Equivalence of Context and Parameter Updates in Modern Transformer Blocks
This provides a foundational framework for understanding how transformer models process prompts, which is incremental but broadens applicability to diverse architectures.
The paper extends a theory that context in transformers can be represented as rank-1 patches to MLP weights, proving an analytical solution for Gemma-style blocks and generalizing it to modern LLM architectures like gating and mixture of experts, showing that perfect implicit weight patches are possible under input and output controllability conditions.
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.