Algorithmic Separation Established Between Constant-Depth and Logarithmic-Depth Neural Networks
A recent arXiv preprint presents the first algorithmic separation between constant-depth and logarithmic-depth neural networks. The authors construct a class of Boolean functions that can be efficiently learned by logarithmic-depth networks using layerwise coordinate descent, while constant-depth networks with regular activations and bounded spectral norms are shown to incur a constant approximation error on these functions. This result provides new theoretical evidence that deeper neural architectures can efficiently learn functions that shallower networks cannot.
Why it matters: The work offers a rigorous theoretical basis for the advantage of deeper neural networks, potentially guiding future neural network design and analysis.
Full story at: arXiv Statistical ML ↗