#universal-approximation

A one-hidden-layer ReLU network can interpolate points exactly. For the points $(0, 0)$, $(1, 2)$, $(2, 1)$, $(3, 1)$ use the units $\mathrm{ReLU}(x - 0)$, $\mathrm{ReLU}(x - 1)$ and $\mathrm{ReLU}(x - 2)$ (one per point except the last) and the output $\hat{y}(x) = \sum_i c_i\,\mathrm{ReLU}(x - x_i)$, where each weight $c_i$ is the change in slope at its point. What is the weight $c_2$ of $\mathrm{ReLU}(x - 1)$?