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arXiv · 2606.00428

Finer Parameter Steps for Low-Rank PEFT: A Controlled Study with CP Tensor Adapters

Xinjue Wang·Xiuheng Wang·Yejun Zhang·Sergiy A. Vorobyov·Esa Ollila·Zhi-Yong Wang
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Abstract

Low-rank adapters are usually compared by sweeping a small set of ranks, but the rank also fixes the resolution of the parameter budget. For a $2048{\times}2048$ OPT attention projection, increasing LoRA by one rank stores $4096$ trainable scalars, leaving large gaps between feasible low-budget adapter sizes. This paper asks whether a tensorized adapter with finer capacity increments changes the observed accuracy--budget trade-off. We instantiate this question with fixed-component canonical polyadic (CP) tensor adapters. Under a $32{\times}64{\times}32{\times}64$ tensorization, one normalized CP component stores $193$ trainable scalars per projection, about $21$ times smaller than one LoRA rank step. We compare CP adapters and LoRA on OPT-1.3B across SST-2, RTE, and BoolQ under matched target modules, training protocol, data caps, and seed schedules. CP trains stably and fills the gaps between LoRA ranks, but the effect is task-dependent: SST-2 reaches an early low-budget plateau, BoolQ benefits from additional CP components before saturating slightly below LoRA, and RTE remains LoRA-favored. Finer parameter steps are therefore useful for diagnosing PEFT budget sensitivity, but they do not by themselves guarantee a better accuracy--budget curve.

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Xinjue Wang, Xiuheng Wang, Yejun Zhang, Sergiy A. Vorobyov, Esa Ollila, Zhi-Yong Wang. 2026-05-29. Finer Parameter Steps for Low-Rank PEFT: A Controlled Study with CP Tensor Adapters. https://arxiv.org/abs/2606.00428

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