Your Transformer Can Hold Two Thoughts at Once: Evidence of Linear Superposition in LLMs
Pavel Tikhonov, Anton Korznikov, Matvey Mikhalchuk, Nikita Dragunov, Temurbek Rahmatullaev, Polina Druzhinina, Anton Razzhigaev, Ivan Oseledets, Elena Tutubalina
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.