Equivalence of Context and Parameter Updates in Modern Transformer Blocks

Adrian Goldwaser, Michael Munn, Javier Gonzalvo, Benoit Dherin
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:35766-35790, 2026.

Abstract

Recent research has established that the impact of context in a vanilla transformer can be represented implicitly by forming a token-dependent, rank-1 patch to its MLP weights. This work extends that foundational theory to the diverse architectures of modern Large Language Models. We first demonstrate a precise, analytical solution for a Gemma-style transformer block, proving that the entire effect of a context can be perfectly mapped to rank-1 patches on its MLP weight matrices and a patch to the RMSNorm scale. We then generalize this result, providing a constructive proof and algorithm for multi-layer models. To unify these findings, we introduce a general framework centered on two core properties: input controllability and output controllability. We prove that a perfect implicit weight patch is possible for any MLP block where the inner function is input-controllable and the outer function is output-controllable. This provides a simpler and more powerful lens for understanding how transformer models transmute prompts into effective weights. This setup generalizes to a wide range of modern LLM architectures including gating, pre-/post-norm, mixture of experts and sequential/parallel transformer blocks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-goldwaser26a, title = {Equivalence of Context and Parameter Updates in Modern Transformer Blocks}, author = {Goldwaser, Adrian and Munn, Michael and Gonzalvo, Javier and Dherin, Benoit}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {35766--35790}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/goldwaser26a/goldwaser26a.pdf}, url = {https://proceedings.mlr.press/v306/goldwaser26a.html}, abstract = {Recent research has established that the impact of context in a vanilla transformer can be represented implicitly by forming a token-dependent, rank-1 patch to its MLP weights. This work extends that foundational theory to the diverse architectures of modern Large Language Models. We first demonstrate a precise, analytical solution for a Gemma-style transformer block, proving that the entire effect of a context can be perfectly mapped to rank-1 patches on its MLP weight matrices and a patch to the RMSNorm scale. We then generalize this result, providing a constructive proof and algorithm for multi-layer models. To unify these findings, we introduce a general framework centered on two core properties: input controllability and output controllability. We prove that a perfect implicit weight patch is possible for any MLP block where the inner function is input-controllable and the outer function is output-controllable. This provides a simpler and more powerful lens for understanding how transformer models transmute prompts into effective weights. This setup generalizes to a wide range of modern LLM architectures including gating, pre-/post-norm, mixture of experts and sequential/parallel transformer blocks.} }
Endnote
%0 Conference Paper %T Equivalence of Context and Parameter Updates in Modern Transformer Blocks %A Adrian Goldwaser %A Michael Munn %A Javier Gonzalvo %A Benoit Dherin %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-goldwaser26a %I PMLR %P 35766--35790 %U https://proceedings.mlr.press/v306/goldwaser26a.html %V 306 %X Recent research has established that the impact of context in a vanilla transformer can be represented implicitly by forming a token-dependent, rank-1 patch to its MLP weights. This work extends that foundational theory to the diverse architectures of modern Large Language Models. We first demonstrate a precise, analytical solution for a Gemma-style transformer block, proving that the entire effect of a context can be perfectly mapped to rank-1 patches on its MLP weight matrices and a patch to the RMSNorm scale. We then generalize this result, providing a constructive proof and algorithm for multi-layer models. To unify these findings, we introduce a general framework centered on two core properties: input controllability and output controllability. We prove that a perfect implicit weight patch is possible for any MLP block where the inner function is input-controllable and the outer function is output-controllable. This provides a simpler and more powerful lens for understanding how transformer models transmute prompts into effective weights. This setup generalizes to a wide range of modern LLM architectures including gating, pre-/post-norm, mixture of experts and sequential/parallel transformer blocks.
APA
Goldwaser, A., Munn, M., Gonzalvo, J. & Dherin, B.. (2026). Equivalence of Context and Parameter Updates in Modern Transformer Blocks. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:35766-35790 Available from https://proceedings.mlr.press/v306/goldwaser26a.html.

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