57 lines
3.8 KiB
Markdown
57 lines
3.8 KiB
Markdown
# Step-by-Step Generation of an Intelligent Meta Prompt
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## 1\. Define the Task Category ($\mathcal{T}$) and Problem Structure
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The Meta Prompting framework (modeled as a functor $\mathcal{M}:\mathcal{T}\rightarrow\mathcal{P}$) begins by identifying a category of tasks ($\mathcal{T}$) that share an invariant solution structure.[2]
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* **Task Category:** Solving *any* quadratic equation in the form $ax^2 + bx + c = 0$.
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* **Invariance:** The fundamental mathematical procedure (calculating the discriminant, applying the quadratic formula) remains constant, regardless of the specific coefficients ($a$, $b$, $c$).
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## 2\. Design the Structured Output Template ($\mathcal{P}$)
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We design a structured prompt template (an object in the category of prompts, $\mathcal{P}$) that uses a formal syntax (like JSON or XML) to impose a rigid format, ensuring the LLM generates a predictable, parsable, and verifiable output.[2] This structure serves as the scaffolding mechanism.[1]
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* **Format:** JSON (ensuring typed fields).
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* **Mandated Fields:** `Problem`, `Solution` (containing sequenced steps), and `Final Answer`.
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## 3\. Decompose the Universal Reasoning Procedure (Compositionality)
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The crucial step is to decompose the task into modular, logical steps that must be executed sequentially.[4, 2] These steps replace the need for content-rich examples found in Few-Shot Prompting.[1, 5]
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| Step in $\mathcal{P}$ | Procedural Instruction (How to Think) | Goal |
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|---|---|---|
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| **Step 1** | Identify coefficients $a$, $b$, and $c$. | Enforce variable isolation. |
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| **Step 2** | Compute the discriminant $\Delta=b^{2}-4ac$. | Enforce the first calculation. |
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| **Step 3** | Determine the nature of the roots (real, single, or complex) by checking $\Delta$. | Enforce conditional branching logic. |
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| **Step 4-6** | Apply the correct formula based on the result of Step 3. | Enforce formula application. |
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| **Step 7** | Summarize the roots in a LaTeX-formatted box. | Enforce output formatting/type. |
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## 4\. The Final Example: Structured Meta Prompt for Quadratic Equations
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This structured meta-prompt provides the complete, reusable "type signature" for solving the quadratic equation category. It guides the model to produce a systematically derived, formatted result for any input values of $a, b, c$.[2]
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```json
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{
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"Task_Category": "Quadratic Equation Solver",
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"Problem": "Solve the quadratic equation $ax^{2}+bx+c=0$ for x.",
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"Solution_Procedure": {
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"Step 1": "Identify the coefficients a, b, and c from the equation.",
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"Step 2": "Compute the discriminant using the formula: $\Delta=b^{2}-4ac.$",
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"Step 3": "Determine the nature of the roots by checking if $\Delta>0$ (two distinct real roots), $\Delta=0$ (one real root), or $\Delta<0$ (two complex roots).",
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"Step 4": "If $\Delta>0$, calculate the two distinct real roots using $x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}.$ ",
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"Step 5": "If $\Delta=0$, calculate the single real root using $x=\frac{-b}{2a}.$ ",
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"Step 6": "If $\Delta<0$, calculate the complex roots using $x_{1,2}=\frac{-b\pm i\sqrt{|\Delta|}}{2a}.$ ",
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"Step 7": "Conclude by summarizing the roots and ensuring the final expression is simplified."
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},
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"Final Answer_Format": "Present the final answer in a LaTeX-formatted box, using the structure: $\\boxed{x_{1,2} =...}$."
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}
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```
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**Intelligence and Efficiency:**
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This example is intelligent because it achieves the core goals of Meta Prompting:
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* **Structural Guidance:** It rigorously imposes a multi-step analytical process, forcing the LLM to process the problem methodically.[2]
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* **Example-Agnosticism:** No actual numerical example is provided (zero-shot efficacy), saving tokens and preventing the model from relying on analogous content.[1, 2]
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* **Compositionality:** It breaks the complex task into simple, reusable computational modules (the steps), aligning with the theoretical modeling of MP as a functor.[2]
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