The Intruder Threshold: A Spectral Law for LoRA Fine-Tuning

תקציר מקורי באנגליתarXiv:2607.23711v1 Announce Type: new Abstract: 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 $s^\ast=\bar\theta/(\gamma\sigma_1(BA))$, 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 mixture-of-experts model, and an encoder-de