cross-pollination-ideation

name

cross-pollination-ideation

description

Generate research ideas by finding cross-disciplinary connections, retrieving obscure theorems from distant fields, and identifying analogies between different mathematical domains. Use when Raman asks for new research directions, when ingesting a paper that might connect to other fields, when looking for "bridges" between topics, or when asked to "find connections," "what other fields use this technique," or "cross-pollinate." Implements the cross-pollination techniques from Woodruff et al. (2026, Section 2.2, 4.x) and AI Behavioral Science's framework for studying AI-human strategic interactions (Jackson et al., 2025).

Cross-Pollination Ideation

Systematic generation of research ideas by finding connections across disciplinary boundaries. Based on the cross-pollination case studies from Woodruff et al. (2026) - where linking Steiner trees to the Kirszbraun Extension Theorem and reframing combinatorics as measure theory led to resolving open problems.

When to use

• Raman asks "what ideas emerge from these papers?" or "give me new research directions"
• A new paper is ingested that uses techniques from a field adjacent to Raman's
• Raman is stuck on a problem and needs a fresh angle
• Exploring whether a technique from one of Raman's topics applies elsewhere
• Enhancing OP3 (Generate new research ideas) from CLAUDE.md

The method

Step 1: Map the technique space

For the source concept or problem, identify:

1. The core mathematical structure: What is the essential abstraction? (e.g., "this is really about finding a fixed point," "this is a convex optimization under constraints," "this is about information asymmetry in a network")
2. The proof/solution techniques used: What tools does the paper deploy? (spectral methods, measure theory, LP duality, potential functions, coupling arguments, etc.)
3. The modeling assumptions: What simplifications does the paper make? Which could be relaxed?

Step 2: Search for analogies

For each core structure identified, search for parallels in Raman's research areas:

Source domain	Target (Raman's domains)	Bridge question
Technique T in field A	Does T apply to network games?	"What if we use T to analyze equilibrium structure on networks?"
Model assumption X	Prospect theory relaxes X	"What happens to the result when agents have biased perceptions?"
Optimization method M	Strategic classification uses similar structure	"Can M give tighter bounds on strategic manipulation?"
Game-theoretic result R	Information design extends R	"What if the principal can design the information environment?"

Key bridges for Raman's program:

• Spectral graph theory <-> Network games: Eigenvalues of the adjacency/Laplacian encode equilibrium structure (Ballester-Calvo-Armengol-Zenou pattern)
• Prospect theory <-> Any game-theoretic model: Replace expected utility with CPT - what changes? (Raman's "Architecture of Illusion" pattern)
• Information design <-> Strategic classification: The principal chooses what information to reveal; the agents best-respond strategically
• Mechanism design <-> Network economics: Design network interventions as mechanisms
• Non-normal matrices <-> Network dynamics: Pseudospectra capture transient behavior that normal analysis misses (Raman's non-normal network games idea)

Step 3: The parameterization test

From Raman's own methodology (the "Architecture of Illusion" pattern):

1. Find the extreme cases: Is paper X the alpha=0 case? Is paper Y the alpha=1 case?
2. Propose the interpolation: What happens for alpha in (0,1)?
3. Check if the interpolation is non-trivial: Does the behavior change qualitatively at some critical alpha*? If so, that's a research contribution.

Examples from Raman's work:

• Risk-neutral (alpha=0) vs fully loss-averse (alpha=1) agents in network games
• Full information (alpha=0) vs no information (alpha=1) in Bayesian persuasion on networks
• Myopic (k=0) vs fully strategic (k=inf) in k-hop awareness models

Step 4: The "obscure theorem" retrieval

This is where AI has a genuine comparative advantage (Woodruff et al., 2026). For the stuck problem:

1. Restate the problem abstractly: Strip away the domain-specific language. What is the pure mathematical structure?
2. Search your knowledge for theorems about that abstract structure from any field:
   • Functional analysis (Stone-Weierstrass, Riesz Representation, Hahn-Banach)
   • Topology (Brouwer, Kakutani, Borsuk-Ulam)
   • Measure theory (Radon-Nikodym, disintegration, optimal transport)
   • Combinatorics (Ramsey, Turan, Lovasz Local Lemma)
   • Information theory (data processing inequality, Fano's inequality)
3. Check if the theorem's conditions are satisfied in Raman's setting
4. If they are: Sketch how the theorem resolves the roadblock

Step 5: The Jackson et al. lens (AI Behavioral Science)

For ideas at the intersection of AI and behavioral/social science:

1. AI as strategic agent: How do AI agents behave in game-theoretic settings? Can we apply behavioral game theory tools (cognitive hierarchy, level-k) to predict AI behavior?
2. AI as tool for behavioral science: Can LLMs simulate participants in network games? Can they predict experimental outcomes in strategic classification settings?
3. Human-AI interaction on networks: How does introducing AI agents into a network game change equilibrium behavior? What are the welfare implications?
4. Information design for AI: How should a principal design information structures when some agents are AI and some are human (heterogeneous rationality)?

Step 6: Quality filter

Before proposing an idea, run these checks:

1. Novelty check: Search the wiki for existing ideas that cover this ground. Search arXiv mentally for whether this has been done.
2. Feasibility check: Can Raman actually prove something here, or is this just hand-waving? What would the first lemma be?
3. Significance check: Does this connect to an existing open question? Does it have implications beyond a technical curiosity?
4. The "why not" test: If this connection is so natural, why hasn't someone done it? (Possible answers: (a) they have and you don't know, (b) there's a technical barrier, (c) the communities don't talk to each other - only (c) is a good sign)

Output format

For each proposed idea:

### Idea: [one-sentence pitch]

**The bridge**: [Source field] -> [Raman's domain]
**The gap**: [What's missing in the literature]
**The key insight**: [Why this connection works]
**First step**: [What the first lemma or result would be]
**Papers it builds on**: [[sources/...]]
**Risk level**: Low (incremental) / Medium (novel combination) / High (speculative)

Propose 3-5 ideas, ranked by feasibility * significance.

Integration with wiki

• Offer to file promising ideas as wiki/ideas/<slug>.md with status seed
• Update relevant topic MOCs with new cross-references
• If the session produces substantial output, file to outputs/research-proposals/
• Log to log.md with op type idea