Canonical Computations in Cellular Automata and Their Application for Reservoir Computing

Abstract

Cellular Automata (CAs) have potential as powerful parallel computational systems, which has lead to the use of CAs as reservoirs in reservoir computing. However, why certain Cellular Automaton (CA) rules, sizes and input encodings are better or worse at a given task is not well understood. We present a method that enables identification and visualization of the specific information content, flow and transformations within the space-time diagram of CA. We interpret each spatio-temporal location in CA’s space-time diagram as a function of its input and call this novel notion the CA’s Canonical Computations (CCs). This allows us to analyze the available information from the space-time diagrams as partitions of the input set. The method also reveals how input-encoder-rule interactions transform the information flow by changing features like spatial and temporal location stability as well as the specific information produced. This general approach for analysing CA is discussed for the engineering of reservoir computing systems.