## 3 Method Description
### Multi-Dimensional Labeling Framework Layer  
#### 3.2.1 HT-BES Multi-Dimensional Labeling Strategy  
The HT-BES multi-dimensional labeling strategy transforms the joint extraction task of entities and relations into a multi-label sequence labeling task based on relation dimensions. Based on the concept of head-tail entity association, the labeling strategy was designed as follows:  
(1) BES Entity Boundary Labels: \"B\" (Begin) represents the beginning token of an entity, \"E\" (End) marks the ending token of an entity, and \"S\" (Single) indicates a single-token entity. Entity boundary information can adapt to entity length variations, allowing for the accurate recognition of entity boundaries. (2) HT Entity Position Labels: \"H\" and \"T\" are used to mark the positions of entities within a triple, where \"H\" represents the head entity and \"T\" represents the tail entity. Positional information can accurately identify the relative positions between head and tail entities, particularly important for handling cases with large distances between entities. (3) Head-Tail Entity Association Classification Labels: To capture associations between token pairs of head and tail entities, entity boundary and position labels are combined by connecting the head and tail entity markers. These label types and meanings are shown in Table 1, with non-entity labels designated as \"-\". Head-tail entity association tagging reflect the dependency between head and tail entities, enabling the accurate identification of head and tail entities within triplets. (4) Relation Label Classification Matrix. To resolve overlapping triplets, an independent label matrix is constructed for each relation, with each element of the matrix representing a token pair under a specific relation. If a relation exists between a token \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Label Type** & **Label Description** & **Label Type** & **Label Description** \\ \hline HB-TB & Head begin–tail begin & HB-TS & Head begin–tail single \\ HB-TE & Head begin–tail end & HE-TS & Head end–tail single \\ HE-TE & Head end–tail end & HS-TB & Head single–tail begin \\ HS-TS & Head single–tail single & HS-TE & Head single–tail end \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Types of tags. pair, the corresponding position is labeled according to the head-tail entity association classification. Thus, an integrated approach to handling all entity relations is achieved. Figure 4 shows an example of applying the HT-BES multi-dimensional labeling strategy. The example sentence \"Cyahlofop butyl controls barnyard grass and Polygonum in rice fields\" contains triplets such as <Cyahlofop butyl, Controls weed, barnyard grass>, <Cyahlofop butyl, Controls weed, Polygonum>, and <Cyahlofop butyl, Treated crop, rice>, representing different relationships. These triplets are densely distributed, and Cyhalo-fop butyl, as the head entity, has relationships with multiple tail entities, resulting in overlapping triplets. For the first triple (\"Cyahlofop butyl\", \"Controls weed\", \"Barnyard grass\"), \"Cyahlofop\" and \"butyl\" were the beginning and ending tokens of the head entity \"Cyahlofop butyl\", while \"Barnyard\" and \"grass\" were the beginning and ending tokens of the tail entity \"Barnyard grass\". Thus, based on the head-tail entity association classification labels, (\"Cyahlofop\", Controls weed, \"Barnyard\") was designated as \"HB-TB\", (\"Cyhalofop\", Controls weed, \"grass\") was designated as \"HB-TE\", and (\"butyl\", Controls weed, \"grass\") was designated as \"HE-TE\". For the second triple, since \"Polygonum\" was the tail entity and a single-token entity, based on the head-tail entity association classification labels, (\"Cyahlofop\", Controls weed, \"Polygonum\") was designated as \"HB-TS\", and (\"butyl\", Controls weed, \"Polygonum\") was designated as \"HE-TS\".