Paper Detail
Brian B. Moser, Ahmed Anwar, Tobias Christian Nauen, Shishir Muralidhara, Federico Raue, René Schuster, Stanislav Frolov, Andreas Dengel
Continual learning regularizers like EWC fight forgetting by penalizing changes from previous-task parameters with per-parameter importance, typically diagonal Fisher values. Per-parameter looks more flexible than per-layer, but each layer's diagonal Fisher is a weak summary of its actual curvature, missing the top-eigenvalue information that controls forgetting. Adversarial bit-flip attacks and Hessian-spectrum studies show that this missing per-layer sensitivity spans orders of magnitude in neural networks. Under a block-diagonal Hessian assumption, the layer-level analogue of EWC's existing diagonal assumption, we prove three things. Forgetting decomposes as a sum of per-layer terms weighted by each layer's top Hessian eigenvalue. Diagonal-Fisher weights cannot recover this eigenvalue. For instance, two layers with identical Fisher averages can have top eigenvalues differing by a factor as large as the layer width. For the same level of forgetting, uniform regularization loses new-task performance by an amount scaling with the layer condition number. Our theoretical analysis leads to a simple recipe: protect early layers strongly, let deeper layers move. We apply this recipe to EWC and SLCA and show clear improvements in average performance and forgetting metrics.
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@article{moser2026layers,
title = {Layers Matter: Why Continual Learning Regularization Should Be Layer-Adaptive},
author = {Brian B. Moser and Ahmed Anwar and Tobias Christian Nauen and Shishir Muralidhara and Federico Raue and René Schuster and Stanislav Frolov and Andreas Dengel},
year = {2026},
abstract = {Continual learning regularizers like EWC fight forgetting by penalizing changes from previous-task parameters with per-parameter importance, typically diagonal Fisher values. Per-parameter looks more flexible than per-layer, but each layer's diagonal Fisher is a weak summary of its actual curvature, missing the top-eigenvalue information that controls forgetting. Adversarial bit-flip attacks and Hessian-spectrum studies show that this missing per-layer sensitivity spans orders of magnitude in ne},
url = {https://arxiv.org/abs/2608.15901},
keywords = {cs.LG, cs.AI},
eprint = {2608.15901},
archiveprefix = {arXiv},
}
{}