# Dropout-GRPO: Variational Stochasticity for Continuous Latent Reasoning

arXiv: https://arxiv.org/abs/2606.10184 · HTML: https://mlsanity.com/paper/2606.10184/

## 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 23 of its 37 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)
- [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)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://mlsanity.com/paper/2311.01460/) (2023)
- [Soft Thinking: Unlocking the Reasoning Potential of LLMs in Continuous Concept Space](https://mlsanity.com/paper/2505.15778/) (2025)
- [Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought](https://mlsanity.com/paper/2505.12514/) (2025)
- [Inner Thinking Transformer: Leveraging Dynamic Depth Scaling to Foster Adaptive Internal Thinking](https://mlsanity.com/paper/2502.13842/) (2025)
- [LLM Latent Reasoning as Chain of Superposition](https://mlsanity.com/paper/2510.15522/) (2025)
- [Continuous Chain of Thought Enables Parallel Exploration and Reasoning](https://mlsanity.com/paper/2505.23648/) (2025)
- [Hybrid Latent Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2505.18454/) (2025)
- [Latent Thinking Optimization: Your Latent Reasoning Language Model Secretly Encodes Reward Signals in Its Latent Thoughts](https://mlsanity.com/paper/2509.26314/) (2025)
- [LEPO: Latent Reasoning Policy Optimization for Large Language Models](https://mlsanity.com/paper/2604.17892/) (2026)

## Abstract (arXiv)

Group Relative Policy Optimization (GRPO) relies on the diversity of K rollouts within each group; otherwise, the group-mean advantage A(k) = r(k) - μr collapses to zero. This presents a structural challenge for latent-reasoning models like Coconut, which feed continuous hidden states recurrently in place of discrete chain-of-thought tokens. Because the latent phase is inherently deterministic given the parameters and prompt, multiple rollouts produce identical trajectories, stalling GRPO's progress. Consequently, applying group-relative reinforcement learning to continuous latent reasoning has proven difficult. To address this, we propose sourcing the necessary stochasticity through structured dropout. By applying a single Bernoulli mask held constant across all latent recurrence steps for a given rollout, we generate essential trajectory variance. This shared mask effectively treats each rollout as a posterior sample from a variational distribution over parameters, allowing GRPO to optimize the expected reward of a Bayesian model-average policy. We provide both theoretical justification for this method -- including unbiasedness, variance reduction, and the well-definedness of the latent gradient -- and empirical validation. On GSM8K, dropout-GRPO improves a Coconut baseline from 27.29% to 29.01% pass@1, demonstrating the viability of GRPO learning for latent-reasoning models. Our work positions this as a practical, theoretically grounded approach for post-training latent-reasoning LLMs.