Twelve Layers, Six Shortcuts

Two networks are built from the same twelve layers. On the backward pass, each layer multiplies the gradient passing through it by a local rate of 0.5.

• Plain: the twelve layers are stacked one after another.
• Residual: the same twelve layers are grouped into six residual blocks of two layers each. Each block computes $F(x) + x$, where $F$ is its two layers, and the shortcut carries $x$ to the block's output unchanged.

In a residual block the backward signal reaches the block's input along two routes, through $F$ and along the shortcut, and the rates of the two routes add.

A gradient of $1$ arrives at the output of each network. How many times larger is the gradient that reaches the input of the residual network than the gradient that reaches the input of the plain network?

Every rate here is an exact power, so work with exact values and give the answer as a whole number.