# Your Transformer Can Hold Two Thoughts at Once: Evidence of Linear Superposition in LLMs

arXiv: https://arxiv.org/abs/2609.29845 · HTML: https://mlsanity.com/paper/2609.29845/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 16 of its 19 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## 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, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Your Transformer is Secretly Linear](https://mlsanity.com/paper/2405.12250/) (2024)
- [DataMUX: Data Multiplexing for Neural Networks](https://mlsanity.com/paper/2202.09318/) (2022)
- [Superposition Prompting: Improving and Accelerating Retrieval-Augmented Generation](https://mlsanity.com/paper/2404.06910/) (2024)
- [MIMONets: Multiple-Input-Multiple-Output Neural Networks Exploiting Computation in Superposition](https://mlsanity.com/paper/2312.02829/) (2023)
- [Everything Everywhere All at Once: LLMs can In-Context Learn Multiple Tasks in Superposition](https://mlsanity.com/paper/2410.05603/) (2024)
- [Superposed Decoding: Multiple Generations from a Single Autoregressive Inference Pass](https://mlsanity.com/paper/2405.18400/) (2024)
- [RevMUX: Data Multiplexing with Reversible Adapters for Efficient LLM Batch Inference](https://mlsanity.com/paper/2410.04519/) (2024)

## Abstract (arXiv)

While Large Language Models (LLMs) rely on highly non-linear components, in this work we demonstrate that they exhibit fundamental linearity: when inputs from distinct text streams are linearly combined, the model outputs a superposition of the individual next-token distributions. We term this the textitSuperposition Linearity Hypothesis. We provide evidence that superposition is an intrinsic property of the Transformer architecture rather than an emergent consequence of training; in fact, we observe that it tends to diminish as pretraining progresses. However, we demonstrate that linearity can be substantially restored through lightweight fine-tuning, significantly reducing the divergence between the predicted next-token distribution and the average of the individual next-token distributions. Finally, we introduce a guided decoding procedure that disentangles superposed outputs, enabling the simultaneous generation of two coherent continuations from a single forward pass.