How Finite-Rank Bottlenecks Shape the Low-Rank Adaptation Landscape
Low-rank adaptation (LoRA) has become the standard method for parameter-efficient fine-tuning of large pretrained models, yet theoretical explanations for why low-rank updates suffice remain incomplete. Most existing analyses rely on the Neural Tangent Kernel (NTK) regime, which linearizes the network around the pretrained weights. In this work, we take a different approach that requires no linearization: our key observation is that, once the backbone is frozen, the loss sees each adapted weight matrix only through a finite-rank linear map induced by the frozen activations. Trace-norm regularization then forces the optimizer to pick a low-rank matrix among all matrices that produce the sa...
| Authors | Long Nguyen-Chi, Quynh Nguyen, Thanh Nguyen-Cung et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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