AR1-ZO: Topology-Aware Rank-1 Zeroth-Order Queries for High-Rank LoRA Fine-Tuning
Zeroth-order (ZO) optimization enables large-language-model fine-tuning without storing backpropagation activations, while LoRA supplies compact trainable adapters. Combining them creates a rank paradox: increasing LoRA rank improves adapter capacity, but standard two-point ZO either perturbs a rank-dependent number of coordinates or, under atomwise updates, can make the finite-difference signal unobservable. This paper shows that the bottleneck is a measurement-topology problem rather than a need for an external subspace. LoRA already decomposes into matched rank-$1$ atoms, each a complete factor-coordinate block of dimension $d_\text{out}+d_\text{in}$. Querying one atom per step keeps t...
| Authors | Ziye Chen, Hongbin Lin, Chenyu Zhang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 19 May 2026 |
| Last updated at source | 19 May 2026 |
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