Defining and Generating Compositional Structure
Quick Answer
The paper formalizes compositional structure using algorithmic information theory, revealing shared structures in parts that are not apparent when modeled separately.
Quick Take
This framework allows for the generation of compositional objects, optimizing their hierarchical reuse and part-whole organization, with implications for machine learning and neural architectures.
Key Points
- Compositional structure emerges when parts reveal shared structure together.
- Algorithmic information theory is used to identify structure in arbitrary data.
- Framework allows generation of compositional objects without specifying content.
- Objects exhibit hierarchical reuse, suggesting a deeper understanding of complexity.
- Implications for machine learning include new perspectives on neural architecture depth.
DeepSignal Analysis
What happened
The paper formalizes the concept of compositional structure through algorithmic information theory, highlighting how parts can reveal shared structures when considered together. This framework enables the generation of compositional objects, optimizing their hierarchical organization. The authors discuss potential implications for machine learning, particularly in neural architectures.
Key evidence
- The authors define compositional structure as emerging when parts reveal shared structures not captured when modeled separately.
- The framework allows for the generation of compositional objects by specifying their structural form without detailing their content.
- The paper suggests that the definition of compositional structure has implications for machine learning, including insights into neural architecture depth.
Why it matters
Understanding compositional structure is crucial for advancing both natural and artificial systems. By formalizing this concept, the authors provide a mathematical basis that could enhance the design of complex systems. The implications for machine learning, particularly in optimizing neural networks and developing curricula for open-ended learning, could lead to significant advancements in AI capabilities.
Paper Resources
📖 Reader Mode
~2 min readAbstract:Compositional structure is pervasive in nature and across scales: atoms combine into molecules, molecules into cells, and cells into organisms, while further compositional hierarchies appear within each level. More broadly, compositionality, the reuse and recombination of parts into novel structures, is a fundamental source of interesting complexity in both natural and artificial systems. Yet despite its importance, and despite our apparent ease in recognizing it, mathematical accounts capturing what we intuitively mean by compositional structure remain limited. Here, we fill this gap by formalizing a simple idea: compositional structure emerges when parts, considered together, reveal shared structure that is not captured when those parts are modeled separately. We express this idea using algorithmic information theory, the mathematics of information and compression, which provides a natural way to identify structure in arbitrary data without specifying in advance what that structure must look like. Applied across scales, our definition informs where and how compositional structure emerges within an object. Using tractable approximations, we then invert the framework to generate compositional objects: we specify the desired form of their compositional structure without prescribing their particular content, and optimize directly over strings and images. The resulting objects exhibit readily recognizable hierarchical reuse and part-whole organization, suggesting that the definition captures compositional structure rather than merely complexity, regularity, or shared information. Finally, we discuss implications for machine learning, including a new perspective on depth in neural architectures and principles for constructing compositional data curricula capable of supporting open-ended learning.
| Subjects: | Artificial Intelligence (cs.AI); Information Theory (cs.IT); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.20922 [cs.AI] |
| (or arXiv:2610.20922v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2610.20922 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Eric Elmoznino [view email]
[v1]
Wed, 14 Oct 2026 20:52:33 UTC (2,643 KB)
— Originally published at arxiv.org
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