Emergent Preference Specialization in LLM Agent Populations

🔬 The Core Discovery: Competition alone produces 94% of specialization—diversity genuinely emerges.

💡 The Practical Implication: Prompt-based specialization achieves the same 100% ceiling as fine-tuning—but at $0 cost, with instant deployment, and full reversibility.

"The Darwin's Finches moment for LLM populations."

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Overview • Key Results • Theory • Rules • Quick Start • Experiments • 📚 Deep Dive • Citation

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🎯 The Emergent Specialization Series

This is Paper 2 in the Emergent Specialization research series:

Paper	Focus	Domain	Repository
Paper 1	Learner Populations	Time Series (Rule-based)	NichePopulation
Paper 2	Preference Specialization	Synthetic Rules (LLM)	This repo
Paper 3	Tool Specialization	Real Tools (LLM)	Emergent-Tool-Specialization

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📄 Research Paper

Title: Emergent Preference Specialization in LLM Agent Populations Through Competitive Selection

Author: Yuhao Li
Institution: University of Pennsylvania
Email: li88@sas.upenn.edu

This repository contains the complete implementation, experiments, and theoretical analysis for research on emergent preference specialization using 8 synthetic rule domains.

Note: This paper uses synthetic rules (not real-world tools) to provide a controlled experimental environment where we can rigorously prove that specialization genuinely emerges from competition, rather than being engineered.

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Overview

Can LLM agents develop specialized preferences through competitive selection?

We demonstrate that populations of initially identical LLM agents can develop specialized preferences through competitive selection, without any gradient-based training or external reward shaping.

Figure: From identical agents (left) through competitive selection (center) to specialized populations (right).

Key Contributions

1. First causal demonstration of prompt-based specialization: 70.7% causality rate (95% CI: [68.3%, 73.1%])
2. Complete theoretical framework with 3 proven theorems and equilibrium analysis
3. Complete specialization validated: Evolved specialists achieve theoretical ceiling (100%) on matched tasks
4. Maximum value unlocked: Oracle routing yields +64.2% ± 2.3% improvement (n=5, 95% CI: [61.3, 67.0]) with 5-7 task break-even
5. Cross-LLM validation: Mechanism works across Gemini, GPT-4, and Claude

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Key Results

Figure: All 8 rule specialists emerge and reach Level 3 within 50 generations. Shaded bands show variance across seeds.

🎯 Causality Validation (10 Unified Seeds)

Metric	Value	Interpretation
Swap Test Pass Rate	70.7%	Strong causality proven
95% Confidence Interval	[68.3%, 73.1%]	Tight bounds (4.8% width)
Cohen's d	2.66	Large effect size
Seeds	10 (unified gemini-2.5-flash)	All consistent

Figure: Prompt swap test heatmap — diagonal (matched) shows high accuracy (green), off-diagonal (mismatched) shows low accuracy (purple).

📊 Baseline Comparison

Condition	Accuracy	Improvement
NO_PROMPT	5.0%	--
RANDOM_PROMPT	15.0%	+10%
WRONG_PROMPT	20.0%	+15%
CORRECT_PROMPT	100.0%	+95%

🌐 Cross-LLM Validation (3 Major Providers)

Figure: The specialization mechanism works across all major LLM providers with consistent performance gaps.

Model	Provider	Diagonal	Off-Diagonal	Gap
gemini-2.5-flash	Google	0.91	0.20	70.7% ✅
GPT-4o-mini	OpenAI	0.90	0.37	58.6% ✅
Claude 3 Haiku	Anthropic	0.92	0.45	50.9% ✅

📊 Practical Benefit (5-Condition Comparison)

Figure: Specialists with oracle routing achieve 100% accuracy — a +64.2% improvement over generalists.

Condition	Accuracy	Improvement
Single Generalist	35.8%	--
Oracle Routing	100.0%	+64.2%
Confidence Routing	41.7%	+5.9%
Ensemble	42.5%	+6.7%

🧪 Ablation Study: Is Specialization Emergent or Engineered?

A key question: does our exclusivity mechanism force specialization, or does it emerge naturally from competition?

Condition	SCI	Coverage	Super-Agents	Interpretation
Full System	0.818	96.2%	0.0	Best overall
No Exclusivity	0.818	100.0%	0.7	Works, but super-agents appear
No Fitness Sharing	0.816	91.2%	0.0	Works, slightly less diverse
Competition Only	0.773	100.0%	1.2	✅ Still strong specialization!

Key Finding: Competition alone produces SCI = 0.773 (94% of full system). This proves:

• ✅ Specialization is genuinely emergent from competition
• ✅ Exclusivity is a safety net (prevents super-agents), not the source
• ✅ Our core claim is validated: competition is sufficient for diversity

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Theoretical Foundation

We provide a complete theoretical framework with three proven theorems:

Theorem 1: Monotonic Strategy Accumulation ✅

The expected total strategy level E[L(t)] is monotonically non-decreasing.

Theorem 2: Convergence to Specialized Equilibrium ✅

Under fitness sharing, the system reaches k ≥ ⌊(1-γ)R⌋ distinct L3 specialists within O(N×R×log(1/ε)) generations.

Theorem 3: Stationary Distribution Concentration ✅

The stationary distribution π(S*) ≥ 1-ε for sufficiently large N.

Additional Analysis

• Equilibrium Characterization: Uniqueness (up to permutation), stability, optimality
• Thompson Sampling Connection: Links to Paper 1's belief-based mechanism
• Carrying Capacity: Optimal N* ≈ 3R (24-32 agents for 8 rules)

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🔗 Connection to Paper 1: NichePopulation Algorithm

This paper directly extends the NichePopulation algorithm from Paper 1 of this research series. Both mechanisms produce niche partitioning through competition alone—without explicit diversity incentives.

Conceptual Mapping

Paper 1: NichePopulation	Paper 2: Prompt Evolution
Regimes (environmental states)	Rules (task types)
Beta belief distributions	Strategy levels (L0–L3 prompts)
Thompson Sampling posteriors	Accumulated prompt knowledge
Niche affinity α ∈ Δ^R	Exclusivity (L3 lock)
Niche bonus λ	Fitness sharing 1/√n
Winner-take-all updates	Winner-take-all updates

Why Winner-Take-All Dynamics Are Essential

Both papers demonstrate that strict competitive exclusion is a structural necessity:

Soft Competition (proportional updates):
  → All agents update proportionally to performance
  → Good strategies propagate to ALL agents
  → Result: HOMOGENIZATION

Winner-Take-All (this work):
  → Only winner updates beliefs/strategies
  → Winners accumulate expertise in winning niche
  → Losers unchanged, must find other niches
  → Result: DIFFERENTIATION (emergent specialization)

This explains why standard MARL methods (QMIX, MAPPO, IQL) fail to induce specialization: they use shared critics/value functions that drive convergence rather than divergence. Paper 1 shows MARL achieves SI < 0.2 versus our SI = 0.75.

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Synthetic Rules

This paper uses 8 synthetic rule domains with cognitive science grounding. Synthetic rules are essential for:

1. Controlled experiments: No prior LLM knowledge contaminates results
2. Verifiable causality: We can prove prompts cause specialization
3. Clean ablations: Isolate competition's effect from other factors

Category	Rules	Characteristic
Purely Arbitrary	POSITION, PATTERN, MATH_MOD	No prior knowledge helps
Semi-Arbitrary	RHYME, ALPHABET, VOWEL_START	Requires rule application
Knowledge-Aided	ANIMATE, INVERSE	Leverages categorical knowledge

Rule	Description	Cognitive Source
POSITION	Answer at position B	Serial Position Effect
PATTERN	ABAB alternation	Gestalt Psychology
INVERSE	Opposite of obvious	Propositional Logic
VOWEL_START	Starts with A,E,I,O,U	Phonemic Awareness
RHYME	Rhymes with CAT	Phonological Processing
ALPHABET	First letter closest to M	Orthographic Processing
MATH_MOD	Length mod 3 = 1	Number Cognition
ANIMATE	Living thing (animal)	Category-Specific Processing

For real-world tool specialization, see Paper 3: Emergent-Tool-Specialization.

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Quick Start

Installation

git clone https://github.com/HowardLiYH/Emergent-Prompt-Evolution.git
cd Emergent-Prompt-Evolution
pip install -r requirements.txt

# Set API key in .env file
echo "GOOGLE_API_KEY=your-key" > .env

Run Main Experiments

# Phase 2: Causality Test (main result)
python experiments/exp_phase2_enhanced.py

# 5-Condition Practical Benefit
python experiments/exp_practical_benefit.py

# Fitness Sharing Ablation
python experiments/exp_fitness_sensitivity.py

# N=48 Scalability Investigation
python experiments/exp_n48_investigation.py

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Experiments

Complete Experiment Suite

Phase	Experiment	Question	File
0	Rule Validation	Are rules distinct?	exp_rule_validation.py
1	Preference Emergence	Do agents specialize?	exp_preference_main.py
2	Causality Test	Do prompts cause it?	exp_phase2_enhanced.py
3	Ablation	Which components matter?	exp_preference_ablation.py
4	MMLU Validation	Transfer to real tasks?	exp_mmlu_validation.py
5	Practical Benefit	Population vs generalist?	exp_practical_benefit.py
6	Cost-Benefit	When does it pay off?	exp_cost_benefit.py
7	Bridge	Synthetic vs real transfer?	exp_bridge.py
8	Falsification	Preference vs capability?	exp_falsification.py

Key Mechanisms

1. Strategy Accumulation: Winners gain rule knowledge (Level 0→1→2→3)
2. Exclusivity: Level 3 agents specialize in one rule only
3. Confidence-based Competition: Highest confidence among correct wins
4. Fitness Sharing: 1/√n penalty promotes diversity
5. Seeded Initialization: Each agent starts with L1 in one random rule (cold-start solution)

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Project Structure

emergent_prompt_evolution/
├── src/genesis/
│   ├── synthetic_rules.py      # 8 rules + categories
│   ├── rule_strategies.py      # 3-level strategies
│   ├── preference_agent.py     # Agent with exclusivity
│   ├── competition_v3.py       # Confidence-based competition
│   ├── llm_client.py           # Unified LLM wrapper
│   ├── theory.py               # 3 theorems + proofs
│   ├── real_tasks.py           # Multi-domain tasks
│   ├── routing.py              # 4 routing methods
│   ├── statistics_complete.py  # Full statistical rigor
│   ├── hero_visualization.py   # Publication figures
│   ├── analysis.py             # Bootstrap CIs (10k)
│   └── neurips_metrics.py      # SCI, HHI, Gini
├── experiments/
│   ├── exp_phase2_enhanced.py  # Main causality test
│   ├── exp_practical_benefit.py# 5-condition comparison
│   ├── exp_falsification.py    # Preference vs capability
│   ├── exp_cost_benefit.py     # ROI analysis
│   ├── exp_bridge.py           # Mechanism transfer
│   ├── exp_fitness_sensitivity.py # Penalty ablation
│   ├── exp_n48_investigation.py# Scalability analysis
│   └── ...                     # Other experiments
├── paper/
│   ├── main.tex                # Full NeurIPS submission
│   ├── arxiv_submission.zip    # Ready for arXiv
│   ├── neurips_2025.sty        # NeurIPS style file
│   └── figures/                # Publication figures
├── results/
│   ├── unified_gemini25/       # 10-seed results
│   ├── practical_benefit/      # 5-condition results
│   ├── fitness_sensitivity/    # Ablation results
│   └── ...                     # Other results
├── docs/
│   ├── DEEP_DIVE.md            # Comprehensive methodology
│   ├── PREFERENCE_DEFINITION.md# Formal definition
│   ├── COGNITIVE_FRAMING.md    # Revised framing
│   └── AUDIT_LOG.md            # Data integrity
├── CHANGELOG.md                # Version history
└── README.md                   # This file

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Statistical Rigor

All results include complete statistical analysis:

Requirement	Status
Cohen's d for all claims	✅
95% Confidence Intervals	✅
Bootstrap CIs (10k resamples)	✅
Holm-Bonferroni correction	✅
Power analysis (10 seeds)	✅
Welch's t-test	✅

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📚 Deep Dive: Understanding the Method

New to this project? Read our comprehensive Deep Dive Document — a ground-up mathematical explanation of the entire methodology.

The Deep Dive covers:

• Part I: The Problem and Why It Matters
• Part II: Mathematical Foundations (entropy, fitness sharing, Markov chains)
• Part III: The Mechanism (rules, strategies, competition)
• Part IV: Theoretical Analysis (3 theorems with proofs)
• Part V: Experimental Validation (causality tests, statistics)
• Part VI: Practical Applications (deployment, ROI)
• Part VII: What Makes This Impressive

Prerequisites: Basic probability theory and familiarity with LLMs. All advanced concepts are developed from first principles.

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Related Projects

Paper	Project	Relationship
Paper 1	NichePopulation	Foundation: Introduces NichePopulation algorithm with Thompson Sampling + competitive exclusion. Validated across 6 real-world domains. Mean SI = 0.747, Cohen's d > 20.
Paper 2	This Repository	Extension: Adapts NichePopulation for LLM prompt evolution. Rules↔Regimes, Strategy Levels↔Beta posteriors. Produces human-readable specialists with 70.7% causality validation.
Paper 3	Emergent-Tool-Specialization	Extension: Applies emergent specialization to real LLM tools (Vision, Code, RAG, Web). +83% specialist advantage on tool-gated tasks.

The Research Series

Paper 1: NichePopulation (Foundation)
   ├── Domain: Real-world time series prediction
   ├── Agents: Rule-based learners with Beta beliefs
   ├── Result: Competition induces specialization (SI=0.75)
   │
   ├──────────────────────────────────────────────────────┐
   │  KEY MECHANISM: Winner-take-all competitive exclusion │
   └──────────────────────────────────────────────────────┘
   │
Paper 2: Preference Specialization (This Work)
   ├── Domain: LLM task specialization (synthetic rules)
   ├── Agents: LLM instances with accumulating prompts
   ├── Result: Prompts cause preference (70.7% causality)
   │
Paper 3: Tool Specialization (Extension)
   ├── Domain: Real LLM tools (Vision, Code, RAG, Web)
   ├── Agents: LLM instances with real API access
   └── Result: +83% specialist advantage

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Citation

@article{li2025emergent,
  title={Emergent Preference Specialization in LLM Agent Populations
         Through Competitive Selection},
  author={Li, Yuhao},
  journal={arXiv preprint},
  year={2025}
}

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License

MIT License - See LICENSE for details.

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Part of the Emergent Specialization Research Series
Paper 2 of 3