Analogical Reasoning (AR): Curing LLM "Tunnel Vision" by Borrowing Solutions from Other Fields

Task: You're launching a new subscription service (something like Amazon Prime, but for B2B). You need a mechanic that reduces customer churn after the first month. You already know the standard advice — it isn't working.

Prompt (Request 1 — Extraction):

The problem to solve: reduce B2B customer churn 
after the first month of a SaaS subscription.

Do the following:

ANALYSIS STEPS:
1. Problem objects — list the key entities:
   (customer, subscription, first month, product value, 
   moment of cancellation, etc.)

2. Relations — how these objects interact:
   (the customer assesses value → decides whether to pay, 
   value reveals itself over time → the customer may not wait 
   long enough, etc.)

3. Find a structural analogy in a COMPLETELY different field — 
   as far from SaaS and business as possible.
   The analogy must include:

   Object mappings (what corresponds to what):
   - [object from SaaS] ↔ [object from the other field]
   - (at least 3-4 mappings)

   Shared relations (what works the same way in both worlds):
   - [a relation that holds in both domains]
   - (at least 2-3 shared relations)

Pick an analogy from a field where this structural problem 
is well studied and has unconventional solutions.

Prompt (Request 2 — Search):

Problem: reduce B2B customer churn after the first month 
of a subscription.

The analogy we found in the previous step: [paste the result 
of Request 1]

Using this analogy:
1. Find a concrete solution used 
   in the analogous field for this structural problem.
2. Describe the mechanics of that solution in detail.
3. Transfer the logic of that solution to the original problem — 
   exactly how it would work to reduce B2B customer churn.

Propose concrete implementation steps.

Result:

In Request 1 the model will find a non-obvious analogy — for example, rotating reserve troops (where new recruits are most vulnerable in the first weeks and need special adaptation protocols), population ecology (where the "first winter" is the critical survival period), or the physics of phase transitions. You'll see concrete mappings: "customer ↔ a new organism in an environment," "product value ↔ nutrient resources," "moment of cancellation ↔ critical threshold."

In Request 2 the model will propose a mechanic from the analogous field — with concrete logic it wouldn't have produced if you'd asked about onboarding directly. For instance, the concept of "buffer environments" from ecology or "critical adaptation periods" from neuroscience — translated into concrete product-onboarding steps.

The LLM's weakness: popular problems have "gravity" — a set of the most frequent answers that pull the model in. It's not stupidity, it's statistics: the model is trained to predict the next word, and the most frequent words after "how to reduce churn" are "email," "onboarding," "trial." The model generates text along a memorized pattern instead of "thinking" about the problem afresh.

The LLM's strength: the model is excellent at finding structural similarity between different fields. It knows physics, biology, history, economics — and it sees patterns that repeat across contexts. That's what cognitive scientists call analogical reasoning — transferring the structure of knowledge from one domain to another.

How the method uses this: the analogy pulls the model away from the "gravity" of the familiar problem. Population ecology has no hard-coded "correct" answer to "how to reduce churn" — it has mechanics of survival, adaptation, buffer zones. The model can't collapse into "onboarding emails" because it's working in someone else's vocabulary.

Control levers:

• Distance of the analogy → the further the field from the original problem, the more surprising the solution. "Find an analogy in physics" gives one thing, "find an analogy in medieval economics" gives another. The study showed: the more distant the domain, the higher the novelty.
• Number of analogies → ask for 3 analogies in the first request, then run a search on each — you'll get 3 completely different directions.
• Requirements for the mappings → the more detail you demand in the object mappings, the more precise the transfer. "Find an analogy" is weaker than "find an analogy with at least 4 object mappings."
• An explicit instruction about distance → add "the analogy must come from a field as far as possible from the original one" — this directly increases distance and novelty right in the prompt.

Request 1 (Extraction):

Problem: {one-paragraph problem description}

Do a structural analysis:

PROBLEM OBJECTS:
List the key entities in the problem (5-7 objects).

RELATIONS:
Describe how the objects interact (4-6 relations).

ANALOGY:
Find a structural analogy in a field as far as possible from {original problem domain}.

Format the analogy like this:

Analogy field: [name of the field]

Object mappings:
- {object from the problem} ↔ [object from the analogy]
- {object from the problem} ↔ [object from the analogy]
(at least {number_of_mappings} mappings)

Shared relations:
- [a relation that holds in both fields]
- [a relation that holds in both fields]

Request 2 (Search):

Original problem: {problem description}

Analogy: [paste the result of Request 1]

Using this analogy:
1. Find a concrete method / approach / solution 
   used in the analogy field for a 
   structurally similar problem.
2. Describe the mechanics of that solution.
3. Transfer the logic to the original problem — 
   concrete steps for applying it.

Placeholders: - {problem description} — describe the essence of your problem in a paragraph, not a single word - {original problem domain} — marketing / management / finance / etc. - {number_of_mappings} — 3 for a quick test, 5-6 for deep analysis

🚀 Quick start — paste into the chat:

Here's an Analogical Reasoning template (a two-step method for finding 
unconventional solutions through analogies). Adapt it to my problem: 
[describe your problem]. Ask me questions to fill in the fields.

[paste the template above]

The LLM will ask about the problem's domain and how distant you want the analogy to be — because the method needs to know what to move away from in order to find the most unconventional field.

⚠️ Simple problems with a known answer: For questions like "how to write an SEO headline" or "the best resume format," the method is overkill. AR shines on open-ended problems with no single right answer.

⚠️ The analogy can be superficial: If you don't demand detailed object mappings, the model sometimes finds a pretty but structurally empty analogy. Specifying "at least 4 mappings" and "shared relations" guards against this.

⚠️ Two requests instead of one: The method requires two separate messages. That's not a bug, it's the architecture — two different "modes of thinking" crammed into one prompt perform worse.

⚠️ Unconventional solutions need vetting: AR finds unusual ideas but doesn't guarantee they're applicable. The model itself rated novelty as a "reasonable approach" in 67% of cases — not 100%. Filtering is still on you.

The Stanford team ran a simple experiment: they took 50 real scientific problems, asked three top models (Claude, GPT, Gemini) for 5 solutions each — and measured how different the answers were. The result was discouraging: with a direct, unconstrained request ("just find a solution"), the models generated effectively 7-8 unique fields out of 150 attempts. Nearly all the answers were the same handful of ideas rephrased in different words.

Also interesting was the "smart" version without analogies — a cross-domain baseline, where models were asked to look for solutions in other fields but without structural transfer. You'd think that would help. It didn't — the collapse was almost as strong. Just saying "look in another field" isn't enough: you have to explicitly build a structural analogy.

To test real-world value and not just metrics, the researchers took four open biomedical problems and actually implemented the AR-proposed solutions in code. All four — with the code written by a Claude-based agent with minimal human intervention — beat the published baselines. The most striking result: predicting the effects of genetic perturbations improved 13x on a distributional metric when AR proposed borrowing the logic of "finite mixtures" from economics (where different consumers react differently to a policy change — structurally the same problem).

Examples of analogies from the paper — showing what a high-quality Request 1 result looks like:

Analogy 1: drug delivery ⟺ environmental engineering

Object Mappings:
- implantable delivery system ↔ leaking underground storage tank
- anticancer drug ↔ contaminant chemical
- tumor microenvironment ↔ subsurface soil layers
- healthy tissue ↔ protected water resources

Shared Relations:
- a stationary source releases substance into heterogeneous medium
- substance disperses forming concentration gradient
- transport pathways remove substance from area

Candidate Solution: MODFLOW with MT3DMS Reactive Transport Modeling 
for Multi-Species Contaminant Plume Prediction from Injection Wells

Analogy 2: biomedical signal processing ⟺ seismology

Object Mappings:
- neural sources ↔ earthquake hypocenters
- scalp electrodes ↔ seismometers
- brain tissue ↔ earth crust and mantle
- electrical signals ↔ seismic waves

Shared Relations:
- internal sources generate propagating waves within a volume conductor
- waves travel through heterogeneous medium with attenuation
- external sensors measure superimposed signals

Candidate Solution: Double-Difference Earthquake Location Algorithm

Context: The researchers used these analogies in two separate API calls (extraction agent + search agent, temperature=1.0). In a chat, that's two consecutive messages.

💡 Adaptation: several analogies at once

Instead of one analogy — three from different fields. Then you pick the most interesting one and run the search on it.

Find 3 structural analogies for the problem {problem} — 
from three completely different fields (for example: physics, 
history, biology — or any that are as unlike each other as possible).

For each one, give:
- Object mappings (at least 3)
- Shared relations (at least 2)
- One or two sentences: why this analogy 
  is structurally accurate

🔧 Technique: an analogy through a specific historical period

A more specific field produces a better analogy. "Physics" is weaker than "the fluid dynamics of turbulent flows."

Replace: "Find an analogy in a field far from the problem" With: "Find an analogy in [a specific narrow field] — for example, army supply logistics in the Napoleonic era / population dynamics of island ecosystems / the mechanics of crystallization"

The more specific the field, the more surprising and precise the mappings.

🔧 Technique: a reverse analogy to test an idea

The method works not only for generating ideas but also for stress-testing them.

I have an idea: {idea description}

Find an analogous situation in another field 
where a similar idea:
a) worked — describe the mechanics of success
b) failed — describe the mechanics of failure

Object mappings for both cases.
What of this applies to my situation?

Paper: Unlocking LLM Creativity in Science through Analogical Reasoning (2025)

Authors: Andrew Shen, Shaul Druckmann, James Zou — Stanford University

Cognitive-science concepts it builds on: Structure-Mapping Theory (Dedre Gentner, 1983) — a theory of how people draw analogies through shared relations rather than object attributes