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Semi-Algebraic Networks: An Attempt to Design Geometric Autopoietic Models

机译：半代数网络：设计几何自生模型的尝试

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摘要

This article focuses on an artificial life approach to some important problems in machine learning such as statistical discrimination, curve approximation, and pattern recognition. We describe a family of models, collectively referred to as semi-algebraic networks (SAN). These models are strongly inspired by two complementary lines of thought: the biological concept of autopoiesis and morphodynamical notions in mathematics. Mathematically defined as semi-algebraic sets, SANs involve geometric components that are submitted to two coupled processes: (a) the adjustment of the components (under the action of the learning examples), and (b) the regeneration of new components. Several examples of SANs are described, using different types of components. The geometric nature of SANs gives new possibilities for solving the bias/variance dilemma in discrimination or curve approximation problems. The question of building multilevel semi-algebraic networks is also addressed, as they are related to cognitive problems such as memory and morphological categorization. We describe an example of such multilevel models.
机译：本文着重介绍一种人工生活方法，以解决机器学习中的一些重要问题，例如统计判别，曲线逼近和模式识别。我们描述了一系列模型，统称为半代数网络（SAN）。这些模型受到两个互补思想的强烈启发：自生的生物学概念和数学中的形态动力学概念。在数学上被定义为半代数集，SAN包含提交给两个耦合过程的几何组件：（a）组件的调整（在学习示例的作用下），以及（b）新组件的再生。使用不同类型的组件描述了SAN的几个示例。 SAN的几何性质为解决歧视或曲线逼近问题中的偏差/方差难题提供了新的可能性。还讨论了构建多层半代数网络的问题，因为它们与诸如记忆和形态分类之类的认知问题有关。我们描述了这种多层次模型的一个例子。

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