Large language models (LLMs) have achieved remarkable performance on vari-ous natural language tasks. However, they are trained on static corpora and theirknowledge can become outdated quickly in the fast-changing world. This moti-vates the development of knowledge editing methods designed to update certainknowledge in LLMs without changing unrelated others. To make selective edits,previous efforts often sought to update a small amount of parameters in some spe-cific layer(s) of a LLM. Nonetheless, in challenging scenarios, they still fall shortin making successful edits while preserving knowledge irrelevant to the updatessimultaneously, resulting in a notable editing-locality trade-off. In this work, wequestion if the trade-offs are caused by the fact that parameter-based updates havea global effect, i.e., edited parameters affect all inputs indiscriminately. In light ofthis, we explore the feasibility of representation fine-tuning, which applied somelinear update to a few representations in a learned subspace, for knowledge edit-ing. While being effective to enhance an LLM’s general ability as demonstrated inthe previous work, we theoretically show that this linear update imposes a tensionin editing-locality trade-off. Subsequently, BaFT is proposed to break the linear-ity. BaFT computes a weight for each basis that spans a dimension of the subspacebased on the input representation. This input-dependent weighting mechanism al-lows BaFT to manage different types of knowledge in an adaptive way, therebyachieving a better editing-locality trade-off. Experiments on three LLMs with fiveediting benchmarks in diverse scenarios show the superiority of our method.