Two Dead Units and a Nudge

A two-layer network maps $\mathbf{x} \in \mathbb{R}^{2}$ to $\mathbf{y} \in \mathbb{R}^{2}$:

$\mathbf{z} = W_1\mathbf{x} + \mathbf{b}_1, \qquad \mathbf{h} = \mathrm{ReLU}(\mathbf{z}), \qquad \mathbf{y} = W_2\mathbf{h} + \mathbf{b}_2$

with

$W_1 = \begin{pmatrix} 2 & -1 \\ 1 & 3 \\ -2 & 1 \\ 1 & 2 \end{pmatrix}, \quad \mathbf{b}_1 = \begin{pmatrix} 1 \\ -6 \\ 0 \\ -1 \end{pmatrix}, \quad W_2 = \begin{pmatrix} 1 & 2 & 3 & -1 \\ 0 & -1 & 2 & 4 \end{pmatrix}, \quad \mathbf{b}_2 = \begin{pmatrix} 0 \\ 1 \end{pmatrix}$

The ReLU derivative is $1$ where its input is positive and $0$ where its input is negative.

The network is evaluated at

$\mathbf{x} = \begin{pmatrix} 2 \\ 1 \end{pmatrix}$

and the input is then nudged by

$\Delta\mathbf{x} = \begin{pmatrix} 0.1 \\ -0.2 \end{pmatrix}$

Using the network's Jacobian $\dfrac{\partial \mathbf{y}}{\partial \mathbf{x}}$ evaluated at $\mathbf{x}$, the predicted output change is $\Delta\mathbf{y} = J\,\Delta\mathbf{x}$.

What is $\lVert \Delta\mathbf{y} \rVert_2$?

Round your answer to 2 decimal places.