ChainLoRA: Geometry-Preserving Task Vector Merging for Continual Learning in LLMs

arXiv:2610.00431v1 Announce Type: cross 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: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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2610.00431 [stat.ML]

(or arXiv:2610.00431v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.00431 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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ChainLoRA: Geometry-Preserving Task Vector Merging for Continual Learning in LLMs

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