## 4 The Proposed Framework
### Overview  
Firstly, we introduce the building blocks of DAGA, designed to distill user and group intents with enhanced granularity for better item recommendation, which are visually encapsulated in Figure 2, exemplified through the processing of a group of users. **MLP Encoder:** Serving as the cornerstone of DAGA, the encoder (MLP Encoder1) leverages the user-item interaction matrix \(R\) as the input, facilitating the derivation of embedded user representations \(Z\) with our multi-head disentangled self-attention encoder. Moreover, the disentangled MLP encoder (MLP Encoder2) is utilized to embed the features obtained from the aforementioned disentangled self-attention encoder to further facilitate the derivation of embedded group representations \(P\) with the subsequent attention-based aggregator. **Disentangled Self-Attention Encoder:** Subsequently, the user representations are encoded with the group's prior information, drawing inspiration from [37]. That is to say, the derivation of user representations can utilize similar preference context information from the other group members to enhance the encoding process. To be specific, the embeddings produced from MLP Encoder1 are transformed by three independent encoders with the same structure, K, Q and V, for preparation of the attention mechanism. These K, Q and V encoders consist of a layer that is a dimensional invariance embedding network and a layer that is an embedding network to complete higher-dimension mapping (from \(|\mathcal{I}|\) to \(d\)), which is followed by a strategic disentanglement of \(Z^{m}\) (the intermediate variable produced by our disentangled self-attention mechanism before obtaining \(Z\)) into \(k\) distinct factors, represented as \(\{Z^{m}_{1},Z^{m}_{2},Z^{m}_{3},\ldots,Z^{m}_{K}\}\). This disentanglement process is predicated on the premise of isolating and elucidating the latent intents embedded within the users' original preferences. The encoder's pivotal function is to coalesce user features, latent within the raw interaction data \(R\), and intrinsically associated with specific factors, into their respective disentangled representations \(Z^{m}_{i}\) and \(Z_{i}\). This mechanism effectively transitions the raw user-item interaction data, reflective of generalized item preferences, to the more nuanced, intent-driven representations associated with distinct attributes. Drawing from the illustrative scenario shown in Figure 1, the encoder's adept utilization facilitates the extraction of user intents pertaining to underlying  
Figure 2: Schematic overview of the proposed DAGA framework illustrating its constituent components and associated loss functions. attributes (e.g., food categories such as main courses, side dishes and beverages, or more complex attributes like flavor profiles, temperature preferences, etc.) from the broader spectrum of user preferences for various food items (e.g., roast chicken, fish, dumplings, steak, sandwic, cola, etc.). Subsequent to generating disentangled user representations, we employ a distinct multi-head self-attention calculation process with independent encoder networks for each factor, facilitating their embedding into another hidden space for further processing. In the illustrative case of food attributes, these disentangled operations yield refined representations that encapsulate the nuanced attributes of potential food selections. **Aggregator:** The objective of the aggregation process is to synthesize disentangled group representations within the hidden space through a meticulous aggregation of the disentangled user representations corresponding to each factor. This phase incorporates an attention aggregator to assign a set of trainable weights to individual group members within each factor. This facilitates a weighted aggregation approach to generate the factor-specific group representations from the constituent member representations.