aiqbench analysis
This research demonstrates that frozen transformer models can function as iterative generative samplers, effectively simulating diffusion processes without parameter updates or explicit energy estimation. By mapping attention mechanisms to responsibility weights and feedforward layers to Euler updates, the study reveals a concrete mathematical pathway for in-context learning to extend into complex data generation tasks. The findings provide theoretical grounding for how pre-trained models can approximate energy-based samplers through specific geometric patterns in their hidden states.
Transformers as In-Context Samplers: From Closed-Form Diffusion to Estimation-Free Sampling
arXiv:2609.08981v1 Announce Type: new 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.
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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Applications (stat.AP); Computation (stat.CO); Machine Learning (stat.ML)
arXiv:2609.08981 [cs.LG]
(or arXiv:2609.08981v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.08981 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 309 words