Compositional Framework Proposed for Open-Ended AI Intelligence

Open-ended intelligence, defined as the ability to adapt to new and substantially different problems and environments beyond initial training, is a critical goal for advanced AI. This research formalizes this concept as a closure generated by a finite set of primitive elements and a set of composition operators. The paper characterizes the properties of this induced closure that enable unbounded compositional generation across diverse tasks and environments. The authors argue that a mathematical foundation for open-ended intelligence requires two main pillars: a minimal set of representational primitives (like states and actions) and algorithmic primitives (such as nearest neighbor operations), combined with composition motifs (like recursion and sequencing) that reflect an acquired compositional grammar. The closure formed by these pillars allows for the generation of an infinite array of adaptive responses in various settings. The framework supports complementary research agendas, including developing evaluation metrics for explainability and interpretability, and constructing AI architectures where compositional generalization is intrinsic. A novel architectural objective, "next primitive prediction," is proposed, which encourages the learning of reusable algorithmic primitives and their compositional rules during training. This enables the generation of new solutions through recombination. The paper suggests that curriculum learning and self-play are key mechanisms for lifelong learning and expanding this compositional closure by discovering new primitives and transition motifs across different task families and worlds, grounding the framework with case studies in physics, evolution, and neuroscience.