如果觉得 LoRA 微调大模型太费钱，κ-LoRA 只挑条件数大的矩阵来更新，参数量砍半，速度提升 16%，精度不降，值得试试。
新方法 κ-LoRA 发现 LoRA 微调中并非所有低秩矩阵都同等重要：条件数（最大与最小奇异值之比）小的矩阵对不同方向已平衡，贡献甚微；条件数大的矩阵包含未充分开发的方向，驱动大部分性能提升。基于此，κ-LoRA 只更新条件数最大的前 50% 权重矩阵，使可训练参数量减半，微调时间平均降低 16.2%，内存开销减少 4.5%，且精度与标准 LoRA 持平。实验表明，被选矩阵的条件数在训练中持续下降，说明方法有效性来自定向谱平衡而非单纯参数选择。
\k{appa}-LoRA: Condition Numbers Reveal Which LoRA Matrices Worth Updating
Low-Rank Adaptation (LoRA) has become a widely adopted technique for efficient neural network fine-tuning, decomposing model updates into low-rank matrices. However, LoRA remains computationally costly because it updates all matrices uniformly, regardless of their actual contribution to adaptation. This cost is especially prohibitive for large-scale models with billions of parameters and for resource-constrained settings such as edge deployment and on-device fine-tuning. We show for the first time that not all LoRA matrices are equally worth tuning: matrices with smaller condition numbers (the ratio of largest to smallest singular value) are already well-balanced across directions and contribute only marginally to adaptation, whereas matrices with larger condition numbers contain underdeveloped directions that span richer subspaces and drive most of the performance gains. This observation itself is a key contribution of our work, and it motivates a more selective approach to fine-tuning. Building on this insight, we propose \k{appa}-LoRA, a method that optimizes LoRA by focusing updates on the matrices with the largest condition numbers, which capture the most informative directions of change. By restricting LoRA updates to the top 50% of weight matrices ranked by condition number, \k{appa}-LoRA halves the trainable parameter count and correspondingly reduces compute and memory cost. Extensive experiments across multiple benchmarks show that this design cuts fine-tuning time by 16.2% on average while matching the accuracy of standard LoRA and reducing memory cost by 4.5%. Further analysis reveals that the condition numbers of the selected matrices consistently decrease over training, suggesting that \k{appa}-LoRA's effectiveness stems from targeted spectral rebalancing rather than parameter selection alone.