Tensorized Clustered LoRA Merging for Multi-Task Interference

Despite the success of the monolithic dense paradigm of large language models (LLMs), the LoRA adapters offer an efficient solution by fine-tuning small task-specific modules and merging them with the base model. However, in multi-task settings, merging LoRA adapters trained on heterogeneous sources frequently causes \textit{task interference}, degrading downstream performance. To address this, we propose a tensorized clustered LoRA (TC-LoRA) library targeting to address the task interference at the \textit{text-level} and \textit{parameter-level}. At the \textit{text-level}, we cluster the training samples in the embedding space to capture input-format similarities, then train a specialized LoRA adapter for each cluster. At the \textit{parameter-level}, we introduce a joint Canonical Polyadic (CP) decomposition that disentangles task-specific and shared factors across LoRA adapters. This joint factorization preserves essential knowledge while reducing cross-task interference. Extensive experiments on out-of-domain zero-shot and skill-composition tasks-including reasoning, question answering, and coding. Compared to strong SVD-based baselines, TC-LoRA achieves +1.4\% accuracy on Phi-3 and +2.3\% on Mistral-7B (+2.3\%), demonstrating the effectiveness of TC-LoRA in LLM adaptation.