Google Team Publish Paper on Differentiable Logic Of Cellular Automata That Learn Complex Patterns with Neural Networks

Differentiable Logic Cellular Automata successfully learns recurrent circuits and generates complex patterns including Conway’s Game of Life, resilient checkerboards, and a lizard shape. Combining differentiable logic gates with neural cellular automata enables gradient-based training while maintaining discrete state operation and demonstrating robustness to perturbations.

The capacity for systems to learn and adapt while retaining the reliability of deterministic computation remains a significant challenge in artificial intelligence. Researchers are now exploring architectures that bridge the gap between the flexibility of neural networks and the precision of logical operations. A team from Google’s Paradigms of Intelligence, comprising Pietro Miotti, Eyvind Niklasson, Ettore Randazzo, and Alexander Mordvintsev, detail their work in ‘Differentiable Logic Cellular Automata: From Game of Life to Pattern Generation’, presenting a novel approach that combines Neural Cellular Automata with Differentiable Logic Gate Networks to achieve this. Their model learns local update rules for cellular automata, operating discretely yet enabling gradient-based training, and demonstrates proficiency in tasks ranging from replicating Conway’s Game of Life to generating complex, resilient patterns.

Differentiable Logic Cellular Automata: A Novel Computational Architecture

Researchers have introduced Differentiable Logic Cellular Automata (DiffLogic CA), a computational architecture integrating Neural Cellular Automata (NCA) with Differentiable Logic Gate Networks (DLGNs). DiffLogic CA utilises differentiable logic gates as fundamental computational units arranged within circuits, operating with discrete states during inference despite employing gradient-based training via full end-to-end differentiability. This addresses a limitation of traditional cellular automata designs by enabling learning of local update rules while retaining discrete characteristics.

Cellular automata (CA) are discrete dynamical systems where the state of a cell evolves over time based on the states of its neighbours and a defined set of rules. NCAs combine this with the learning capabilities of neural networks, allowing the rules to be learned from data. DLGNs are neural networks designed to mimic the behaviour of traditional logic gates (AND, OR, NOT, etc.) but with differentiable outputs, enabling gradient-based optimisation.

This research demonstrates a functional system capable of learning complex patterns and behaviours. The system successfully learned the rules governing Conway’s Game of Life, a benchmark for computational complexity within cellular automata, and generated resilient checkerboard patterns, exhibiting robustness against both noise and simulated damage. Beyond these simple patterns, the model grew a lizard-like form and generated multi-colour coordinated patterns, showcasing its capacity for more intricate visual outputs and confirming its ability to learn recurrent circuits capable of producing desired target patterns.

The architecture exhibits significant generalization capabilities and robustness, adapting to different computational paradigms and maintaining performance under varying conditions. Experiments demonstrated successful pattern generation using both synchronous and asynchronous update mechanisms, indicating adaptability. The system also maintained pattern fidelity under varying conditions, demonstrating resilience to perturbations.

Researchers highlight the potential for diverse applications in fields ranging from robotics to materials science. The combination of DLGNs and NCA represents a step towards robust computing systems, merging binary logic, neural network adaptability, and localised processing. This approach offers a pathway to adaptable and resilient computation, suggesting potential applications in areas requiring these characteristics.