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

Hugging Face Daily Papers Papers

Summary

This paper demonstrates that Transformers in LLMs exhibit linear superposition when combining inputs, supporting the Superposition Linearity Hypothesis, and introduces a guided decoding method to disentangle superposed outputs.

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 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.
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Paper page - Your Transformer Can Hold Two Thoughts at Once: Evidence of Linear Superposition in LLMs

Source: https://huggingface.co/papers/2609.29845

Abstract

WhileLargeLanguageModels(LLMs)relyonhighlynon-linearcomponents,inthisworkwedemonstratethattheyexhibitfundamentallinearity:wheninputsfromdistincttextstreamsarelinearlycombined,themodeloutputsasuperpositionoftheindividualnext-tokendistributions.WetermthistheSuperpositionLinearityHypothesis.WeprovideevidencethatsuperpositionisanintrinsicpropertyoftheTransformerarchitectureratherthananemergentconsequenceoftraining;infact,weobservethatittendstodiminishaspretrainingprogresses.However,wedemonstratethatlinearitycanbesubstantiallyrestoredthroughlightweightfine-tuning,significantlyreducingthedivergencebetweenthepredictednext-tokendistributionandtheaverageoftheindividualnext-tokendistributions.Finally,weintroduceaguideddecodingprocedurethatdisentanglessuperposedoutputs,enablingthesimultaneousgenerationoftwocoherentcontinuationsfromasingleforwardpass.

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