[Paper Review] Driven by Compression Progress: A Simple Principle Explains Essential Aspects of Subjective Beauty, Novelty, Surprise, Interestingness, Attention, Curiosity, Creativity, Art, Science, Music, Jokes

Jürgen Schmidhuber|ArXiv.org|Dec 23, 2008

Leadership, Courage, and Heroism Studies3 citations

TL;DR

This paper proposes that subjective beauty, curiosity, creativity, and attention arise from a drive to maximize compression progress—improving one's ability to predict and compress sensory data. By treating compression progress as intrinsic reward, the framework explains diverse phenomena from art and music to scientific discovery and humor through a unified principle of learning-driven subjective interestingness.

ABSTRACT

I argue that data becomes temporarily interesting by itself to some self-improving, but computationally limited, subjective observer once he learns to predict or compress the data in a better way, thus making it subjectively simpler and more beautiful. Curiosity is the desire to create or discover more non-random, non-arbitrary, regular data that is novel and surprising not in the traditional sense of Boltzmann and Shannon but in the sense that it allows for compression progress because its regularity was not yet known. This drive maximizes interestingness, the first derivative of subjective beauty or compressibility, that is, the steepness of the learning curve. It motivates exploring infants, pure mathematicians, composers, artists, dancers, comedians, yourself, and (since 1990) artificial systems.

Motivation & Objective

• To explain why certain stimuli are perceived as beautiful, surprising, or interesting through a single principle: compression progress.
• To formalize curiosity as the intrinsic drive to discover novel regularities that allow for improved data compression.
• To unify diverse phenomena—art, science, music, jokes—under a common computational framework based on learning and prediction.
• To provide a computationally grounded, self-improving mechanism for artificial agents to explore and learn without external reward.
• To demonstrate that subjective beauty and interestingness emerge naturally from the first derivative of compressibility over time.

Proposed method

• Formalize subjective beauty as the degree of compressibility of sensory data using algorithmic information theory.
• Define intrinsic curiosity reward as the rate of improvement in prediction accuracy or compression efficiency over time.
• Use a reinforcement learning framework where agents are rewarded not for external outcomes but for discovering new regularities that reduce data complexity.
• Model compression progress as the change in the length of the shortest program describing observed data, with reward proportional to this improvement.
• Implement the framework using predictors or compressors that update their internal models based on new observations, with reward tied to performance gain.
• Apply the framework to artificial agents, showing how it drives active exploration, attention allocation, and creative behavior.

Experimental results

Research questions

• RQ1 How can subjective beauty and interestingness be formally defined in terms of data compression?
• RQ2 Why do humans and artificial agents find certain patterns surprising or beautiful while others are ignored?
• RQ3 What is the computational mechanism underlying curiosity and attention in learning systems?
• RQ4 How can creativity and artistic expression emerge from a drive to improve data compression?
• RQ5 Can the same principle explain diverse phenomena like music, jokes, scientific discovery, and visual art?

Key findings

• Subjective beauty arises from the current level of compressibility of data, with higher compressibility perceived as more beautiful.
• Subjective interestingness is defined as the first derivative of compressibility—the rate of improvement in prediction or compression performance.
• Curiosity emerges naturally as the drive to maximize compression progress, leading to active exploration even without external rewards.
• Art, music, and jokes are by-products of the compression progress drive, as they exploit novel regularities that allow for efficient encoding.
• The framework explains why humans and artificial agents focus attention on stimuli that promise new, non-arbitrary regularities.
• The model provides a mathematically rigorous, self-referential framework (via Gödel machines) for optimal self-improvement in learning agents.