aiqbench analysis
This research identifies a fundamental linearity within Transformer architectures, proving they can mathematically superpose distinct text streams rather than just processing them sequentially. By restoring this property through fine-tuning and using guided decoding, the study enables a single model pass to generate two coherent continuations simultaneously, challenging the assumption that LLMs are purely non-linear systems.
Your Transformer Can Hold Two Thoughts at Once: Evidence of Linear Superposition in LLMs
arXiv:2609.29845v1 Announce Type: new 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.
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.
Computation and Language (cs.CL); Artificial Intelligence (cs.AI)
arXiv:2609.29845 [cs.CL]
(or arXiv:2609.29845v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2609.29845 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 229 words
