Cybernetical Concepts for Cellular Automaton and Artificial Neural Network Modelling and Implementation (2001.02037v3)

Abstract: As a discipline cybernetics has a long and rich history. In its first generation it not only had a worldwide span, in the area of computer modelling, for example, its proponents such as John von Neumann, Stanislaw Ulam, Warren McCulloch and Walter Pitts, also came up with models and methods such as cellular automata and artificial neural networks, which are still the foundation of most modern modelling approaches. At the same time, cybernetics also got the attention of philosophers, such as the Frenchman Gilbert Simondon, who made use of cybernetical concepts in order to establish a metaphysics and a natural philosophy of individuation, giving cybernetics thereby a philosophical interpretation, which he baptised allagmatic. In this paper, we emphasise this allagmatic theory by showing how Simondon's philosophical concepts can be used to formulate a generic computer model or metamodel for complex systems modelling and its implementation in program code, according to generic programming. We also present how the developed allagmatic metamodel is capable of building simple cellular automata and artificial neural networks.

• The paper introduces an allagmatic metamodel that bridges Simondon's cybernetic theory with practical implementations in cellular automata and neural networks.
• It demonstrates the model through CA experiments using Wolfram's rule 110 and feedforward ANN setups with perceptron learning rules.
• The research highlights the potential for philosophical integration to unify deterministic and statistical approaches in complex system modeling.

Overview of Cybernetical Concepts for Cellular Automaton and Artificial Neural Network Modelling

The paper "Cybernetical Concepts for Cellular Automaton and Artificial Neural Network Modelling and Implementation" by Patrik Christen and Olivier Del Fabbro explores the integration of philosophical and cybernetical frameworks to propose a metamodel for complex systems modeling. This research bridges Simondon's allagmatic theory with practical implementations in computer science, particularly focusing on cellular automata (CA) and artificial neural networks (ANN).

The authors elucidate the historical context of cybernetics and its philosophical interpretations, emphasizing the relevance of Gilbert Simondon's concepts. Simondon's approach offers insights into the building blocks of complex systems: structure and operation. These concepts are translated into a generic framework—referred to as the allagmatic metamodel—that serves as a foundation for modeling complex systems in programmatic form.

Philosophical Underpinnings

Simondon's philosophy, which posits that systems consist of structural and operational elements, is foundational to this work. Structure refers to the spatial configuration of system components, while operation denotes the temporal dynamics governing these components. The interrelation between structure and operation forms the basis of systems' behavior, where philosophical constructs are methodically integrated into computational models.

The paper adopts these philosophical constructs to define and implement the allagmatic metamodel. This approach involves representing structure as entities and their connections (milieus) and operation as update functions affecting these entities over time. By employing these abstract concepts, the authors propose a metamodel capable of computing CA and ANN models.

Implementation and Experiments

The practical implementation of the allagmatic metamodel exploits the notion of a metastable system—a transitory phase where structure and operation combine under specific parameters to form a computable model. The authors demonstrate this through the construction of both cellular automata and artificial neural networks.

For cellular automata, a discrete cellular state space with defined local value space and boundary conditions is employed. The research particularly highlights the application of Wolfram's rule 110 to illustrate the CA's generative capability, showcasing procedural adaptation to achieve a target pattern.

Multilayer feedforward artificial neural networks are also constructed within the metamodel framework. Neurons are represented as entities, whereas synaptic weights are incorporated into the milieu matrix. The neural network employs a perceptron learning rule for iterative weight adjustments and activation thresholds, demonstrating the model's adaptability to solve computational tasks.

Implications and Future Prospects

This paper lays groundwork for further philosophical integration in the field of computational modeling through an allagmatic method that adapts and extends classical cybernetic concepts into contemporary computer science. The inclusion of philosophical concepts within programmatic designs underscores a potential shift in meta-modelling approaches, offering a unified theoretical basis for various model types.

Future exploration may delve into cross-model computational translations, leveraging the metamodel to translate simulations between CAs and ANNs. This interoperability could engender advancements in AI interpretability and transparency by combining deterministic and statistical model aspects.

Christen and Del Fabbro's work affirms the potential of philosophical frameworks to inform and guide complex systems modeling, underscoring the relevance of foundational cybernetical concepts as tools for innovative model building in artificial intelligence and beyond. The allagmatic metamodel offers a dynamic and generic foundation upon which myriad complex systems can be systematically developed and explored.