论文标题
多项式生活：自适应系统的结构
Polynomial Life: the Structure of Adaptive Systems
论文作者
论文摘要
我们扩展了关于控制论系统的组成结构的早期工作，以说明此类系统的体现。他们所有的相互作用都通过身体的边界进行：感觉在其表面上影响，而动作与配置的变化相对应。我们使用多项式函子正式化了这种形态学的观点。显示系统的“内部宇宙”构成了多项式统计游戏的索引类别。它们的动态形成了行为的索引类别。我们将“主动推论学说”描述为此类类别之间的索引函子，解决了早期工作中的许多开放问题，并指出“自由能原理”的形式化是此类学说的伴随。我们通过生物学的基本例子（包括体内平衡，形态发生和自动烟雾）来说明我们的框架，并提出空间导航与证明过程之间的正式联系。
We extend our earlier work on the compositional structure of cybernetic systems in order to account for the embodiment of such systems. All their interactions proceed through their bodies' boundaries: sensations impinge on their surfaces, and actions correspond to changes in their configurations. We formalize this morphological perspective using polynomial functors. The 'internal universes' of systems are shown to constitute an indexed category of statistical games over polynomials; their dynamics form an indexed category of behaviours. We characterize 'active inference doctrines' as indexed functors between such categories, resolving a number of open problems in our earlier work, and pointing to a formalization of the 'free energy principle' as adjoint to such doctrines. We illustrate our framework through fundamental examples from biology, including homeostasis, morphogenesis, and autopoiesis, and suggest a formal connection between spatial navigation and the process of proof.
