Hessian Surgery: Class-Targeted Post-Hoc Rebalancing via Hessian Spike Perturbation
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 derivat...
| Authors | Hugo Vigna, Samuel Bontemps |
|---|---|
| Primary category | cs.LG |
| Published | 8 May 2026 |
| Last updated at source | 17 May 2026 |
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