# Thoughtbubbles: an Unsupervised Method for Parallel Thinking in Latent Space

arXiv: https://arxiv.org/abs/2510.00219 · HTML: https://mlsanity.com/paper/2510.00219/

## 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 23 of its 48 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## 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, 23 of 23)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [Mixture-of-Depths: Dynamically allocating compute in transformer-based language models](https://mlsanity.com/paper/2404.02258/) (2024)
- [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://mlsanity.com/paper/2502.21074/) (2025)
- [Let's Think Dot by Dot: Hidden Computation in Transformer Language Models](https://mlsanity.com/paper/2404.15758/) (2024)
- [A Mechanistic Analysis of a Transformer Trained on a Symbolic Multi-Step Reasoning Task](https://mlsanity.com/paper/2402.11917/) (2024)
- [MrT5: Dynamic Token Merging for Efficient Byte-level Language Models](https://mlsanity.com/paper/2410.20771/) (2024)
- [Thinking Tokens for Language Modeling](https://mlsanity.com/paper/2405.08644/) (2024)
- [Exact Expressive Power of Transformers with Padding](https://mlsanity.com/paper/2505.18948/) (2025)
- [Prompt-SAW: Leveraging Relation-Aware Graphs for Textual Prompt Compression](https://mlsanity.com/paper/2404.00489/) (2024)
- [Enhancing Latent Computation in Transformers with Latent Tokens](https://mlsanity.com/paper/2505.12629/) (2025)
- [Pause Tokens Strictly Increase the Expressivity of Constant-Depth Transformers](https://mlsanity.com/paper/2505.21024/) (2025)
- [Supervised Chain of Thought](https://mlsanity.com/paper/2410.14198/) (2024)
- [Skip-Layer Attention: Bridging Abstract and Detailed Dependencies in Transformers](https://mlsanity.com/paper/2406.11274/) (2024)
- [Rethinking Thinking Tokens: Understanding Why They Underperform in Practice](https://mlsanity.com/paper/2411.11371/) (2024)

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

- [The Latent Space: Foundation, Evolution, Mechanism, Ability, and Outlook](https://mlsanity.com/paper/2604.02029/) (2026)
- [mHC-lite: You Don't Need 20 Sinkhorn-Knopp Iterations](https://mlsanity.com/paper/2601.05732/) (2026)
- [Bridging the Gap Between Latent and Explicit Reasoning with Looped Transformers](https://mlsanity.com/paper/2606.31779/) (2026)
- [Are Latent Reasoning Models Easily Interpretable?](https://mlsanity.com/paper/2604.04902/) (2026)

## Abstract (arXiv)

Current approaches for scaling inference-time compute in transformers train them to emit explicit chain-of-thought tokens before producing an answer. While these methods are powerful, they are limited because they cannot be applied during pretraining and rely solely on serially-generated, natural-language verbalization. In this work, we propose Thoughtbubbles, a transformer variant that natively performs parallel adaptive computation in latent space by learning to fork or delete residual streams. Thus, tokens requiring more computation can form a "bubble" of cloned residuals in the middle of the network. Crucially, this behavior is learned during pretraining with only language modeling loss. Using half of the training budget, Thoughtbubbles outperforms the perplexity and zero-shot evals of both standard decoder LMs and those using non-adaptive parallel computation approaches. These results hold across model sizes from 150M to 1.9B. Thoughtbubbles achieves competitive GSM8K results using half of the baseline's token budget. The implicit nature of our method enables models to begin learning adaptive computation at pretraining time, paving the way to unified train-time and test-time scaling behaviors.