# Centralized Database Access: Transformer Framework and LLM/Chatbot Integration-Based Hybrid Model
## 3 Modeling a Hybrid Model
### Model Architecture
#### 3.2.1 Text and Position Embedding  
This section deals with the embedding of words and positional information in the model. It goes beyond the concepts of traditional word embeddings; it transforms words into vectors while considering positional aspects of word order. Through this integration, the model is able to position words precisely in context, increasing the depth of its language understanding. The model receives input in the form of a sequence of words or tokens representing textual data. Each token undergoes a transformation process into a vector that includes both textual and positional embedding.  
Sophisticated word embedding techniques include advanced methods to represent words as dense vectors in a high-dimensional space. The main goal of these methods is to encapsulate the semantic and contextual relationships between words in a deeper and more efficient way. Within the proposed hybrid model developed for the management of educational materials, the integration of sophisticated word embedding techniques plays a central role in significantly improving the model's capabilities in understanding and processing textual data.  
The use of sophisticated word embedding techniques in the proposed hybrid model proves to be indispensable and serves as a cornerstone for the creation of semantically enriched representations derived from the input data. Through this embedding, the model is able to recognize the subtleties of language to promote a comprehensive understanding of educational materials. The use of these advanced techniques is essential for the model's skillful handling of complicated textual data. This includes recognizing grammatical structures and extracting relevant information from educational materials. By incorporating sophisticated word embedding methods, the proposed hybrid model experiences a remarkable improvement in its capabilities, ensuring a more nuanced and accurate interpretation of educational content. These methods contribute significantly to the model's capabilities and enable it to navigate through complex linguistic constructs. This enables a deeperunderstanding of educational materials and ultimately increases the overall effectiveness of the educational materials management system.  
Mathematically, this can be expressed as follows:  
Let input represent a sequence of words or tokens \(\{w_{i}\}\) that represent textual data. Vector representations are defined for each word \(w_{i}\) as \(Embed(w_{i})\), where \(Embed(w_{i})\) represents the embedding of the word. Let \(PositionEmbedding(p_{i})\) be the vector representation of position \(p_{i}\). The integration of words and position information can be described as follows:  
\[Embedfinal(w_{i})=LayerNorm(W_{q}\cdot Embed(w_{i})+W_{k}\cdot PositionEmbedding (pos_{i})) \tag{1}\]  
where \(W_{q}\) and \(W_{k}\) are weight matrices for query (\(q\)) and key (\(k\)), and \(p_{i}\) stands for the position of the word \(w_{i}\). \(Embedfinal\) is the resulting embedding for the word \(w_{i}\). \(Embedfinal\) is the resulting embedding for the word \(w_{i}\). Each embedding \(Embedfinal(w_{i})\) undergoes a transformation process into a vector that includes both textual and positional embedding.  
In matrix form this can be expressed as follows:  
\[Embed_{final}(w_{i})=LayerNorm\bigg{(}\begin{bmatrix}W_{q}&W_{k}\end{bmatrix} \cdot\begin{bmatrix}Embed(w_{i})\\ PositionEmbedding(pos_{i})\end{bmatrix}\bigg{)} \tag{2}\]