{
  "abstract": "Continual parameter-efficient fine-tuning for large language models (LLMs) must balance retention of previously acquired knowledge, adaptation to new tasks, and strict parameter budgets. We present \\textbf{ChainLoRA}, a replay-free continual merging framework built on chain-updated task-vector geometry. From a parameter-merging perspective, we formulate a geometric view of forgetting through a measurable interaction between task updates, separating directional overlap from coefficient coupling. Building on this view, ChainLoRA combines chain-updated training with post-stream adaptive SVD merging. During training, initialization and a one-sided orthogonality proxy use only the last carrier, keeping their historical-state footprint and regularization overhead constant as the task stream grows. At merging time, Adaptive SVD extracts a shared carrier and aligns it to the latest task through Procrustes adaptation. Our theoretical analysis shows that Procrustes adaptation facilitates geometric approximate separation of shared and task-specific components. The one-sided proxy further bounds inter-task interference. An effective-rank penalty additionally promotes efficient utilization of the task subspace during continual learning. Experiments show that ChainLoRA achieves state-of-the-art performance among the evaluated replay-free methods on the Large and SuperNI benchmarks, while remaining competitive on Standard CL and attaining almost the closest average scores to the evaluated replay-based method across all three benchmarks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00431",
  "author_total": 6,
  "authors": [
    {
      "name": "Hang Yin"
    },
    {
      "name": "Haozhe Wang"
    },
    {
      "name": "Yuhua Luo"
    },
    {
      "name": "Zhangqi Pan"
    },
    {
      "name": "Xiaoxing Wang"
    },
    {
      "name": "Junchi Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aeeg8ast5wnx7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00431",
  "fulltext_url": null,
  "id": "aeeg8ast5wnx7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00431",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Domain Adaptation and Few-Shot Learning"
    ]
  ],
  "openalex": "W7216251542",
  "pdf_url": "https://arxiv.org/pdf/2610.00431",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aeeg8ast5wnx7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:14Z",
      "native_id": "2610.00431",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00431"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "ChainLoRA: Geometry-Preserving Task Vector Merging for Continual Learning in LLMs",
  "title_text": "ChainLoRA: Geometry-Preserving Task Vector Merging for Continual Learning in LLMs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:14Z",
  "url": "https://research.draconitic.com/paper/aeeg8ast5wnx7",
  "venue": "arXiv",
  "versions": []
}