compression-progress

Compression Progress Skill: Curiosity-Driven Learning

Status: ✅ Production Ready Trit: +1 (PLUS - generator) Color: #D82626 (Red) Principle: Learning = Compression improvement Frame: Compressor improvement rate as reward signal

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Overview

Compression Progress measures the derivative of compression ability over time. When a learner compresses data better than before, that improvement is intrinsic reward—the formal theory of curiosity and creativity.

1. Compressor C(t): Current world model
2. Compression ratio: |C(data)| / |data|
3. Progress: C(t) - C(t-1) improvement
4. Reward: Proportional to progress, not absolute compression

Core Formula

r(t) = |C(t-1)(data)| - |C(t)(data)|

Curiosity reward = compression improvement rate
Boredom = zero progress (already compressed or incompressible)

def compression_progress(compressor_old, compressor_new, data) -> float:
    """Intrinsic reward from model improvement."""
    old_bits = len(compressor_old.compress(data))
    new_bits = len(compressor_new.compress(data))
    return old_bits - new_bits  # positive = learned something

Key Concepts

1. Curiosity as Compression Gradient

class CuriousAgent:
    def __init__(self):
        self.world_model = Compressor()
        self.history = []
    
    def intrinsic_reward(self, observation) -> float:
        old_len = self.world_model.compressed_length(observation)
        self.world_model.update(observation)
        new_len = self.world_model.compressed_length(observation)
        return old_len - new_len  # curiosity signal
    
    def should_explore(self, state) -> bool:
        """Explore where compression progress is expected."""
        return self.expected_progress(state) > self.threshold

2. Creativity as Compression Search

def generate_interesting(compressor) -> Data:
    """Generate data that maximizes expected compression progress."""
    candidates = sample_latent_space()
    return max(candidates, 
               key=lambda x: expected_progress(compressor, x))