In this paper we propose an approach for measuring growth of complexity of emerging patterns in complex systems such as cellular automata. We discuss several ways how a metric for measuring the complexity growth can be defined. This includes approaches based on compression algorithms and artificial neural networks. We believe such a metric can be useful for designing systems that could exhibit open-ended evolution, which itself might be a prerequisite for development of general artificial intelligence. We conduct experiments on 1D and 2D grid worlds and demonstrate that using the proposed metric we can automatically construct computational models with emerging properties similar to those found in the Conway's Game of Life, as well as many other emergent phenomena. Interestingly, some of the patterns we observe resemble forms of artificial life. Our metric of structural complexity growth can be applied to a wide range of complex systems, as it is not limited to cellular automata.

Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for enough computational capacity. Understanding complex computations happening in cellular automata and other systems capable of emergence poses many challenges, especially in large-scale systems. We propose methods for coarse-graining cellular automata based on frequency analysis of cell states, clustering and autoencoders. These innovative techniques facilitate the discovery of large-scale structure formation and complexity analysis in those systems. They emphasize interesting behaviors in elementary cellular automata while filtering out background patterns. Moreover, our methods reduce large 2D automata to smaller sizes and enable identifying systems that behave interestingly at multiple scales.

It is common to evaluate the performance of a machine learning model by measuring its predictive power on a test dataset. This approach favors complicated models that can smoothly fit complex functions and generalize well from training data points. Although essential components of intelligence, speed and data efficiency of this learning process are rarely reported or compared between different candidate models. In this paper, we introduce a benchmark of increasingly difficult tasks together with a data efficiency metric to measure how quickly machine learning models learn from training data. We compare the learning speed of some established sequential supervised models, such as RNNs, LSTMs, or Transformers, with relatively less known alternative models based on reservoir computing. The proposed tasks require a wide range of computational primitives, such as memory or the ability to compute Boolean functions, to be effectively solved. Surprisingly, we observe that reservoir computing systems that rely on dynamically evolving feature maps learn faster than fully supervised methods trained with stochastic gradient optimization while achieving comparable accuracy scores. The code, benchmark, trained models, and results to reproduce our experiments are available at https://github.com/hugcis/benchmark_learning_efficiency/.

No abstract