## 4 Auto-HPIF Modeling Approaches
### The Implicit Heterogeneous Intent-Slot Interaction Module  
The implicit interaction part of the module implements mutual guidance of slot and intent information by further using prior knowledge to identify intents and slots in the user input. The module learns embedded representations based on a heterogeneous graph network and then combines these representations with intent labels to form an embedded multi-intent predictor. When processing user input, the module can process different intent and slot information simultaneously and optimize and adjust them through bidirectional information flow, thus improving the accuracy and efficiency of NLU. As shown in part (c) of Figure 2, a rational intent decoder and slot decoder are introduced to achieve fine-grained multi-intent prediction, and a heterogeneous graph network captures the interaction between different input elements. Specifically, based on the word-level representations and slot label sequences generated by module (b) for multi-intent prediction, embedded representations are further learned using the heterogeneous graph network to improve the ability to encode the semantic relationships between different input elements. Finally, these learned embedded representations are combined with the intent labels and processed by the rational intent decoder and slot decoder to obtain the final fine-grained multi-intent prediction results. * **Heterogeneous Graph Layer. ** This module combines graph attention [27] and self-attention mechanisms to construct a heterogeneous network graph layer. The heterogeneous network layer is used to learn the relationship between each word in a sentence and calculate the importance of other words related to that word. At the same time, prior knowledge is used to guide the model to learn how to match different types of slot information with the input sentences. By integrating the feature representations of these words with higher importance and the degree of matching with the slot predefined, an embedding vector can be generated for that input sentence, and the corresponding intent category and slot values can be extracted from it. Specifically, the predicted intent labels \(y_{t}^{\text{II}}=[s_{1},s_{2},\dots,s_{t}]\) and slot information \(y_{t}^{\text{IS}}\)= \([l_{1},l_{2}\,,L,l_{t}]\) output by module (b) and each word-level embedding \(H=[h_{1},h_{2},\cdots,h_{n}]\) and representation are considered as three classes of nodes, and three types of edges are defined: 1. Adjacency relationship edges between word nodes, representing the contextual information between words in a sentence; 2. The relationship edge between the intent label and the word node, indicating the connection between the intent label and each word in the input sentence; 3. Relational edges between slot information and word nodes, representing the connection between slot information and each word in the input sentence. All the above three edges are directed edges, and their weights indicate the importance or similarity of that edge. During model training and prediction, the weights of these edges are computed and aggregated to generate global context-aware embedding vectors and finally complete the tasks of categorizing intents and filling slots. Through the interaction of these edges, each word in the input sentence and the relationship between them, as well as the degree of match between each word and the target slot value, can be considered simultaneously to generate a comprehensive embedding vector representation. The heterogeneous network graph layer \(G=(V,E)\) is constructed using the graph neural network node feature representation and attention mechanism to handle the similarity scores between nodes.