Your Transformer Can Hold Two Thoughts at Once: Evidence of Linear Superposition in LLMs
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Computer Science > Computation and Language
arXiv:2609.29845 (cs)
[Submitted on 24 Sep 2026]
Title:Your Transformer Can Hold Two Thoughts at Once: Evidence of Linear Superposition in LLMs
Authors:Pavel Tikhonov, Anton Korznikov, Matvey Mikhalchuk, Nikita Dragunov, Temurbek Rahmatullaev, Polina Druzhinina, Anton Razzhigaev, Ivan Oseledets, Elena Tutubalina
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Abstract: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 \textit{Superposition 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.
| Subjects: | Computation and Language (cs.CL); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2609.29845 [cs.CL] |
| (or arXiv:2609.29845v1 [cs.CL] for this version) | |
| https://doi.org/10.48550/arXiv.2609.29845
arXiv-issued DOI via DataCite (pending registration)
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View a PDF of the paper titled Your Transformer Can Hold Two Thoughts at Once: Evidence of Linear Superposition in LLMs, by Pavel Tikhonov and 8 other authors
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