Interestingness as an Inductive Heuristic for Futur... | AI Research

Interestingness as an Inductive Heuristic for Future Compression Progress
This paper addresses a fundamental challenge in creating autonomous, self-improving AI systems: how to identify which tasks or data are worth learning. To achieve true open-ended progress, an AI must be able to prospectively choose its own learning goals without human intervention. The authors propose that "interestingness" can be formalized as an inductive heuristic—a way to predict future compression progress based on the trajectory of past discoveries. By using tools from Algorithmic Information Theory, the research provides a theoretical and empirical framework for determining whether a new piece of information will lead to meaningful insight or simply represent noise.

Defining Interestingness as Compression

The authors argue that a system is truly learning when it can compress its data more efficiently. In this view, an object is "interesting" if it allows the system to reduce the total size of its internal model plus the remaining data. Unlike post-hoc measures that only evaluate learning after the fact, this approach focuses on the potential for future breakthroughs. The researchers analyze how a system’s "complexity-runtime profile"—the relationship between the computational effort spent and the resulting reduction in description length—can signal whether further study of a specific task will yield new, learnable structure.

The Predictability of Discovery

A key finding of the paper is that the likelihood of future compression progress is not random; it is statistically linked to the history of the system's progress. The authors prove that the probability of achieving a new "compression drop" decreases exponentially as the time since the last breakthrough increases. This suggests that stagnation is a strong indicator of a dead end. By analyzing different mathematical priors—specifically the Length, Algorithmic, and Speed priors—the researchers demonstrate that the Algorithmic Prior is significantly more optimistic, predicting a quadratic increase in expected discovery compared to the standard Length Prior.

Empirical Validation

To ensure these theoretical findings hold in practice, the authors tested their framework across three different universal computational paradigms: 2-Tag systems, Rule 110 cellular automata, and the Brainfuck programming language. These diverse environments confirmed that the theoretical trends regarding complexity and runtime profiles are consistent in physically realizable regimes. This validation supports the idea that the inductive property of interestingness—using past progress to forecast future discovery—is a viable strategy for guiding autonomous, self-improving intelligence.

Important Considerations

The authors note that while this framework provides a rigorous way to quantify potential progress, it remains a challenge to implement in real-world systems. Because evaluating "interestingness" requires computational effort, a system must be able to predict the value of a task before fully committing to it. The paper acknowledges that meta-cognitive properties like curiosity are difficult to learn due to the non-stationary nature of learning, the high cost of obtaining ground-truth labels, and the difficulty of assigning credit to specific data points. Despite these hurdles, the research establishes a stable, algorithmic foundation for building systems that can autonomously navigate their own learning frontiers.