Equivalence of Context and Parameter Updates in Modern Transformer Blocks

• URL: http://arxiv.org/abs/2511.17864v1
• Date: Sat, 22 Nov 2025 01:17:15 GMT
• Title: Equivalence of Context and Parameter Updates in Modern Transformer Blocks
• Authors: Adrian Goldwaser, Michael Munn, Javier Gonzalvo, Benoit Dherin,
• Abstract summary: 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 weights.<n>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.<n>We then generalize this result, providing a constructive proof and algorithm for multi-layer models.
• Score: 8.364690240329411
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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.

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