The Intruder Threshold: A Spectral Law for LoRA Fine-Tuning
LoRA fine-tuning can create intruder dimensions: new leading singular vectors of the updated weight matrix $W+BA$ that are nearly orthogonal to all pretrained singular vectors and that drive catastrophic forgetting. Since their discovery, no theory has predicted, layer by layer on measured spectra, when they appear. We derive a per-layer critical update strength $s^\ast=\barθ/(γσ_1(BA))$, computed from the measured spectrum of $W$ alone through the rectangular spiked-deformation transform, together with an exact secular-equation characterization of the updated spectrum, with no fitted parameters. In a pre-specified study spanning four dense Transformer families, a state-space model, a mix...
| Authors | Peng Xie, Amr Alanwar |
|---|---|
| Primary category | cs.LG |
| Published | 26 July 2026 |
| Last updated at source | 12 September 2026 |
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