A Loss Hidden Behind a Shift

A three-class network outputs the logit vector

$\mathbf{z} = [\,7.0794,\; 5.0000,\; 5.0000\,]$

for one training example. These logits are passed through softmax,

$p_i = \frac{e^{z_i}}{\sum_{j=1}^{3} e^{z_j}}$

and the result is scored with the cross-entropy (negative log likelihood) loss $L = -\ln(p_{\text{true}})$.

The ground-truth label for this example is class 3.

What is the loss, in nats?

You may use $\ln 2 \approx 0.6931$ and $\ln 5 \approx 1.6094$. No calculator is needed.