Cellular automata (CA) provide a minimal formalism for investigating how simple local interactions generate rich spatiotemporal behavior in domains as diverse as traffic flow, ecology, tissue morphogenesis and crystal growth. However, automatically discovering the local update rules for a given phenomenon and using them for quantitative prediction remains challenging. Here we present AutomataGPT, a decoder-only transformer pretrained on around 1 million simulated trajectories that span 100 distinct two-dimensional binary deterministic CA rules on toroidal grids. When evaluated on previously unseen rules drawn from the same CA family, AutomataGPT attains 98.5% perfect one-step forecasts and reconstructs the governing update rule with up to 96% functional (application) accuracy and 82% exact rule-matrix match. These results demonstrate that large-scale pretraining over wider regions of rule space yields substantial generalization in both the forward (state forecasting) and inverse (rule inference) problems, without hand-crafted priors. By showing that transformer models can faithfully infer and execute CA dynamics from data alone, our work lays the groundwork for abstracting real-world dynamical phenomena into data-efficient CA surrogates, opening avenues in biology, tissue engineering, physics and AI-driven scientific discovery.

The logic-based methods that learn first-order rules from knowledge graphs (KGs) for knowledge graph completion (KGC) task are desirable in that the learnt models are inductive, interpretable and transferable. The challenge in such rule learners is that the expressive rules are often buried in vast rule space, and the procedure of identifying expressive rules by measuring rule quality is costly to execute. Therefore, optimizations on rule generation and evaluation are in need. In this work, we propose a novel bottom-up probabilistic rule learner that features: 1.) a two-stage procedure for optimized rule generation where the system first generalizes paths sampled from a KG into template rules that contain no constants until a certain degree of template saturation is achieved and then specializes template rules into instantiated rules that contain constants; 2.) a grouping technique for optimized rule evaluation where structurally similar instantiated rules derived from the same template rules are put into the same groups and evaluated collectively over the groundings of the deriving template rules. Through extensive experiments over large benchmark datasets on KGC task, our algorithm demonstrates consistent and substantial performance improvements over all of the state-of-the-art baselines.