It is shown that any continuous piecewise affine (CPA) function $\mathbb{R}^2\to\mathbb{R}$ with $p$ pieces can be represented by a ReLU neural network with two hidden layers and $O(p)$ neurons. Unlike prior work, which focused on convex pieces, this analysis considers CPA functions with connected but potentially non-convex pieces.

翻译：本文证明了任意具有 $p$ 个分片的连续分段仿射函数 $\mathbb{R}^2\to\mathbb{R}$ 可由包含两个隐藏层、神经元数量为 $O(p)$ 的 ReLU 神经网络表示。与先前聚焦于凸分片的研究不同，本分析考虑了分片连通但可能非凸的分段仿射函数。