godel-machine

Gödel Machine Skill

"A Gödel Machine can rewrite any part of itself, including the learning algorithm, provided it can first prove that the rewrite is beneficial." — Jürgen Schmidhuber

Overview

The Gödel Machine is a self-improving system that:

1. Contains a formal proof system (e.g., Lean4, Coq)
2. Has a utility function defining "better"
3. Can rewrite any part of itself if it proves the rewrite improves utility
4. The proof constraint prevents reckless self-modification

Core Architecture

┌─────────────────────────────────────────────────────┐
│                  GÖDEL MACHINE                      │
├─────────────────────────────────────────────────────┤
│  ┌─────────────┐    ┌─────────────┐                │
│  │   Policy    │───▶│   Prover    │                │
│  │  (current)  │    │  (verifier) │                │
│  └─────────────┘    └──────┬──────┘                │
│         ▲                   │                       │
│         │            ┌──────▼──────┐                │
│         │            │  Candidate  │                │
│         │            │   Policy    │                │
│         │            └──────┬──────┘                │
│         │                   │                       │
│  ┌──────┴──────┐     ┌──────▼──────┐               │
│  │   Rewrite   │◀────│  Utility    │               │
│  │   if proof  │     │   Check     │               │
│  └─────────────┘     └─────────────┘               │
└─────────────────────────────────────────────────────┘

Darwin Gödel Machine (DGM)

Combines evolutionary search with formal proofs:

class DarwinGodelMachine:
    """
    DGM: Open-ended evolution of self-improving agents.
    
    Archive of agents, LLM-based mutation, fitness evaluation,
    keep if novel and beneficial.
    """
    
    def __init__(self, initial_agent: Agent, prover: TheoremProver):
        self.archive = [initial_agent]
        self.prover = prover
        self.generation = 0
    
    def evolve_step(self) -> Agent:
        # Sample parent from archive (fitness-proportionate)
        parent = self.sample_archive()
        
        # LLM-based mutation
        child = self.llm_mutate(parent)
        
        # Evaluate on benchmarks
        fitness = self.evaluate(child)
        
        # Optionally: verify improvement formally
        if self.prover.can_prove(f"utility({child}) > utility({parent})"):
            child.proven = True
        
        # Add if novel and good
        if self.is_novel(child) and fitness > 0:
            self.archive.append(child)
        
        return child
    
    def llm_mutate(self, agent: Agent) -> Agent:
        """Use LLM to generate improved version."""
        prompt = f"""
        Current agent code:
        {agent.code}
        
        Current fitness: {agent.fitness}
        
        Suggest an improvement to make this agent better.
        Return only the improved code.
        """
        
        new_code = self.llm.generate(prompt)
        return Agent(code=new_code, generation=self.generation + 1)