Summary
Large language models like transformers don’t just memorize information; they can learn and make predictions using examples given to them on the spot, without changing their internal settings. This paper shows that transformers can also create new data by simulating complex processes usually used to generate samples, like diffusion models. The researchers found that parts of the transformer perform specific mathematical roles in this process, and the model’s internal states change in a predictable way when given examples related to certain topics. This means transformers can act as flexible generators of data based only on the examples they see in their input.
TransformerIn-context learningGenerative modelsDiffusion samplerSoftmax attentionEnergy-based modelsHidden state representationFeedforward layersEuler updateSemantic-topic sampling
Authors
Arman Adibi, Alireza Jafari, Mohammad Ghavamzadeh, Hadi Daneshmand
Abstract
A growing body of work establishes that large language models are not mere statistical memorizers, but are capable of in-context learning: performing inference at test time using only examples provided in the prompt, without any parameter updates. Prior theoretical work has shown that this capability extends to supervised learning tasks such as linear regression. We prove that in-context learning extends further to \emph{data generation}: frozen transformers can simulate iterative generative samplers from in-context samples. We first show that transformers can realize closed-form and smoothed closed-form diffusion samplers. The construction identifies a concrete generative role for softmax attention: it computes responsibility weights and weighted empirical averages, while feedforward layers implement Euler updates. To empirically relate these constructions to pretrained language models, we study \emph{semantic-topic sampling}: prompts consisting of words drawn from a common semantic category, such as animals, foods, or cities. Across transformer layers, the normalized hidden states exhibit a two-stage geometry: they move toward a uniform spherical reference in intermediate layers and then return to structured, topic-dependent representations near the output. We further measure an interacting-particle energy on these hidden-state clouds and observe the same U-shape pattern. We then prove that transformers can approximate an energy-based sampler, constructing the same U-shape energy across the layers.