复杂性是优势：系统对不同观察者产生差异化的预测误差，从而形成信息优势。
Complexity as Advantage: A Regret-Based Perspective on Emergent Structure
- 从观察者视角定义复杂性，以预测误差衡量系统难易度
- 复杂系统对部分观察者易预测，对另一些则难，形成信息差
- 适用于研究学习、进化与智能体中的涌现行为
我们提出复杂性即优势（CAA）框架，将系统的复杂性定义为相对于一组观察者的相对属性。不同于将复杂性视为内在特性，该框架通过评估不同观察者在建模系统时产生的预测后悔（regret）来衡量复杂性。当某些观察者容易预测而另一些难以预测时，系统即为复杂，由此产生信息优势。该框架统一了多重尺度熵、预测信息和观察者依赖结构等涌现行为概念。研究表明，‘有趣’的系统正是那些能在观察者间制造差异化后悔的系统，为复杂性的功能性价值提供了量化基础。我们通过简单的动力学模型验证了该思想，并讨论其在学习、演化及人工智能体中的意义。
原文摘要 · Abstract (English)
We introduce Complexity as Advantage (CAA), a framework that defines the complexity of a system relative to a family of observers. Instead of measuring complexity as an intrinsic property, we evaluate how much predictive regret a system induces for different observers attempting to model it. A system is complex when it is easy for some observers and hard for others, creating an information advantage. We show that this formulation unifies several notions of emergent behavior, including multiscale entropy, predictive information, and observer-dependent structure. The framework suggests that "interesting" systems are those positioned to create differentiated regret across observers, providing a quantitative grounding for why complexity can be functionally valuable. We demonstrate the idea through simple dynamical models and discuss implications for learning, evolution, and artificial agents.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。