SourceCapability Localization: Capabilities Can be Localized rather than Individual Knowledge
The authors propose CNL, which identifies neurons whose gradient contribution exceeds a threshold (σ=6) across a dataset. On GSM8K, the overlap of located neurons between two data splits is 96.42% (Llama2-7B), with only 0.14% of MLP parameters targeted. Fine-tuning only these located neurons (0.15% of parameters) improves average performance by 5.17% over random at epoch 1 (Llama2-7B, σ=6). Erasing the located neurons degrades Llama2-13B average performance by 18.68% at σ=3, compared to 0.21% for random. Cross-dataset experiments show that enhancing GSM8K-located neurons improves MetaMath performance by 22% while leaving other datasets largely unaffected, indicating the neurons encode a transferable capability.