/2502.03275/) (2025)
- [Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models](https://mlsanity.com/paper/2412.15287/) (2024)
- [S-GRPO: Early Exit via Reinforcement Learning in Reasoning Models](https://mlsanity.com/paper/2505.07686/) (2025)
- [Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems](https://mlsanity.com/paper/2505.15201/) (2025)
- [Think Silently, Think Fast: Dynamic Latent Compression of LLM Reasoning Chains](https://mlsanity.com/paper/2505.16552/) (2025)
- [A Survey on Latent Reasoning](https://mlsanity.com/paper/2507.06203/) (2025)
- [Reasoning Beyond Language: A Comprehensive Survey on Latent Chain-of-Thought Reasoning](https://mlsanity.com/paper/2505.16782/) (2025)
- [Reinforcement Learning Enhanced LLMs: A Survey](https://mlsanity.com/paper/2412.10400/) (2024)
- [SIM-CoT: Supervised Implicit Chain-of-Thought](https://mlsanity.com/paper/2509.20317/) (2025)
- [Defeating the Training-Inference Mismatch via FP16](https://mlsanity.com/paper/2510.26788/) (2025)

## Built on by (most cited first, 21 of 21)

- [The Latent Space: Foundation, Evolution, Mechanism, Ability, and Outlook](https://mlsanity.com/paper/2604.02029/) (2026)
- [Latent-GRPO: Group Relative Policy Optimization for Latent Reasoning](https://mlsanity.com/paper/2604.27998/) (2026)
- [LaDi-RL: Latent Diffusion Reasoning Prevents Entropy Collapse in Reinforcement Learning](https://mlsanity.com/paper/2602.01705/) (2026)
- [LEPO: Latent Reasoning Policy Optimization for Large Language Models](https://mlsanity.com/paper/2604.17892/) (2026)
- [Agentic ESOpt: Fine-Tuning Long-Horizon LLM Agents with Minimal GPU Requirements](https://mlsanity.com/paper/2608.17310/) (2026)
- [Demystifying Hidden-State Recurrence: Switchable Latent Reasoning with On-Policy Reinforcement Learning](https://mlsanity.com/paper/2606.13106/) (2026)
- [MUX: Continuous Reasoning via Multiplexed Tokens](https://mlsanity.com/paper/2607.18264/) (2026)
- [Learning Concepts, Not Tokens: Self-Supervised Semantic Alignment for Language Models](https://mlsanity.com/paper/2603.29123/) (2026)
- [Latent Thought Credit: Multi-Answer Credit Assignment for Latent Reasoning](https://mlsanity.com/paper/2608.01593/) (2026)
- [Hyper-ES: Effective Evolution Strategies for LLM Reasoning via Descent Direction Merging](https://mlsanity.com/paper/2608.05541/) (2026)
- [Understanding Evolution Strategies for LLM Reasoning: Broader Reasoning Coverage than GRPO](https://mlsanity.com/paper/2608.27351/) (2026)
- [RuPLaR : Efficient Latent Compression of LLM Reasoning Chains with Rule-Based Priors From Multi-Step to One-Step](https://mlsanity.com/paper/2605.09346/) (2026)
- [Value-Gradient Hypothesis of RL for LLMs](https://mlsanity.com/paper/2605.21654/) (2026)
- [TARPO: Token-Wise Latent-Explicit Reasoning via Action-Routing Policy Optimization](https://mlsanity.com/paper/2606.05859/) (2026)
- [One Token per Multimodal Evidence: Latent Memory for Resource-Constrained QA](https://mlsanity.com/paper/2606.10572/) (2026)
- [N-GRPO: Embedding-Level Neighbor Mixing for Enhanced Policy Optimization](https://mlsanity.com/paper/2606.10768/) (2026)
- [The Weight of Silence: A Causal Case for Weights Over the Scratchpad in Latent Chess Reasoning](https://mlsanity.com/paper/2607.20952/) (2026)
- [A Model with No Head and Many Thoughts](https://mlsanity.com/paper/2608.31069/) (2026)
- [The Dynamics of Continuous Mixture Collapse in Language Models](https://mlsanity.com/paper/2609.02049/) (2026)
- [Soft Spatial Reasoning](https://mlsanity.com/paper/2609.38717/) (2026)
- [Beyond Policy Rollouts: Embedding-Space Directional Exploration with Anchored Noise for LLM RLVR](https://mlsanity.com/paper/2610.16105/) (2026)

## Abstract (arXiv)

The soft-thinking paradigm for Large Language Model (LLM) reasoning can outperform the conventional discrete-token Chain-of-Thought (CoT) reasoning in some scenarios, underscoring its research and application value. However, while the discrete-token CoT reasoning pattern can be reinforced through policy optimization algorithms such as group relative policy optimization (GRPO), extending the soft-thinking pattern with Reinforcement Learning (RL) remains challenging. This difficulty stems from the complexities of injecting stochasticity into soft-thinking tokens and updating soft-thinking policies accordingly. As a result, previous attempts to combine soft-thinking with GRPO typically underperform their discrete-token GRPO counterparts. To fully unlock the potential of soft-thinking, this paper presents a novel policy optimization algorithm, SofT-GRPO, to reinforce LLMs under the soft-thinking reasoning pattern. SofT-GRPO injects the Gumbel noise into logits, employs the Gumbel-Softmax technique to avoid soft-thinking tokens outside the pre-trained embedding space, and leverages the reparameterization trick in policy gradient. We conduct experiments across base LLMs ranging from 1.5B to 7B parameters, and results demonstrate that SofT-GRPO enables soft-thinking LLMs to slightly outperform discrete-token GRPO on Pass@1 (+0.13% on average accuracy), while exhibiting a substantial uplift on Pass@32 (+2.19% on average accuracy). Codes and weights are available on https://github.com/zz1358m/SofT-GRPO-master