Paper Deep Dive: Your Transformer Can Hold Two Thoughts at Once — Blend Two Texts and the LLM Still Remembers Both

Average the embeddings of two unrelated texts, run a single forward pass, and an LLM's output still keeps both streams' next-token candidates near the top. We walk through the paper's evidence that this 'superposition linearity' fades during pretraining, comes back with light fine-tuning, and can be partially decoded into two continuations.

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

What this paper claims

The paper is "Your Transformer Can Hold Two Thoughts at Once: Evidence of Linear Superposition in LLMs" by Tikhonov et al. (arXiv:2609.29845), posted on September 24, 2026.

Here is the abstract in plain terms. LLMs are built from heavily non-linear parts, yet at a basic level they behave linearly: if you linearly combine inputs from two separate text streams, the output is a superposition of the two individual next-token distributions. The authors call this the Superposition Linearity Hypothesis. They argue it is a built-in property of the Transformer architecture rather than something learned in training — in fact it tends to weaken as pretraining goes on. Light fine-tuning brings much of it back, sharply shrinking the gap between the mixed-input prediction and the average of the two separate predictions. Finally, they propose a guided decoding procedure that untangles the superposed output, producing two coherent continuations from a single forward pass.

An analogy: two stations on one frequency

Picture a radio where two stations bleed into each other — the news and a baseball broadcast at once. It's grating, but with a little practice you can tell which words belong to the anchor and which cheer belongs to the game. Sound waves simply add in the air, so both original signals are still there, stacked on top of each other.

The question is whether the same thing happens inside an LLM. A Transformer stacks components that don't pass sums through cleanly: the softmax in attention, the activation functions in the MLPs. It would be entirely reasonable for the two broadcasts to melt into static that belongs to neither.

The intuition: feed the model an "averaged word"

The experiment is strikingly simple. Take two texts A and B of equal length and average their embedding vectors token by token: position 1 gets the mean of A's first token and B's first token, and so on. Run that through an ordinary LLM once, and inspect the next-token distribution that comes out.

An embedding turns a token into a list of numbers with a direction (Embeddings from Scratch). Averaging two vectors gives a direction that is partly like each. Rotate the vectors in the figure below: the further apart they point, the smaller the dot product and cosine. The average sits a little away from both, so from the model's point of view it is reading a long run of tokens that are neither one word nor the other.

The mechanism: three equations define the question

The authors first write down how inputs are mixed (§2.1).

$E$ maps a token to its embedding, $x_t$ and $y_t$ are the $t$-th tokens of the two texts, and $e_t(z)$ is the mixed input actually handed to the model. In words: add the two vectors at the same position and divide by two.

If the model were perfectly linear, its output should approach this distribution (§2.3):

$P(x\mid A)$ is the next-token distribution when the model reads text A alone. The target, which says it plainly, is a 50/50 blend of "what it would predict for A" and "what it would predict for B".

To measure how far off the real output is, they define a ratio:

$\mathcal{D}$ is a distance between distributions such as KL divergence, and $P_{\text{mix}}$ is the model's actual output on the mixed input. The numerator is "how far reality is from the target"; the denominator is "how far apart two unrelated texts' predictions are". A value well below 1 means the mixed output is much closer to the target than an unrelated distribution would be. KL divergence itself is covered in Information Theory for AI.