The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning
We consider the Multiscale Single-Index Model (MSIM), first introduced in \cite{oymak2021learning}, as a stylized model for hierarchical learning with \emph{scale separation}. Each layer extracts a shared single-index feature at one physical scale and passes it to the next, thus defining a tractable setting in which to study how deep architectures learn multiscale representations. Under non-degeneracy and delocalization assumptions on the link function and planted features respectively, for fixed depth $K$ and local scale $d$, the first Wiener chaos of the target behaves as a perturbed spiked tensor, where the perturbation of order $d^{-1/2}$ comes from the non-linearity -- revealing the ...
| Authors | Joan Bruna |
|---|---|
| Primary category | cs.LG |
| Published | 3 July 2026 |
| Last updated at source | 3 July 2026 |
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