Semi-algebraic networks: an attempt to design geometric autopoietic models

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 ...