Q: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
Some recent work has shown separation between the expressive power of depth-2 and depth-3 neural networks. These separation results are shown by constructing functions and input distributions, so that the function is well-approximable by a depth-3 neural network of polynomial size but it cannot be well-approximated under the chosen input distribution by any depth-2 neural network of polynomial size. These results are not robust and require carefully chosen functions as well as input distributions.

We show a similar separation between the expressive power of depth-2 and depth-3 sigmoidal neural networks over a large class of input distributions, as long as the weights are polynomially bounded. While doing so, we also show that depth-2 sigmoidal neural networks with small width and small weights can be well-approximated by low-degree multivariate polynomials.
A:
depth-2-vs-3 separation for sigmoidal neural networks over general distributions