A Compositional Framework for Open-ended Intelligence

2026-06-13

AI Summary

This work addresses the challenge of enabling intelligent systems to continually adapt and generalize in out-of-distribution tasks and environments. It proposes a mathematically formalized framework for open-ended intelligence, constructing a closure space from a finite set of representational and algorithmic primitives together with compositional operators that support infinite combinatorial generation. By framing architecture design around the objective of “next primitive prediction,” the system intrinsically acquires compositional generalization capabilities. Lifelong learning is further facilitated through curriculum learning and self-play mechanisms. The approach demonstrates effectiveness across case studies grounded in physics, evolutionary dynamics, and neuroscience, offering both interpretability and the capacity to generate infinitely adaptive responses across families of tasks.

Abstract

Open-ended intelligence is the capacity to adapt to novel problems and environments that are substantially different from those in training. We formalize open-ended intelligence as the closure induced by a finite primitive set \(P\) and a set of composition operators \(C\). We characterize properties of the induced closure \(\mathcal{L}(P,C)\) that support unbounded compositional generation across families of tasks and worlds. A mathematics of open-ended intelligence requires two pillars: a minimal set of representational primitives (e.g., states, actions) and algorithmic primitives (e.g., nearest neighbor), together with composition motifs (e.g., recursion, sequencing) that reflect an acquired compositional grammar. The closure of these two pillars enables the generation of infinite adaptive responses across a wide range of settings. The mathematics supports complementary research agendas, including evaluation metrics for explanation and interpretability, as well as building architectures where compositional generalization is native. We propose next primitive prediction as a novel architectural objective, where the training objective encourages the acquisition of reusable algorithmic primitives and their compositional grammar, such that new solutions are generated through recombination. Curriculum learning and self-play enable lifelong learning and expansion of the closure by discovering reusable primitives and transition motifs across families of tasks and worlds. We ground the framework through case studies in physics, evolution, and neuroscience.

Problem

• open-ended intelligence
• compositional generalization
• representational primitives
• algorithmic primitives
• closure

Innovation

• compositional framework
• open-ended intelligence
• primitive prediction
• closure
• compositional generalization