Asymptotic convexity of wide and shallow neural networks
arXiv:2507.01044v2h-index: 14
Originality Incremental advance
AI Analysis
This work offers theoretical insight into the optimization properties of neural networks, which is incremental but relevant for researchers in machine learning theory.
The authors tackled the problem of understanding why wide and shallow neural networks perform well by showing that the epigraph of their input-output map approximates a convex function, providing a plausible explanation for this observed performance.
For a simple model of shallow and wide neural networks, we show that the epigraph of its input-output map as a function of the network parameters approximates epigraph of a. convex function in a precise sense. This leads to a plausible explanation of their observed good performance.