通过扰动模型权重提升分类准确率，无需重新训练。
Hessian Surgery: Class-Targeted Post-Hoc Rebalancing via Hessian Spike Perturbation
- 沿特征值尖峰方向调整权重，实现类间准确率再平衡。
- 在CIFAR-10和ISIC-2019上提升平衡准确率与稳定性。
- 适合需要微调且无法重训练的部署场景。
训练好的深度网络的海森谱具有特定结构：大部分特征值接近零，少数为显著的异常值（尖峰），其数量等于类别数减一，印证了随机矩阵理论在深度学习中的适用性。现有研究虽描述此结构，但未实操利用。本文提出Hessian Surgery，一种无需重训练的后处理优化方法，直接沿尖峰特征向量扰动模型权重以实现类间准确率再平衡。引入（i）尖峰-类别敏感度矩阵，量化每类准确率沿各尖峰方向的变化率；（ii）受约束的扰动系数优化，针对弱类别调整而保护强类别；（iii）自适应幅度控制，根据迭代改进信号动态调节扰动强度。在CIFAR-10和ISIC-2019数据集上均取得良好效果，提升了平衡准确率与标准差。
原文摘要 · Abstract (English)
The Hessian spectrum of trained deep networks exhibits a characteristic structure: a continuous bulk of near-zero eigenvalues and a small number of large outlier eigenvalues (spikes), confirming the relevance of Random Matrix Theory in deep learning. The spike count matches the number of classes minus one. While prior work has described this structure, no method has exploited it operationally to improve classification performance. We propose Hessian Surgery, a post-hoc optimization method that directly perturbs model weights along spike eigenvectors to rebalance per-class accuracy without retraining. We introduce (i) a spike-class sensitivity matrix that quantifies the directional derivative of each class's accuracy along each spike eigenvector, (ii) a constrained optimization of perturbation coefficients that targets weak classes while preserving strong ones, and (iii) an adaptive amplitude control that raises or lowers the perturbation budget based on iteration-level improvement signals. We obtain encouraging results on CIFAR-10 and ISIC-2019 on both balanced accuracy and standard deviation.
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