## 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.

\n ## Diagram: Analogy of Prompting Techniques ### Overview The image presents a diagram comparing three different prompting techniques for Large Language Models (LLMs): 0-shot, Few-shot CoT (Chain of Thought), and Analogical Prompting (labeled as "Ours"). Each technique is illustrated with a "Model Input" and, for Few-shot CoT and Analogical Prompting, a "Model Output" section. The diagram highlights the differences in how each technique approaches problem-solving. ### Components/Axes The diagram is structured into three main columns, each representing a prompting technique. Within each column, there are two sections: "Model Input" and, where applicable, "Model Output". There are also two smaller boxes at the bottom of the first two columns labeled "Generic guidance of reasoning" and "Needed exemplars of reasoning" respectively. A green checkmark and text "Exemplars are automatically generated and tailored to each problem" are present in the bottom right corner. ### Detailed Analysis or Content Details **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)?" **Few-shot CoT:** * **Model Input 1:** "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?" * **Model Output 1:** "A: Roger started with 5 balls. 2 cans of 3 balls each is 6 balls. The answer is 5 + 6 = 11." * **Model Input 2:** "Q: What is the area of the square with the four vertices at (-2, 2), (2, -2), (-2, -6), and (-6, -2)?" **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)?" * **Model Output:** * "# Instruction: ## Recall relevant exemplars: ## Solve the initial problem:" * "# Relevant exemplars: Q: What is the area of a 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." **Bottom Boxes:** * **Left Box:** "Generic guidance of reasoning" * **Middle Box:** "Needed exemplars of reasoning" * **Right Box:** "Exemplars are automatically generated and tailored to each problem" (with a green checkmark) ### Key Observations * 0-shot prompting directly asks the question without providing any examples. * Few-shot CoT provides an example problem and its solution before presenting the target question. * Analogical Prompting also provides an example, but it's framed as "relevant exemplars" and includes an explicit instruction to recall them and solve the initial problem. * The "Ours" method highlights the automatic generation of tailored exemplars, indicated by the green checkmark. * The Few-shot CoT method requires manually curated exemplars. ### Interpretation The diagram illustrates a progression in prompting techniques for LLMs. 0-shot relies solely on the model's pre-existing knowledge. Few-shot CoT enhances performance by providing a single example of reasoning. The "Analogical Prompting (Ours)" technique aims to improve upon this by automatically generating relevant examples, potentially leading to more accurate and efficient problem-solving. The green checkmark emphasizes the key advantage of this approach: the automation of exemplar creation, which addresses the limitation of manual curation in Few-shot CoT. The diagram suggests that the "Ours" method is designed to leverage analogies to improve the model's reasoning capabilities. The inclusion of "# Instruction", "# Relevant exemplars", and "# Solve the initial problem" in the output of the "Ours" method demonstrates a structured approach to problem-solving. The diagram is a visual representation of a research or development effort focused on improving LLM performance through more sophisticated prompting strategies.

## [Diagram Type]: Comparative Prompting Strategies for Language Models ### Overview The image is a **comparative diagram** illustrating three prompting strategies for a language model: *0-shot*, *Few-shot Chain-of-Thought (CoT)*, and *Analogical Prompting (labeled “Ours”)*. It contrasts how each method structures model input (and output, for Analogical Prompting) to elicit reasoning, with brief descriptions of their approaches. ### Components/Sections The diagram is divided into three vertical sections (left, middle, right), each representing a prompting strategy: #### 1. Left: 0-shot and 0-shot CoT - **0-shot**: - *Model Input*: A question: *“What is the area of the square with the four vertices at (-2, 2), (2, -2), (-2, -6), and (-6, -2)?”* (no additional guidance). - **0-shot CoT**: - *Model Input*: The same square-area question, with a red dashed box containing: *“Think step by step.”* - Below: A red bullet: *“Generic guidance of reasoning”* (describes the approach: prompting with generic “step-by-step” guidance). #### 2. Middle: Few-shot CoT - *Model Input*: - First, a labeled exemplar (a different problem with reasoning): *“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.”* - Then, the target square-area question: *“What is the area of the square with the four vertices at (-2, 2), (2, -2), (-2, -6), and (-6, -2)?”* - Below: A red bullet: *“Need labeled exemplars of reasoning”* (describes the approach: using human-provided, labeled exemplars to guide reasoning). #### 3. Right: Analogical Prompting (Ours) - *Model Input*: - The square-area question, with instructions: *“# 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 \( (\sqrt{32})^2 = 32 \).”* - Below: A green bullet: *“Exemplars are automatically generated and tailored to each problem”* (with a green checkmark, emphasizing the innovation). ### Detailed Analysis - **0-shot**: No reasoning guidance—only the question. - **0-shot CoT**: Adds *generic* guidance (“Think step by step”) to prompt reasoning. - **Few-shot CoT**: Uses *labeled exemplars* (human-provided, e.g., the tennis ball problem) to guide reasoning, then applies it to the target question. - **Analogical Prompting**: Automatically generates *tailored exemplars* (e.g., a square with side length 5) and uses them to solve the target problem (calculating side length via distance formula, then area). ### Key Observations - **0-shot**: Minimal guidance, relying on the model’s default reasoning. - **0-shot CoT**: Generic “step-by-step” prompt (no problem-specific exemplars). - **Few-shot CoT**: Requires human-provided, labeled exemplars (labor-intensive). - **Analogical Prompting**: Automates exemplar generation (tailored to the problem), reducing manual effort and providing targeted guidance. ### Interpretation This diagram highlights the evolution of prompting strategies for enhancing language model reasoning: - *0-shot* is basic but lacks guidance. - *0-shot CoT* adds generic guidance but is not problem-specific. - *Few-shot CoT* uses labeled exemplars (effective but labor-intensive). - *Analogical Prompting (Ours)* innovates by **automatically generating tailored exemplars**, enabling the model to recall relevant reasoning patterns (e.g., “square area = side²”) and apply them to new problems (e.g., calculating side length via distance formula). The output for Analogical Prompting demonstrates successful reasoning transfer: the model recalls a relevant exemplar (square with side length 5) and applies its method (squaring side length) to the target problem (calculating side length via distance, then area). This reduces reliance on manual exemplar creation (as in Few-shot CoT) and provides more targeted guidance than generic 0-shot CoT.

## 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.