The authors investigate whether transformer‑based LLMs behave linearly when presented with a mixture of two independent text streams. They form a combined input by taking a weighted sum of the token embeddings (or hidden states) of each stream and feed it through the model. The resulting next‑token distribution is compared to the average of the distributions obtained from each stream alone. Experiments show that, despite the model’s nonlinear components, the output closely approximates a linear superposition of the individual predictions, supporting the Superposition Linearity Hypothesis. Analysis reveals that this linearity is an inherent property of the transformer architecture: it is strongest in randomly initialized networks and gradually weakens during standard pretraining, suggesting that training introduces non‑linear distortions. However, applying a short, lightweight fine‑tuning phase (e.g., a few gradient steps on a mixed‑stream objective) substantially recovers the linear behavior, markedly reducing the divergence between the model’s output and the ideal superposition. Building on this finding, the researchers devise a guided decoding scheme that separates the superposed logits into two coherent continuations, allowing a single forward pass to generate two distinct, plausible continuations simultaneously.