Position: Interestingness is an Inductive Heuristic for Future Compression Progress

Vincent Herrmann, Jürgen Schmidhuber
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:170512-170543, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-herrmann26a, title = {Position: Interestingness is an Inductive Heuristic for Future Compression Progress}, author = {Herrmann, Vincent and Schmidhuber, J\"{u}rgen}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {170512--170543}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/herrmann26a/herrmann26a.pdf}, url = {https://proceedings.mlr.press/v306/herrmann26a.html}, 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.} }
Endnote
%0 Conference Paper %T Position: Interestingness is an Inductive Heuristic for Future Compression Progress %A Vincent Herrmann %A Jürgen Schmidhuber %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-herrmann26a %I PMLR %P 170512--170543 %U https://proceedings.mlr.press/v306/herrmann26a.html %V 306 %X 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.
APA
Herrmann, V. & Schmidhuber, J.. (2026). Position: Interestingness is an Inductive Heuristic for Future Compression Progress. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:170512-170543 Available from https://proceedings.mlr.press/v306/herrmann26a.html.

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