Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks
Despite the empirical advantages of deep networks over shallow ones, theoretical depth separations largely concern approximation power, while algorithmic results are mostly limited to comparisons between two- and three-layer networks. In this work, we prove the first algorithmic separation between constant-depth and logarithmic-depth networks. Specifically, we identify a class of Boolean functions with hierarchically structured Fourier spectra that logarithmic-depth networks can learn efficiently using layerwise coordinate descent by reconstructing the spectra hierarchically and adaptively. We also exhibit a subclass for which every constant-depth, polynomial-width network with sufficient...
| Authors | Yunwei Ren, Zihao Wang, Jason D. Lee |
|---|---|
| Primary category | cs.LG |
| Published | 28 July 2026 |
| Last updated at source | 28 July 2026 |
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