Quantifying alignment between instruction edits and induced low-rank weight updates

Quantify the alignment between instruction edits in Instruction-Level Weight Shaping (ILWS) and the effective low-rank updates they induce in transformer models by developing formal metrics or bounds that relate specific instruction-space edits to the magnitude and direction of the corresponding parameter perturbations and the resulting behavioral effects.

Background

Instruction-Level Weight Shaping (ILWS) treats curated system instructions as external, auditable pseudo-parameters that are updated via post-session reflection and user feedback, with optional distillation into model weights. The paper argues that instruction edits can act as explicit counterparts to implicit low-rank weight shaping effects induced by context in transformer blocks, drawing analogies to LoRA/IA^3.

In the theoretical discussion, the authors provide a local, qualitative argument that small edits to instruction tokens can induce controlled low-rank perturbations in MLP layers, but they do not furnish quantitative measures or guarantees of this relationship. They highlight that attention mechanisms are not globally Lipschitz, making global bounds difficult. Consequently, rigorously quantifying how instruction-space edits align with and translate into effective low-rank weight updates remains unresolved.