Defining and generating hierarchical compositional structures from data
Defining and Generating Compositional Structure
Artificial IntelligenceInformation TheoryMachine Learning
Summary
Many natural and artificial things are made by combining smaller parts into bigger parts in layers, like atoms forming molecules and molecules forming cells. The paper offers a clear way to define what it means for something to have this layered, reusable structure using ideas from information theory. The authors show how to spot these structures in data without guessing what they look like beforehand, and also how to create new objects with these layered parts. This helps us better understand complexity in nature and could improve how machines learn by showing them how to build from parts in a flexible way.
What this means in practice
- •For machine learning engineers: Create training data that mimics real-world part reuse, improving models’ ability to learn complex concepts by building from simpler parts.
- •For computer graphics developers: Generate images and objects with realistic hierarchical and reusable parts by optimizing their compositional structure directly.
Authors
Eric Elmoznino, Tejas Kasetty, Blaise Agüera y Arcas, Yoshua Bengio, Guillaume Lajoie
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 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.