Learning the identity: a case study of how SGD selects among functional decompositions
One might think that learning the identity function with a deep linear residual network is trivial - the path along residual connections already implements the identity, and so the network need only drive its weights to zero. However, this zero-weight solution is just one point on an entire manifold of population-loss minimizers, each corresponding to a different decomposition of the identity across the network's layers. Although the population loss does not distinguish among these solutions, stochastic gradient descent (SGD) reproducibly favors particular ones. For instance, under anisotropic label noise, the learned layers exhibit a noise-dependent spectrum; even with weight decay, SGD ...
| Authors | Andy Arditi, Weian Xie, David Bau et al. |
|---|---|
| Primary category | cs.LG |
| Published | 30 September 2026 |
| Last updated at source | 30 September 2026 |
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