OPLoRA: Orthogonal Projection LoRA Prevents Catastrophic Forgetting during Parameter-Efficient Fine-Tuning

• URL: http://arxiv.org/abs/2510.13003v2
• Date: Sat, 08 Nov 2025 10:43:01 GMT
• Title: OPLoRA: Orthogonal Projection LoRA Prevents Catastrophic Forgetting during Parameter-Efficient Fine-Tuning
• Abstract summary: Low-Rank Adaptation (LoRA) enables efficient fine-tuning of large language models.<n>LoRA suffers from catastrophic forgetting when learned updates interfere with the dominant singular directions.<n>We propose Orthogonal Projection LoRA to prevent this interference.
• Score: 19.425615290786386
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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