Defining and Generating Compositional Structure

arXiv cs.AIOctober 16, 2026en

arXiv:2610.20922v1 Announce Type: new Abstract: 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 emerge

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