Position: Interestingness is an Inductive Heuristic for Future Compression Progress

Vincent Herrmann, Jürgen Schmidhuber

TL;DR: The interestingness of an object is the expected compression progress under further engagement; it is exponentially determined by the recency of the last progress.

Abstract: This position paper argues one of the bottlenecks on the way towards recursively self-improving systems is the challenge of *interestingness*: the ability to prospectively identify which tasks or data hold the potential for future progress. We formalize interestingness as an inductive heuristic for future compression progress and investigate its predictability using tools from Kolmogorov Complexity and Algorithmic Statistics. By analyzing complexity-runtime profiles under Length, Algorithmic, and Speed priors, we demonstrate that the *inductive property of interestingness*—the capacity for past progress to signal future discovery—is theoretically viable and empirically supported. We prove that expected future progress depends exponentially on the recency of the last observed breakthrough. Furthermore, we show that the Algorithmic Prior is significantly more optimistic than the Length Prior, yielding a quadratic increase in expected discovery for the same observed profile. These findings are experimentally validated across three diverse universal computational paradigms.

Lay Summary: We argue that artificial intelligence systems pursuing open-ended, creative tasks face a fundamental challenge: determining what is *interesting*—i.e., what is worthwhile or promising to do when there is no direct outside feedback. We define the "interestingness" of an object (like new piece of data) as the amount of insight we expect to gain by exploring it further. But can we actually predict how much is left to learn based purely on our past learning progress? As it turns out, yes! Under natural assumptions, we prove that what matters most is the *recency of progress*. If we uncovered an insight recently, we are much more likely to find another one soon. We show this principle also through a series of experiments.

Primary Area: Other topic (use sparingly and specify relevant keywords)

Keywords: Open-Ended Learning, Algorithmic Information Theory, Intrinsic Motivation

Submission Number: 1008