====== Analogical Prompting ======

**Analogical Prompting** is a prompt engineering technique introduced by Yasunaga et al. (2023) from Google DeepMind and Stanford University that instructs large language models to self-generate relevant examples through analogical reasoning before solving a target problem. Inspired by how humans recall past experiences when facing new challenges, this method eliminates the need for manually labeled few-shot exemplars while adapting generated demonstrations to each specific problem.

===== Motivation =====

Existing chain-of-thought (CoT) prompting methods face a trade-off:

  * **Zero-shot CoT** ("think step by step") is convenient but provides generic guidance insufficient for complex tasks
  * **Few-shot CoT** provides detailed exemplars but requires labor-intensive manual labeling, and fixed exemplars may not be relevant to every problem

Analogical Prompting achieves the best of both worlds: //automatically generated, problem-specific exemplars// with no manual labeling required.

===== Method =====

The approach follows three steps within a single LLM call:

=== Step 1: Problem Statement ===

Present the target problem to the LLM.

=== Step 2: Self-Generate Exemplars ===

Instruct the model to recall or generate 3-5 relevant problems (with solutions) that are structurally similar to the target. The prompt explicitly asks for //distinct// and //relevant// examples.

=== Step 3: Solve the Original Problem ===

The LLM uses its self-generated exemplars as context to solve the original problem.

<code python>
# Analogical Prompting implementation

def analogical_prompt(problem, llm, n_exemplars=3):
    prompt = (
        f"Your task is to solve the following problem.\n\n"
        f"Problem: {problem}\n\n"
        f"Before solving, recall {n_exemplars} relevant and distinct problems "
        f"you have encountered before. For each:\n"
        f"1. State the problem\n"
        f"2. Explain the solution step by step\n"
        f"3. Identify the key principle or technique used\n\n"
        f"After generating these exemplars, solve the original problem using "
        f"insights from the analogies above.\n"
    )
    response = llm.generate(prompt)
    return response


# Self-Generated Knowledge + Exemplars variant (for code generation)
def analogical_prompt_with_knowledge(problem, llm, n_exemplars=3):
    prompt = (
        f"Your task is to solve the following problem.\n\n"
        f"Problem: {problem}\n\n"
        f"First, identify the core concepts and techniques relevant to this problem.\n"
        f"Provide a brief tutorial or key takeaways for each concept.\n\n"
        f"Then, recall {n_exemplars} relevant and distinct problems. For each:\n"
        f"1. State the problem\n"
        f"2. Explain the solution step by step\n\n"
        f"Finally, solve the original problem using the knowledge and exemplars above.\n"
    )
    response = llm.generate(prompt)
    return response
</code>

===== Two Variants =====

The paper introduces two complementary approaches:

=== Basic Analogical Prompting ===

Generates relevant exemplar problems and solutions. Works well for mathematical reasoning and general problem-solving tasks.

=== Self-Generated Knowledge + Exemplars ===

For complex tasks like code generation, the model may over-rely on low-level exemplar patterns. This variant adds an instruction to first identify **core concepts** and provide high-level tutorials before generating exemplars. This mitigates overfitting to surface-level similarities.

===== How It Differs from Other Methods =====

^ Method ^ Exemplars ^ Adaptability ^ Manual Effort ^
| Zero-Shot CoT | None (generic instruction) | Low | None |
| Few-Shot CoT | Fixed, manually labeled | Low (same for all problems) | High |
| Retrieval-Augmented CoT | Retrieved from database | Medium | Medium (requires database) |
| **Analogical Prompting** | **Self-generated per problem** | **High** | **None** |

The key advantage is //adaptability//: generated exemplars are tailored to each problem's specific structure, providing more relevant guidance than any fixed set of demonstrations.

===== Cognitive Science Foundation =====

The approach draws from **analogical reasoning** in cognitive psychology (Vosniadou & Ortony, 1989):

  * Humans routinely solve new problems by recalling structurally similar past experiences
  * The quality of analogical transfer depends on //structural alignment// between source and target
  * LLMs, trained on vast corpora, have implicit access to enormous problem-solving experience that can be activated through appropriate prompting

===== Results =====

Evaluated with GPT-3.5-turbo and GPT-4 across diverse reasoning benchmarks:

^ Benchmark ^ Task Type ^ Improvement over 0-shot CoT ^
| GSM8K | Math reasoning | Significant |
| MATH | Advanced math | Significant |
| Codeforces | Code generation | Significant (with Knowledge variant) |
| BIG-Bench | Diverse reasoning | Average +5% accuracy |

Key findings:
  * Outperforms both 0-shot CoT and manual few-shot CoT across tasks
  * 3-5 self-generated exemplars is the optimal range
  * The Knowledge + Exemplars variant is critical for code generation tasks
  * Single-pass generation (exemplars + solution in one call) is both efficient and effective

===== Prompt Template =====

A minimal template for analogical prompting:

  [Insert problem here]

  Instruction: Before solving, recall 3 relevant and distinct problems
  as exemplars. For each, describe the problem and solution. Then solve
  the initial problem step by step.

<mermaid>
graph LR
    A[Target Problem] --> B[LLM Self-Generates Exemplars]
    B --> C[Exemplar 1: Problem + Solution]
    B --> D[Exemplar 2: Problem + Solution]
    B --> E[Exemplar 3: Problem + Solution]
    C --> F[Solve Original Problem]
    D --> F
    E --> F
    F --> G[Final Answer]
</mermaid>

===== References =====

  * [[https://arxiv.org/abs/2310.01714|Yasunaga et al. "Large Language Models as Analogical Reasoners" (2023). arXiv:2310.01714]]
  * [[https://deepmind.google/research/publications/51283/|Google DeepMind publication page]]
  * [[https://openreview.net/forum?id=4990dad2c1696224de42573d0222554a|ICLR 2024 proceedings]]

===== See Also =====

  * [[chain_of_thought|Chain of Thought]]
  * [[few_shot_prompting|Few-Shot Prompting]]
  * [[self_consistency|Self-Consistency]]
  * [[generated_knowledge_prompting|Generated Knowledge Prompting]]