Formalising the Logit Shift Induced by LoRA: A Technical Note

This technical note provides a first-order formalisation of the logit shift and fact-margin change induced by Low-Rank Adaptation (LoRA). Using a first-order Fr\'echet approximation around the base model trajectory, we show that the multi-layer LoRA effect can be decomposed into a linear summation of layerwise contributions and a higher-order remainder term representing inter-layer coupling.