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This arXiv preprint proposes OPLoRA, a parameter-efficient fine-tuning method that constrains LoRA updates to the orthogonal complement of a frozen model's dominant singular directions, aiming to reduce catastrophic forgetting. The provable preservation of top-k singular triples is a useful theoretical property, but the evidence rests on experiments with two 7B-scale models (LLaMA-2 7B and Qwen2.5 7B), so practical gains across other architectures and scales remain to be shown. Practitioners fine-tuning LLMs should watch whether the reported forgetting reductions hold up under independent replication.
OPLoRA: Orthogonal Projection LoRA Prevents Catastrophic Forgetting during Parameter-Efficient Fine-Tuning
arXiv:2510.13003v2 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) enables efficient fine-tuning of large language models but suffers from catastrophic forgetting when learned updates interfere with the dominant singular directions that encode essential pre-trained knowledge. We propose Orthogonal Projection LoRA (OPLoRA), a theoretically grounded approach that prevents this interference through double-sided orthogonal projections. By decomposing frozen weights via SVD, OPLoRA constrains LoRA updates to lie entirely within the orthogonal complement of the top-$k$ singular subspace using projections $P_L = I - U_k U_k^\top$ and $P_R = I - V_k V_k^\top$. We prove that this construction exactly preserves the top-$k$ singular triples, providing mathematical guarantees for knowledge retention. To quantify subspace interference, we introduce $\rho_k$, a metric measuring update alignment with dominant directions. Extensive experiments across commonsense reasoning, mathematics, and code generation demonstrate that OPLoRA significantly reduces forgetting while maintaining competitive task-specific performance on LLaMA-2 7B and Qwen2.5 7B, establishing orthogonal projection as an effective mechanism for knowledge preservation in parameter-efficient fine-tuning.
Abstract:Low-Rank Adaptation (LoRA) enables efficient fine-tuning of large language models but suffers from catastrophic forgetting when learned updates interfere with the dominant singular directions that encode essential pre-trained knowledge. We propose Orthogonal Projection LoRA (OPLoRA), a theoretically grounded approach that prevents this interference through double-sided orthogonal projections. By decomposing frozen weights via SVD, OPLoRA constrains LoRA updates to lie entirely within the orthogonal complement of the top-$k$ singular subspace using projections $P_L = I - U_k U_k^\top$ and $P_R = I - V_k V_k^\top$. We prove that this construction exactly preserves the top-$k$ singular triples, providing mathematical guarantees for knowledge retention. To quantify subspace interference, we introduce $\rho_k$, a metric measuring update alignment with dominant directions. Extensive experiments across commonsense reasoning, mathematics, and code generation demonstrate that OPLoRA significantly reduces forgetting while maintaining competitive task-specific performance on LLaMA-2 7B and Qwen2.5 7B, establishing orthogonal projection as an effective mechanism for knowledge preservation in parameter-efficient fine-tuning.
Computation and Language (cs.CL); Machine Learning (cs.LG); Optimization and Control (math.OC)
arXiv:2510.13003 [cs.CL]
(or arXiv:2510.13003v2 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2510.13003 Focus to learn more arXiv-issued DOI via DataCite
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