# Formalising the Logit Shift Induced by LoRA: A Technical Note

arXiv: https://arxiv.org/abs/2604.20313 · HTML: https://mlsanity.com/paper/2604.20313/

## Key facts

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- First posted on arXiv 22 Apr 2026.

## Abstract (arXiv)

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.