## 3 Fine-Grained NER Model  
To detect word boundaries (i.e., morpheme boundaries) in Korean, many NER models perform morphological analysis in advance. Then, they generally use morphemes and POS tags of an input sentence as inputs. Under this kind of pipeline architecture, errors of morphological analysis directly lead to diminished performance in NER models. To overcome this limitation, we use character n-grams as inputs. Given \(n\) characters, \(C_{1,n}\), in a sentence \(S\), let \(E^{c}_{1,n}\) and \(E^{f}_{1,n}\) denote sequences of coarse-grained NE tags and fine-grained NE tags in \(S\), respectively. Table 2 presents NE tags that are defined according to the well-known begin-inner-outer (BIO) character-level tagging scheme. The fine-grained NER model named FG-NER can then be formally expressed in the following equation. \[FG-NER(S)\overset{\text{def}}{=}argmaxP(E^{c}_{1,n},E^{f}_{1,n}|C_{1,n}) \tag{1}\]  
According to the chain rule, (1) can be rewritten as the following equation. \begin{table}
\begin{tabular}{l c} \hline \hline
**NE Tag** & **Description** \\ \hline B-(PER \(|\) LOC \(|\) ORG \(|\)...) & Beginning character of an NE with the category following “B-” \\ I-(PER \(|\) LOC \(|\) ORG \(|\)...) & Inner character of an NE with the category following “I-” \\ O & Character out of any NE boundary \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Character-unit NE tags. \[FG-NER(S)\stackrel{{\text{def}}}{{=}}argmaxP(E_{1,n}^{c}|C_{1,n})P(E_{1,n }^{f}|C_{1,n}) \tag{2}\]  
As shown in (2), coarse-grained NEs depend on input characters, and fine-grained NEs depend on input characters and the given coarse-grained NEs. To simplify (2), we adopt the following two assumptions: a first-order [PERSON] assumption that a current tag is dependent on the previous tag, and a conditional independent assumption that a current tag is dependent only on its current observational information. Based on these assumptions, we rewrite (2) as the following equation. Note that the reason why we used two assumptions is to simplify Equation (2). \[FG-NER(S)\stackrel{{\text{def}}}{{=}}argmax\prod_{i=1}^{n} \left\{\frac{P(E_{i}^{c}|C_{i})P(E_{i}^{c}|E_{i-1}^{c})}{P(E_{i}^{f}|C_{i},E_{i }^{c})P(E_{i}^{f}|E_{i-1}^{f})}\right\} \tag{3}\]  
To obtain the sequence labels, \(E_{1,n}^{f}\), that maximize (3) by using coarse-grained NEs as additional contextual information, we adopt a stacked BI-LSTM-LAN [17]. Figure 1 shows the architecture of the proposed fine-grained NER (FG-NER) model. This model comprises a \(k\)-stacked feature fusion layer (shown on the left) and a dual-stacked output layer (shown on the right). The feature fusion layer shown in Figure 1 accepts different levels of input embeddings that are fed into each layer of a three-stack BI-LSTM to yield a sequence of forward hidden and backward hidden states, respectively. Subsequently, these two states of each layer are concatenated to reflect bidirectional contextual information, as shown in the following equation. \[ \begin{array}{l}\overrightarrow{h}_{i}^{k}=LSTM(Emb_{i}^{k}, \overrightarrow{h}_{i-1}^{k})\\ \overleftarrow{h}_{i}^{k}=LSTM(Emb_{i}^{k},\overleftarrow{h}_{i-1}^{k})\\ \overleftarrow{h}_{i}^{k}=[\overrightarrow{h}_{i}^{k},\overleftarrow{h}_{i} ^{k}]\\ \overleftarrow{H}^{k}=[\overleftarrow{h}_{1}^{k},\overleftarrow{h}_{2}^{k}, \overleftarrow{h}_{3}^{k},...,\overleftarrow{h}_{n}^{k}\}\end{array}  \tag{4}\]  
where \(Emb_{i}^{k}\) is the \(i\)-th input embedding in the \(k\)-th stacked LSTM. Then, \(\overleftarrow{h}_{i}^{k}=[\overrightarrow{h}_{i}^{k};\overleftarrow{h}_{i} ^{k}]\) is the concatenation of the forward hidden state \(\overrightarrow{h}_{i}^{k}\) and the backward hidden state \(\overleftarrow{h}_{i}^{k}\) of the \(i\)-th input in the \(k\)-th stacked LSTM. In the first stacked feature fusion layer (i.e., the lowest layer) of Figure 1, \(C_{0},C_{i}\), and \(C_{n+1}\) are a special beginning symbol of a sentence, the \(i\)-th one of n input characters, and a special ending symbol of a sentence, respectively.