SOURCE-LINKED INTELLIGENCE

How Much Rank Does LoRA Need? Rank-Error Bounds for Transformer Attention

arXiv · AI, language, vision and robotics · article · Aug 26, 2026 · UTC

Choosing the rank of a low-rank adaptation (LoRA) update is usually an empirical task. In this paper, we provide a task-dependent theory of the approximation error achievable at each LoRA rank for Transformer attention. We fix a pretrained attention head, a target attention function, and a distribution over inputs from the downstream task, and bound the smallest expected Kullback--Leibler (KL) error achievable by a rank-$r$ query LoRA update. When target attention probabilities are bounded away from zero, we prove a lower bound of the error proportional to $ψ(\|d\|_2)$, where $d$ is the differ

Read original source ↗ Open in workspace

recordType

paper

region

Global