#### 2.4 Real path score

In section 2.3, we supposed that every possible path has a score $ P_{i} $ and there are totally $ N $ possible paths, the total score of all the paths is $ P_{total} = P_1 + P_2 + … + P_N = e^{S_1} + e^{S_2} + … + e^{S_N} $, $ e $ is the mathematical constant $ e $.

Obviously, there must be a path is the real one among all the possible paths. For exmaple, the real path of the sentence in section 1.2 is **“START B-Person I-Person O B-Organization O END”**. The others are incorrect such as “START B-Person B-Organization O I-Person I-Person B-Person”. $ e^{S_i} $ is the score of $ i^{th} $ path.

During the training process, the crf loss function only need two scores: the score of the real path and the total score of all the possbile paths. **The proportion of the real path score among the scores of all the possible paths will be increased gradually.**

The calculation of a real path score, $e^{S_i}$, is very straightforward.