Feature Learning in L2-regularized DNNs: Attraction/Repulsion and Sparsity

@article{Jacot2022FeatureLI,
  title={Feature Learning in L2-regularized DNNs: Attraction/Repulsion and Sparsity},
  author={Arthur Jacot and Eugene Golikov and Cl{\'e}ment Hongler and Franck Gabriel},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.15809}
}
We study the loss surface of DNNs with L 2 regularization. We show that the loss in terms of the parameters can be reformulated into a loss in terms of the layerwise activations Z (cid:96) of the training set. This reformulation reveals the dynamics behind feature learning: each hidden representations Z (cid:96) are optimal w.r.t. to an attraction/repulsion problem and interpolate between the input and output representations, keeping as little information from the input as necessary to… 

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