Cross-Domain Solution Matcher

AI ResearchOctober 5, 2025

A Multi-Stage DSPy Pipeline for Analogical Problem Solving. Solves problems by finding creative solutions from completely different domains—like using immune system strategies to reduce customer churn.

DSPy
LLM
Python
AI
Analogical Reasoning
Chain-of-Thought

Key Features

  • 4-stage pipeline (analyze → map → extract → synthesize)
  • Chain-of-Thought reasoning for all modules
  • Cross-domain analogical reasoning automation
  • Structured input/output contracts with DSPy signatures
  • Multi-domain solution synthesis
  • Claude Sonnet 4.5 powered

Overview

The Cross-Domain Solution Matcher (CDSM) is a novel multi-stage DSPy pipeline that leverages large language models to find analogous solutions from disparate domains. By abstracting problems to their core challenges, mapping them to diverse fields, extracting domain-specific solutions, and synthesizing actionable recommendations, CDSM enables creative problem-solving through cross-domain analogical reasoning.

Core Principle

Problems that look different may share the same underlying structure.

At its core, analogical reasoning rests on a simple premise. Consider these two scenarios:

  1. A glacier flowing down a mountain
  2. A queue of customers waiting at a service counter

On the surface, these share nothing. Yet both involve:

  • Flow constrained by capacity
  • Buildup when input exceeds output
  • Dynamics influenced by environmental factors

By stripping away surface details to reveal structural essence, we can transport solutions between domains.

Architecture

The system consists of four sequential modules, each implemented as a DSPy module using Chain-of-Thought reasoning:

Stage 1: Problem Analyzer

Purpose: Extract the essence of the problem independent of its original domain.

  • Input: Raw problem description from the user
  • Output: Core challenge, key characteristics, desired outcome

Stage 2: Domain Mapper

Purpose: Identify analogous domains where structurally similar problems have been solved.

  • Input: Core challenge and key characteristics
  • Output: List of 5-7 analogous domains with reasoning

Stage 3: Solution Extractor

Purpose: For each identified domain, extract specific solutions and strategies.

  • Input: Original problem, core challenge, and target domain
  • Output: Domain-specific solution, mapping strategy, implementation ideas

Stage 4: Solution Synthesizer

Purpose: Integrate insights across all domains into coherent recommendations.

  • Input: Original problem and all domain solutions
  • Output: Common patterns, unique insights, prioritized recommendations

Example: Customer Churn Reduction

User Problem: "How do I reduce customer churn in my SaaS product?"

Core Challenge: Maintaining sustained engagement with voluntary participants over time.

Domains Identified:

  • Biological Immune Systems (Maintaining defense against constant threats)
  • Ecosystem Resilience (Systems that persist despite perturbations)
  • Social Network Dynamics (Why people stay in communities)
  • Addiction Psychology (Mechanisms that create compulsive behavior)
  • Jazz Improvisation (Keeping audience engaged through unpredictability)

Key Recommendations:

  1. Build an early warning system (from Immune Systems)
  2. Create variable reward structures (from Addiction Psychology)
  3. Foster user communities (from Social Networks)

Design Principles

Chain-of-Thought for All Modules

Every module uses dspy.ChainOfThought rather than basic dspy.Predict. This forces the model to articulate its reasoning, achieving:

  • Better quality through step-by-step reasoning
  • Interpretability for users to inspect how analogies were formed
  • Debuggability to trace failures to specific reasoning steps

Multi-Stage Pipeline Architecture

The four-stage design reflects the natural cognitive process of analogical reasoning:

  1. Understanding what the problem really is (abstraction)
  2. Recalling where similar problems exist (memory search)
  3. Retrieving specific solutions (knowledge extraction)
  4. Adapting solutions to the current context (transfer)

Structured Input/Output Contracts

DSPy signatures define explicit contracts between stages, providing type safety, documentation, and composability.

Performance Characteristics

  • Latency: 30-90 seconds per problem
  • API Calls: 4 + N (where N = domains, typically 5-7)
  • Token Usage: 15,000 + 5,000N tokens
  • Cost: 1.20 per problem using Claude Sonnet 4.5

Technical Implementation

class CrossDomainSolutionMatcher(dspy.Module):
    def __init__(self, max_domains=5):
        super().__init__()
        self.max_domains = max_domains
        self.problem_analyzer = ProblemAnalyzer()
        self.domain_mapper = DomainMapper()
        self.solution_extractor = SolutionExtractor()
        self.solution_synthesizer = SolutionSynthesizer()
 
    def forward(self, problem_description):
        # Stage 1: Analyze the problem
        analysis = self.problem_analyzer(problem_description)
 
        # Stage 2: Map to analogous domains
        domain_mapping = self.domain_mapper(
            analysis.core_challenge,
            analysis.key_characteristics
        )
 
        # Stage 3: Extract solutions from each domain
        domain_solutions = []
        for domain in domain_mapping.analogous_domains[:self.max_domains]:
            solution = self.solution_extractor(
                problem_description,
                analysis.core_challenge,
                domain
            )
            domain_solutions.append(solution)
 
        # Stage 4: Synthesize all solutions
        synthesis = self.solution_synthesizer(
            problem_description,
            domain_solutions
        )
 
        return dspy.Prediction(
            problem=problem_description,
            core_challenge=analysis.core_challenge,
            domains=domain_mapping.analogous_domains,
            solutions=domain_solutions,
            synthesis=synthesis
        )

Future Extensions

Retrieval-Augmented Generation

Add retrieval to access domain-specific textbooks, papers, and up-to-date information on emerging domains.

Parallel Solution Extraction

Process domains concurrently to reduce latency by N times.

DSPy Compiler Optimization

Use BootstrapFewShot, MIPRO, or Ensemble techniques to optimize prompts automatically.

Domain Specialization

Train domain-specific modules or maintain knowledge bases for frequently effective domains like biology, physics, and psychology.

User Feedback Loop

Implement rating systems and outcome tracking to iteratively refine domain selection heuristics.

Conclusion

The Cross-Domain Solution Matcher demonstrates how large language models can be orchestrated to perform sophisticated cognitive tasks through careful architectural design. By decomposing analogical reasoning into explicit stages, maintaining clear interfaces between components, and forcing step-by-step reasoning, CDSM achieves both quality and interpretability.

The system's true value lies not in replacing human creativity, but in augmenting it—surfacing unexpected connections, providing domain expertise, and generating actionable starting points.


TL;DR: CDSM breaks down "thinking across domains" into 4 clear steps, uses Chain-of-Thought to show its work, and costs ~$1 to potentially unlock million-dollar insights. The future of creative AI isn't about replacing humans—it's about giving them better thinking tools.