Cross-Entropy from Logits

Compute the categorical cross-entropy loss of one example from its raw logits and the index of the true class, using the log-sum-exp trick for stability.

Implement solve(logits, target).

Returns. Return a non-negative float: $\log {\sum }_j{e}^{z_j}-z_{\text{target}}\backslash log\backslash sum\_j\; e^\{z\_j\}-z\_\{\backslash text\{target\}\}$.

Examples

Example 1

Input:

solve([1.0, 2.0, 3.0], 2)

Output:

0.407606

Example 2

Input:

solve([5.0], 0)

Output:

0.0

Example 3

Input:

solve([1000.0, 0.0], 0)

Output:

0.0