Constrained Belief Updates and Geometric Structures in Transformer Representations for the RRXOR Process

Brianna Grado-White

In this work, we seek to further understand the computational structure formed by transformers trained to predict the next token of a data set. In particular, we extend the work of (Piotrowski et al., 2025) by analyzing if and how these transformers implement constrained Bayesian updating, focusing on data generated by a Random-Random-XOR (RRXOR) process. Unlike the MESS3 processes studied originally in (Piotrowski et al., 2025), the RRXOR process leads to slightly more nuanced theoretical and practical models. Nevertheless, we verify some of the main claims of (Piotrowski et al., 2025). Namely, we find attention patterns that decay exponentially with distance. We further analyze the behavior of OV vectors.

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Cite this work

@misc {

title={

@misc {

},

author={

Brianna Grado-White

},

date={

7/27/25

},

organization={Apart Research},

note={Research submission to the research sprint hosted by Apart.},

howpublished={https://apartresearch.com}

}

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This work was done during one weekend by research workshop participants and does not represent the work of Apart Research.
This work was done during one weekend by research workshop participants and does not represent the work of Apart Research.