4. Writing the Main Section to Emphasize the Technical Soundness of the Methodology

The main section conveys the core content of the paper, detailing the technical soundness of the proposed methodology and establishing its design and logical foundation. This section should use methodological structure, mathematical definitions, and theoretical proofs, complemented by visual aids and equations to enhance clarity and persuasiveness.

4-1. Structure of the Main Section

1. Redefining the Research Problem and Solution Strategy

• Purpose: Reframe the core problem in technical terms and outline the strategy for solving it.

• How to Write:

  1. Reformulate the research problem using mathematical or technical terminology.
  2. Summarize the key concepts and directions of the solution strategy.

  Example:

  • "To address the contextual similarity deficiency in existing models, this study designs a function $f(X)$ that maximizes contextual dependency between input data $X$ and output data $Y$."
  • "This work proposes a novel transformer-based architecture that extends the Attention mechanism to effectively integrate contextual information in multilingual translation."

2. Structure of the Proposed Model/Methodology

• Purpose: Visually and descriptively explain the structure of the proposed model or system, highlighting how each component contributes to problem-solving.

• How to Write:

  1. Overview of the Entire Structure:

     • Provide a high-level description of the system or model, supported by diagrams.
     • Example:
       "The Encoder-Decoder structure consists of an Encoder that learns the input context and a Decoder that generates the translated output."

  2. Component-Wise Explanation:

     • Describe the key components of the model and their roles.
     • Example:
       • Encoder: "Learns the contextual information of the input sequence using a Multi-Head Attention mechanism."
       • Decoder: "Generates output sequences based on the contextual information, incorporating positional encodings."

  3. Utilization of Visual Aids:

     • Illustrate the model structure or data flow through diagrams.
     • Example:
       A diagram showcasing the interaction between Encoder and Decoder, with arrows indicating data flow and key modules labeled.

  4. Mathematical Definitions:

     • Define the operational principles of the model mathematically.
     • Example:
       $Attention(Q, K, V) = softmax\left(\frac{QK^T}{\sqrt{d_k}}\right)V$
       where $Q$, $K$, and $V$ represent the Query, Key, and Value matrices, respectively.

3. Theoretical Validity of the Proposed Methodology

• Purpose: Justify the effectiveness of the methodology theoretically.

• How to Write:

  1. Connect to Existing Theories:

     • Discuss how the proposed approach builds on or extends existing theories.
     • Example:
       "The Attention mechanism, as established in previous studies, effectively captures key relationships within input sequences."

  2. Explain Functional Effectiveness:

     • Detail how each component contributes to solving the problem.
     • Example:
       "Multi-Head Attention enables the parallel learning of diverse contextual information within input sequences, enhancing translation quality."

  3. Analyze Computational Complexity:

     • Provide a complexity analysis of the proposed methodology.
     • Example:
       "The computational complexity of the proposed model is $O(n^2)$, similar to existing architectures, ensuring scalability for large datasets."

4. Necessity of Mathematical Proofs

• Purpose: Guarantee the theoretical validity of the proposed methodology.

• How to Write:

  1. Clarity and Step-by-Step Proof:

     • Structure proofs in steps to facilitate understanding.
     • Example:
       • Proposition 1: "The proposed Attention mechanism ensures parameter convergence."
       • Proof: $\cdots$

  2. Highlight Key Results:

     • Emphasize the outcomes of proofs.
     • Example:
       • Proposition 1: Minimizing $\mathcal{L}$ improves BLEU scores.

  3. Incorporate Real Data:

     • Use actual data to support the logical structure of the proofs.

5. Harmonizing Visuals and Equations

• Purpose: Integrate visuals and equations to convey both conceptual explanations and theoretical justifications.
• How to Write:
  1. Use of Diagrams:
     • Visually depict model structures, data flows, and key operations.
  2. Mathematical Definitions:
     • Define the principles governing each component mathematically.
  3. Logical Integration:
     • Ensure that diagrams and equations complement the narrative. For example, a diagram can illustrate a concept while an equation formally defines it.

4-2. Tips for Writing the Main Section

1. Maintain Logical Flow:

   • Follow a coherent structure: problem definition → solution strategy → model structure → theoretical validation → proofs.

2. Ensure Clarity:

   • Write equations, visuals, and explanations in a concise and comprehensible manner.

3. Leverage Visual and Mathematical Complementarity:

   • Use visuals to clarify concepts and equations to establish technical validity.

4. Justify Technical Decisions:

   • Explain the reasoning behind each design choice to strengthen persuasiveness.

5. Acknowledge Limitations:

   • Discuss potential weaknesses and suggest possible solutions or future directions.

4-3. Example for the Main Section

1. Problem Redefinition and Solution Strategy:
"This study addresses the contextual similarity deficiency in existing models by extending the Attention mechanism. The proposed method learns cross-linguistic contextual dependencies to improve translation accuracy."

2. Model Structure and Mathematical Definition:
"The Encoder learns the contextual information of the input sequence, and the Attention Score is computed as follows:

where $Q, K, V$ represent the Query, Key, and Value matrices. Figure 1 illustrates the Encoder-Decoder structure."

3. Theoretical Validity:
"Multi-Head Attention learns diverse contextual relationships in parallel, leading to a 20% improvement in BLEU scores over existing single-head structures."

4. Mathematical Proof:
Proposition 1: "The proposed optimization method guarantees convergence and improves model performance."
Proof: $\cdots$