| Abstract: |
| In this talk, we present an extension of the traditional concept of cellular automata (CAs) by broadening the range of possible states. This new framework is inspired by the need to establish dynamics on random graphs. We propose that the state space consists of all probability measures defined over a fundamental alphabet A. This definition simplifies to the classical notion of cellular automata when we use Dirac probability measures for individual elements of the alphabet.
We will discuss several results related to the convergence of these generalized cellular automata, particularly under specific conditions on the transition map. Additionally, we will provide various examples to illustrate how this extended approach can be applied in different scenarios. Furthermore, we will explore how cellular automata can be utilized to enhance the explainability of machine learning training processes. This talk aims to enhance our understanding of cellular automata while exploring their potential applications in complex systems. |
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