Elementary cellular automata (ECAs) generate critical spacetime patterns in a few local rules, which are expected to have advantages in reservoir computing (RC). However, previous studies have not revealed the advantages of critical spacetime patterns in RC. In this paper, we focus on the distractor’s length in the time series data for learning and clarify the advantages of the critical spacetime patterns. Furthermore, we propose asynchronously tuned ECAs (AT_ECAs) to generate universally critical spacetime patterns in many local rules. Based on the results achieved in this study, we propose RC based on AT_ECAs. Moreover, we show that the universal criticality of AT_ECAs is effective for learning time series data.
The internal description of spacetime can reveal ambiguity regarding an observer's perception of the present, where an observer can refer to the present as if he were outside spacetime while actually existing in the present. This ambiguity can be expressed as the compatibility between an element and a set, and is here called a/{a}-compatibility. We describe a causal set as a lattice and a causal history as a quotient lattice, and implement the a/{a}-compatibility in the framework of a causal histories approach. This leads to a perpetual change of a pair of causal set and causal history, and can be used to describe subjective spacetime including the déjà vu experience and/or schizophrenic time.
In this paper, we propose asynchronously tuned elementary cellular automata (AT_ECA) as models that implement a new type of selforganized criticality (SOC). SOC in AT_ECA is based on asynchronously updating and locally tuning the consistency between dual modes of transition. A previous work showed that AT_ECA generate class 4-like spacetime patterns over a wide area of the rule space, and the density decay follows a power law for some of the rules. In this study, we performed a spectral analysis of AT_ECA, of which a great number of rules were found to exhibit 1 f noise, suggesting that AT_ECA realize critical states without selecting specific rules or finetuning parameters.
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