While the XOR function cannot be calculated by a single perceptron, it can be calculated by a layered network of units, such as a two-layer network of ReLU-based units. In the accompanying figure, the numbers on the arrows represent the weights for each unit, and $h_1$ and $h_2$ form a hidden layer that represents the input in a new linearly separable $h$ space. The solution to the XOR problem requires a network of units with non-linear activation functions. This is because a network formed by many layers of purely linear units can always be reduced to a single layer of linear units with appropriate weights.