# A Compositional Framework for Open-ended Intelligence

arXiv: https://arxiv.org/abs/2606.15386 · HTML: https://mlsanity.com/paper/2606.15386/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 130 references that are in the map.
- First posted on arXiv 13 Jun 2026.

## Builds on (most cited first, 30 of 37)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Eureka: Human-Level Reward Design via Coding Large Language Models](https://mlsanity.com/paper/2310.12931/) (2023)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Curriculum Learning for Reinforcement Learning Domains: A Framework and Survey](https://mlsanity.com/paper/2003.04960/) (2020)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [Robots that can adapt like animals](https://mlsanity.com/paper/1407.3501/) (2014)
- [Open-Ended Learning Leads to Generally Capable Agents](https://mlsanity.com/paper/2107.12808/) (2021)
- [Evolving Curricula with Regret-Based Environment Design](https://mlsanity.com/paper/2203.01302/) (2022)
- [Human-Timescale Adaptation in an Open-Ended Task Space](https://mlsanity.com/paper/2301.07608/) (2023)
- [Procedural Content Generation via Machine Learning (PCGML)](https://mlsanity.com/paper/1702.00539/) (2017)
- [Quality and Diversity Optimization: A Unifying Modular Framework](https://mlsanity.com/paper/1708.09251/) (2017)
- [A Laplacian Framework for Option Discovery in Reinforcement Learning](https://mlsanity.com/paper/1703.00956/) (2017)
- [Enhanced POET: Open-Ended Reinforcement Learning through Unbounded Invention of Learning Challenges and their Solutions](https://mlsanity.com/paper/2003.08536/) (2020)
- [ARC Prize 2024: Technical Report](https://mlsanity.com/paper/2412.04604/) (2024)
- [AI-GAs: AI-generating algorithms, an alternate paradigm for producing general artificial intelligence](https://mlsanity.com/paper/1905.10985/) (2019)
- [Open-Endedness is Essential for Artificial Superhuman Intelligence](https://mlsanity.com/paper/2406.04268/) (2024)
- [Top-Down Synthesis for Library Learning](https://mlsanity.com/paper/2211.16605/) (2022)
- [Neural population geometry: An approach for understanding biological and artificial neural networks](https://mlsanity.com/paper/2104.07059/) (2021)
- [From Entropy to Epiplexity: Rethinking Information for Computationally Bounded Intelligence](https://mlsanity.com/paper/2601.03220/) (2026)
- [MAESTRO: Open-Ended Environment Design for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2303.03376/) (2023)

## Built on by (most cited first, 2 of 2)

- [Beyond Fixed Representations: The Vocabulary and Verifier Gaps in Open-Ended AI](https://mlsanity.com/paper/2607.09560/) (2026)
- [Benchmarking World Models for Continual Learning on Compositional Tasks](https://mlsanity.com/paper/2609.22055/) (2026)

## Abstract (arXiv)

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