@inproceedings{zhang-etal-2026-polynomial,
    title = "Polynomial Expansion Rank Adaptation: Enhancing Low-Rank Fine-Tuning with High-Order Interactions",
    author = "Zhang, Wenhao  and
      Mu, Lin  and
      Ni, Li  and
      Jin, Peiquan  and
      Zhang, Yiwen",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.findings-acl.650/",
    pages = "13287--13303",
    ISBN = "979-8-89176-395-1",
    abstract = "Low-rank adaptation (LoRA) is a widely used strategy for efficient fine-tuning of large language models (LLMs), but its strictly linear structure fundamentally limits expressive capacity. The bilinear formulation of weight updates captures only first-order dependencies between low-rank factors, restricting the modeling of nonlinear and higher-order parameter interactions.In this paper, we propose Polynomial Expansion Rank Adaptation (PERA), a novel method that introduces structured polynomial expansion directly into the low-rank factor space.By expanding each low-rank factor to synthesize high-order interaction terms before composition, PERA transforms the adaptation space into a polynomial manifold capable of modeling richer nonlinear coupling without increasing rank or inference cost.We provide theoretical analysis demonstrating that PERA offers enhanced expressive capacity and more effective feature utilization compare to existing linear adaptation approaches.Empirically, PERA consistently outperforms state-of-the-art methods across diverse benchmarks. Notably, our experiments show that incorporating high-order nonlinear components{---}particularly square terms{---}is crucial for enhancing expressive capacity and maintaining strong and robust performance under various rank settings."
}