The span vector v is then passed through a span classifier, with two fully- connected layers and one ReLU activation function, whose output dimensionality is the number of possible non-terminal labels:
$$s(\left ( i,j \right ) = {W2}\times ReLU\left (  LayerNorm\left ( W1\times {v(i, j)} \right )\right )$$

University of Colorado at Boulder

Instead of providing numerosity of all possible parsing trees, span-based neural constituency parsing only offer the best parsing tree. Its intuition is to train a neural classifier to assign a score to each constituent and find out the best-scoring parse tree based on those assigned scores.


Span-Based Neural Constituency Parsing

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

Each fencepost contains two vectors.
A span is represented by concatenating the difference of each of its fencepost vectors:  
$$v(i,j)=[y_j^{\rightarrow} {-} y_i^{\rightarrow } ;y_{j+1}^{\leftarrow }-y_{i+1}^{\leftarrow }]$$

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