用压缩进展预测未来突破，发现越近的突破越可能带来新进展
Interestingness as an Inductive Heuristic for Future Compression Progress
- 将有趣性定义为未来压缩进步的归纳启发，基于算法复杂度理论建模
- 过去突破越近，未来预期进展呈指数增长，算法先验比长度先验更乐观
- 在三种通用计算范式中验证了该方法的有效性，适合研究自进化系统的学者
通往递归自进化系统的一大瓶颈在于“有趣性”：即前瞻性识别哪些任务或数据具有未来进展潜力的能力。本文将有趣性形式化为未来压缩进展的归纳启发，并运用柯尔莫哥洛夫复杂度与算法统计学工具进行分析。通过考察在长度、算法和速度先验下的复杂度-运行时间分布，证明了有趣性的归纳特性——过去进展能预示未来发现——在理论上可行且经实验支持。我们证明，预期未来进展随最近一次突破的时效呈指数依赖；此外，算法先验显著优于长度先验，在相同观测模式下使预期发现实现二次增长。这些发现已在三种不同通用计算范式中得到实验验证。
原文摘要 · Abstract (English)
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 confirmed across three diverse universal computational paradigms.
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