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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 the stored adapter rank $r$ while removing $r$ from the single-query perturbation dimension. The naive atomwise query is still miscalibrated: if it inherits canonical LoRA scaling $\\alpha/r$, the active finite-difference signal shrinks as $1/r$ and the ","title":"AR1-ZO: Topology-Aware Rank-1 Zeroth-Order Queries for High-Rank LoRA Fine-Tuning","url":"https://arxiv.org/abs/2605.19767","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.19767v1 Announce Type: cross \nAbstract: 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. 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