Learnability and Privacy Vulnerability are Entangled in a Few Critical Weights

arXiv 2603.13186·high signal

A small subset of 'critical weights' in neural networks drives both learnability and membership privacy vulnerability simultaneously — they are not separable properties. Prior privacy-preservation methods waste compute by updating all weights; targeted defense on this critical subset achieves better privacy-utility tradeoff at a fraction of the cost. Practical implication: fine-tuning practitioners can focus privacy budgets on ~5% of weights and achieve stronger guarantees than full-network methods.