LifeGPT: topology-agnostic generative pretrained transformer model for cellular automata

Conway’s Game of Life (Life), a famous cellular automata (CA) algorithm, exhibits complex, initial condition-sensitive dynamics. Modeling Life without knowing the system’s topology presents a challenge, motivating the development of algorithms capable of generalizing across grid configurations and boundary conditions. We introduce LifeGPT, a decoder-only generative pretrained transformer (GPT) model with rotary positional embedding (RoPE) and forgetful causal masking (FCM), capable of computing a single-timestep global state transition in Life on a toroidal grid without prior knowledge of grid size or boundary conditions. LifeGPT is topology-agnostic, achieving near-perfect accuracy in capturing the deterministic rules of Life given sufficiently diverse training data. We show recursive simulation of Life is possible using LifeGPT within an autoregressive loop. LifeGPT can also be trained on grids of varying sizes while retaining near-perfect accuracy. Finally, we propose future research, like using LifeGPT-like models to infer CA rulesets from real-world data, which could advance predictive modeling.