We present a method of generating a collection of neural cellular automata (NCA) to design video game levels. While NCAs have so far only been trained via supervised learning, we present a quality diversity (QD) approach to generating a collection of NCA level generators. By framing the problem as a QD problem, our approach can train diverse level generators, whose output levels vary based on aesthetic or functional criteria. To efficiently generate NCAs, we train generators via Covariance Matrix Adaptation MAP-Elites (CMA-ME), a quality diversity algorithm which specializes in continuous search spaces. We apply our new method to generate level generators for several 2D tile-based games: a maze game, Sokoban, and Zelda. Our results show that CMA-ME can generate small NCAs that are diverse yet capable, often satisfying complex solvability criteria for deterministic agents. We compare against a Compositional Pattern-Producing Network (CPPN) baseline trained to produce diverse collections of generators and show that the NCA representation yields a better exploration of level-space.

We give a simple Sch\"onhage Storage Modification Machine that simulates one iteration of the Rule 110 cellular automaton. This provides an alternative construction to Sch\"onhage's original proof of the Turing completeness of the eponymous machines.

We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models represent a promising direction since they allow the (bottom-up) emergence of complex computational structures from simple rules. In this paper, we propose an abstract machine, called the composition machine, which allows the definition and the execution of such models. Unlike typical abstract machines, our proposal does not compute individual programs but enables the emergence of multiple programs at once. We particularly present the machine's semantics and provide examples to demonstrate its operation with well-known rules from the realm of Boolean logic and elementary cellular automata.

Evolutionary neural architecture search (ENAS) has recently received increasing attention by effectively finding high-quality neural architectures, which however consumes high computational cost by training the architecture encoded by each individual for complete epochs in individual evaluation. Numerous ENAS approaches have been developed to reduce the evaluation cost, but it is often difficult for most of these approaches to achieve high evaluation accuracy. To address this issue, in this paper we propose an accelerated ENAS via multifidelity evaluation termed MFENAS, where the individual evaluation cost is significantly reduced by training the architecture encoded by each individual for only a small number of epochs. The balance between evaluation cost and evaluation accuracy is well maintained by suggesting a multi-fidelity evaluation, which identifies the potentially good individuals that cannot survive from previous generations by integrating multiple evaluations under different numbers of training epochs. For high diversity of neural architectures, a population initialization strategy is devised to produce different neural architectures varying from ResNet-like architectures to Inception-like ones. Experimental results on CIFAR-10 show that the architecture obtained by the proposed MFENAS achieves a 2.39% test error rate at the cost of only 0.6 GPU days on one NVIDIA 2080TI GPU, demonstrating the superiority of the proposed MFENAS over state-of-the-art NAS approaches in terms of both computational cost and architecture quality. The architecture obtained by the proposed MFENAS is then transferred to CIFAR-100 and ImageNet, which also exhibits competitive performance to the architectures obtained by existing NAS approaches. The source code of the proposed MFENAS is available at https://github.com/DevilYangS/MFENAS/.

In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method is based on classifying the asymptotic behavior of the average computation time in a given system before entering a loop. We were able to identify a critical region of behavior that corresponds to a phase transition from ordered behavior to chaos across various classes of dynamical systems. To show that our approach can be applied to many different computational systems, we demonstrate the results of classifying cellular automata, Turing machines, and random Boolean networks. Further, we use this method to classify 2D cellular automata to automatically find those with interesting, complex dynamics. We believe that our work can be used to design systems in which complex structures emerge. Also, it can be used to compare various versions of existing attempts to model open-ended evolution (Ray (1991), Ofria et al. (2004), Channon (2006)).

The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the ability of automata to emulate one another, and we use this notion to define such a set of naturally emerging tasks. We present the results for elementary cellular automata, although the core ideas can be extended to other computational systems. We compute a graph showing which elementary cellular automata can be emulated by which and show that certain chaotic automata are the only ones that cannot emulate any automata non-trivially. Finally, we use the emulation notion to suggest a novel definition of chaos that we believe is suitable for discrete computational systems. We believe our work can help design parallel computational systems that are Turing-complete and also computationally efficient.

This paper is both an introduction and an invitation. It is an introduction to CARLE, a Life-like cellular automata simulator and reinforcement learning environment. It is also an invitation to Carle's Game, a challenge in open-ended machine exploration and creativity. Inducing machine agents to excel at creating interesting patterns across multiple cellular automata universes is a substantial challenge, and approaching this challenge is likely to require contributions from the fields of artificial life, AI, machine learning, and complexity, at multiple levels of interest. Carle's Game is based on machine agent interaction with CARLE, a Cellular Automata Reinforcement Learning Environment. CARLE is flexible, capable of simulating any of the 262,144 different rules defining Life-like cellular automaton universes. CARLE is also fast and can simulate automata universes at a rate of tens of thousands of steps per second through a combination of vectorization and GPU acceleration. Finally, CARLE is simple. Compared to high-fidelity physics simulators and video games designed for human players, CARLE's two-dimensional grid world offers a discrete, deterministic, and atomic universal playground, despite its complexity. In combination with CARLE, Carle's Game offers an initial set of agent policies, learning and meta-learning algorithms, and reward wrappers that can be tailored to encourage exploration or specific tasks.

Differentiable Architecture Search (DARTS) is a recently proposed neural architecture search (NAS) method based on a differentiable relaxation. Due to its success, numerous variants analyzing and improving parts of the DARTS framework have recently been proposed. By considering the problem as a constrained bilevel optimization, we propose and analyze three improvements to architectural weight competition, update scheduling, and regularization towards discretization. First, we introduce a new approach to the activation of architecture weights, which prevents confounding competition within an edge and allows for fair comparison across edges to aid in discretization. Next, we propose a dynamic schedule based on per-minibatch network information to make architecture updates more informed. Finally, we consider two regularizations, based on proximity to discretization and the Alternating Directions Method of Multipliers (ADMM) algorithm, to promote early discretization. Our results show that this new activation scheme reduces final architecture size and the regularizations improve reliability in search results while maintaining comparable performance to state-of-the-art in NAS, especially when used with our new dynamic informed schedule.

Reaction-Diffusion (RD) systems provide a computational framework that governs many pattern formation processes in nature. Current RD system design practices boil down to trial-and-error parameter search. We propose a differentiable optimization method for learning the RD system parameters to perform example-based texture synthesis on a 2D plane. We do this by representing the RD system as a variant of Neural Cellular Automata and using task-specific differentiable loss functions. RD systems generated by our method exhibit robust, non-trivial 'life-like' behavior.

This article reviews recent progress in the development of the computing framework Vector Symbolic Architectures (also known as Hyperdimensional Computing). This framework is well suited for implementation in stochastic, nanoscale hardware and it naturally expresses the types of cognitive operations required for Artificial Intelligence (AI). We demonstrate in this article that the ring-like algebraic structure of Vector Symbolic Architectures offers simple but powerful operations on high-dimensional vectors that can support all data structures and manipulations relevant in modern computing. In addition, we illustrate the distinguishing feature of Vector Symbolic Architectures, "computing in superposition," which sets it apart from conventional computing. This latter property opens the door to efficient solutions to the difficult combinatorial search problems inherent in AI applications. Vector Symbolic Architectures are Turing complete, as we show, and we see them acting as a framework for computing with distributed representations in myriad AI settings. This paper serves as a reference for computer architects by illustrating techniques and philosophy of VSAs for distributed computing and relevance to emerging computing hardware, such as neuromorphic computing.