## Prompting Method Comparison: 0-shot, Few-shot CoT, and Analogical Prompting ### Overview The image presents a comparison of three different prompting methods for a language model: 0-shot, Few-shot Chain-of-Thought (CoT), and Analogical Prompting. Each method is illustrated with an example of a model input and, where applicable, a model output. The image highlights the key characteristics and requirements of each prompting approach. ### Components/Axes * **Titles (Top):** * 0-shot * Few-shot CoT * Analogical Prompting (Ours) * **Sections:** Each method has a section containing: * "Model Input" box: Shows the prompt given to the model. * "Model Output" box (Analogical Prompting only): Shows the model's response. * **Annotations:** * 0-shot CoT: "Think step by step." (within a dashed red box) * 0-shot CoT: "Generic guidance of reasoning" (below the input box, preceded by a red bullet point) * Few-shot CoT: "Need labeled exemplars of reasoning" (below the input box, preceded by a red bullet point) * Analogical Prompting: "Exemplars are automatically generated and tailored to each problem" (below the output box, preceded by a green bullet point) and a green checkmark. ### Detailed Analysis or ### Content Details **1. 0-shot:** * **Model Input:** * Q: What is the area of the square with the four vertices at (-2, 2), (2, -2), (-2, -6), and (-6, -2)? **2. 0-shot CoT:** * **Model Input:** * Q: What is the area of the square with the four vertices at (-2, 2), (2, -2), (-2, -6), and (-6, -2)? * Think step by step. (Prompt added to encourage chain-of-thought reasoning) * **Annotation:** * Generic guidance of reasoning **3. Few-shot CoT:** * **Model Input:** * Q: Roger has 5 tennis balls. He buys 2 more cans of tennis balls. Each can has 3 tennis balls. How many tennis balls does he have? * A: Roger started with 5 balls. 2 cans of 3 balls each is 6 balls. The answer is 5 + 6 = 11. * ... (Indicates more examples would be included in a true few-shot setting) * Q: What is the area of the square with the four vertices at (-2, 2), (2, -2), (-2, -6), and (-6, -2)? * **Annotation:** * Need labeled exemplars of reasoning **4. Analogical Prompting (Ours):** * **Model Input:** * Q: What is the area of the square with the four vertices at (-2, 2), (2, -2), (-2, -6), and (-6, -2)? * \# Instruction: * \#\# Recall relevant exemplars: * \#\# Solve the initial problem: * **Model Output:** * \# Relevant exemplars: * Q: What is the area of the square with a side length of 5? * A: The area of a square is found by squaring the length of its side. So, the area of this square is 5^2 = 25. ... * \# Solve the initial problem: * To find the area of the square, we need to find the side length. The length is ... \sqrt{(2-(-2))^2 + (-2 - 2)^2} = \sqrt{32}. So, the area of the square is (\sqrt{32})^2 = 32. * **Annotation:** * Exemplars are automatically generated and tailored to each problem ### Key Observations * **0-shot:** The model is given the question directly without any examples or specific instructions. * **0-shot CoT:** The model is prompted to "Think step by step" to encourage a chain-of-thought approach. * **Few-shot CoT:** The model is provided with example question-answer pairs before being asked the target question. * **Analogical Prompting:** The model is instructed to recall relevant exemplars and then solve the initial problem. The model output includes both the relevant exemplars and the solution. ### Interpretation The image illustrates different prompting strategies to improve the reasoning capabilities of language models. 0-shot prompting is the simplest, while Few-shot CoT leverages examples to guide the model. Analogical Prompting, the method proposed by the authors ("Ours"), aims to automatically generate and tailor exemplars to each problem, potentially offering a more efficient and effective approach compared to manually curated examples in Few-shot CoT. The green checkmark suggests that the Analogical Prompting method is considered successful or preferred by the authors. The use of "Instruction" and "Relevant exemplars" in the Analogical Prompting section indicates a structured approach to problem-solving.

## Diagram: Comparison of Prompting Strategies ### Overview This diagram illustrates the evolution and differences between four distinct prompting methodologies for Large Language Models (LLMs): 0-shot, 0-shot Chain-of-Thought (CoT), Few-shot CoT, and Analogical Prompting. The diagram contrasts the input requirements and reasoning processes of these methods, highlighting the limitations of manual prompting versus the automated nature of the "Analogical Prompting" approach. ### Components/Axes The diagram is organized into three vertical columns representing the different prompting strategies: * **Left Column:** Contains "0-shot" and "0-shot CoT". * **Middle Column:** Contains "Few-shot CoT". * **Right Column:** Contains "Analogical Prompting (Ours)". Annotations are color-coded: * **Red text/dashed boxes:** Indicate limitations or manual requirements. * **Green text/highlighting:** Indicate advantages or automated features. --- ### Detailed Analysis #### 1. 0-shot (Left, Top) * **Model Input Box:** * "Q: What is the area of the square with the four vertices at (-2, 2), (2, -2), (-2, -6), and (-6, -2)?" #### 2. 0-shot CoT (Left, Bottom) * **Model Input Box:** * "Q: What is the area of the square with the four vertices at (-2, 2), (2, -2), (-2, -6), and (-6, -2)?" * [Red dashed box surrounding:] "Think step by step." * **Annotation (Red):** "• Generic guidance of reasoning" #### 3. Few-shot CoT (Middle) * **Model Input Box:** * [Red dashed box surrounding:] "Q: Roger has 5 tennis balls. He buys 2 more cans of tennis balls. Each can has 3 tennis balls. How many tennis balls does he have? A: Roger started with 5 balls. 2 cans of 3 balls each is 6 balls. The answer is 5 + 6 = 11. ..." * "Q: What is the area of the square with the four vertices at (-2, 2), (2, -2), (-2, -6), and (-6, -2)?" * **Annotation (Red):** "• Need labeled exemplars of reasoning" #### 4. Analogical Prompting (Ours) (Right) * **Model Input Box:** * "Q: What is the area of the square with the four vertices at (-2, 2), (2, -2), (-2, -6), and (-6, -2)?" * "# Instruction:" * [Green highlighted:] "## Recall relevant exemplars:" * [Green highlighted:] "## Solve the initial problem:" * **Model Output Box:** * [Green highlighted:] "# Relevant exemplars:" * [Green highlighted:] "Q: What is the area of the square with a side length of 5? A: The area of a square is found by squaring the length of its side. So, the area of this square is 5^2 = 25. ..." * "# Solve the initial problem:" * "To find the area of the square, we need to find the side length. The length is ... \sqrt{(2 - (-2))^2 + (-2 - 2)^2} = \sqrt{32}. So, the area of the square is (\sqrt{32})^2 = 32." * **Annotation (Green):** "• Exemplars are automatically generated and tailored to each problem" (accompanied by a green checkmark). --- ### Key Observations * **Progression of Complexity:** The diagram shows a progression from simple, unguided prompts (0-shot) to prompts requiring manual, domain-specific examples (Few-shot CoT), and finally to a self-contained, automated process (Analogical Prompting). * **Manual vs. Automated:** The red annotations for the first three methods emphasize the "cost" of these methods: either they lack specific guidance (0-shot CoT) or they require the user to manually provide labeled examples (Few-shot CoT). * **Self-Generation:** The "Analogical Prompting" section is the only one featuring green indicators, signifying that the model itself generates the relevant examples, thereby removing the burden from the user. ### Interpretation The data suggests that "Analogical Prompting" is presented as a superior methodology because it solves the "exemplar bottleneck." In traditional Few-shot CoT, a user must manually curate examples relevant to the specific problem at hand. The diagram demonstrates that Analogical Prompting automates this by instructing the model to first "Recall relevant exemplars" and then "Solve the initial problem." This creates a self-improving loop where the model tailors its own reasoning context to the specific problem, rather than relying on generic instructions or static, pre-provided examples.

## Textual Comparison of Prompting Methods for Math Problem Solving ### Overview The image compares three prompting approaches for solving a math problem: 0-shot, Few-shot Chain-of-Thought (CoT), and Analytical Prompting (Ours). Each method demonstrates how a language model processes a question about calculating the area of a square with specific vertices, using different reasoning strategies. ### Components/Axes 1. **Methods**: - **0-shot**: Direct question without guidance - **Few-shot CoT**: Includes labeled reasoning examples - **Analytical Prompting (Ours)**: Uses automated exemplar generation 2. **Textual Elements**: - Model Input sections (questions and context) - Model Output sections (reasoning and answers) - Annotations (red dots, green checkmark) ### Detailed Analysis #### 0-shot Method - **Model Input**: ``` Q: What is the area of the square with the four vertices at (-2, 2), (-2, -2), (-2, -6), and (-6, -2)? ``` - **Model Output**: ``` Think step by step. ``` - **Annotations**: Red dot labeled "Generic guidance of reasoning" #### Few-shot CoT Method - **Model Input**: ``` Q: Roger has 5 tennis balls. He buys 2 more cans of tennis balls. Each can has 3 tennis balls. How many tennis balls does he have? ``` (Irrelevant context) - **Model Output**: ``` A: Roger started with 5 balls. 2 cans of 3 balls each = 6 balls. The answer is 5 + 6 = 11. ``` - **Annotations**: Red dot labeled "Need labeled exemplars of reasoning" #### Analytical Prompting (Ours) - **Model Input**: ``` Q: What is the area of the square with the four vertices at (-2, 2), (-2, -2), (-2, -6), and (-6, -2)? # Instruction: Recall relevant exemplars # Solve the initial problem: ``` - **Model Output**: ``` # Relevant exemplars: Q: What is the area of the square with a side length of 5? A: The area of a square is found by squaring the length of its side. So, the area of this square is 5² = 25. # Solve the initial problem: To find the area of the square, we need to find the side length. The length is ... sqrt((-2 - (-2))² + (-2 - 2)²) = sqrt(32). So, the area of the square is (sqrt(32))² = 32. ``` - **Annotations**: Green checkmark with "Exemplars are automatically generated and tailored to each problem" ### Key Observations 1. **0-shot** provides no reasoning guidance 2. **Few-shot CoT** uses irrelevant exemplars (tennis balls) for a geometry problem 3. **Analytical Prompting** generates contextually relevant exemplars (square area calculation) 4. The correct answer (32) only appears in the Analytical Prompting output 5. Spatial positioning shows progression from generic to specialized reasoning support ### Interpretation The image demonstrates that: 1. **Analytical Prompting** outperforms other methods by: - Generating problem-specific exemplars - Enabling correct mathematical reasoning - Automatically adapting to problem context 2. **Few-shot CoT** fails due to: - Irrelevant exemplar selection - Inability to transfer knowledge across domains 3. **0-shot** approach lacks: - Any reasoning scaffolding - Domain-specific knowledge activation 4. The red/green annotations visually reinforce the effectiveness hierarchy: - Red = limitations in current methods - Green = successful implementation of novel approach This comparison highlights the importance of context-aware exemplar generation in enabling mathematical reasoning capabilities in language models.