ReCoLoRA: Spectrum-Aware Recursive Consolidation for Continual LLM Fine-Tuning Researchers introduced ReCoLoRA, a spectrum-aware recursive consolidation method for continual fine-tuning of large language models, which prevents task interference by re-decomposing the effective weight before each new task. On a six-task GLUE sequence across four 7-8B backbones, ReCoLoRA achieved the best final average score on three backbones while training fewer parameters than baselines like LoRA, PiSSA, AdaLoRA, and DoRA. arXiv:2607.07719v1 Announce Type: new Abstract: Parameter-efficient fine-tuning adapts a large language model to one task cheaply, but across a task sequence LoRA-style methods keep stacking low-rank updates on the same frozen weight, so each new task tends to overwrite the previous ones. We present ReCoLoRA Recursive Consolidation of Low-Rank Adapters , a spectrum-aware framework for continual fine-tuning: adapters are initialized from a randomized SVD of the pretrained weight, per-layer effective ranks are selected by an elbow criterion, and the principal subspace is adapted before residual capacity is opened. Before each new task, ReCoLoRA re-decomposes the current effective weight, rather than the original one, into a frozen residual, a slowly updated principal component, and a fresh adapter recursive consolidation , so every task starts from the model that has already absorbed its predecessors. On a six-task continual GLUE sequence over four 7-8B backbones, ReCoLoRA attains the best final average score on three of the four backbones against rank-swept LoRA, PiSSA, AdaLoRA, and DoRA baselines while training fewer parameters; an oracle-routed task-bank variant serves as an upper bound under full task isolation. Code: https://github.com/bhqy666/ReCoLoRA.