Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this compositional structure is reflected in the the inputs’ learned representations. While the assessment of compositionality in languages has received significant attention in linguistics and adjacent fields, the machine learning literature lacks general-purpose tools for producing graded measurements of compositional structure in more general (e.g. vector-valued) representation spaces. We describe a procedure for evaluating compositionality by measuring how well the true representation-producing model can be approximated by a model that explicitly composes a collection of inferred representational primitives. We use the procedure to provide formal and empirical characterizations of compositional structure in a variety of settings, exploring the relationship between compositionality and learning dynamics, human judgments, representational similarity, and generalization. We have introduced a new evaluation method called TRE for generating graded judgments about compositional structure in representation learning problems where the structure of the observations is understood. TRE infers a set of primitive meaning representations that, when composed, approximate the observed representations, then measures the quality of this approximation. We have applied TRE-based analysis to four different problems in representation learning, relating compositionality to learning dynamics, linguistic compositionality, similarity and generalization.Many interesting questions regarding compositionality and representation learning remain open. The most immediate is how to generalize TRE to the setting where oracle derivations are not available; in this case Equation 2 must be solved jointly with an unsupervised grammar induction problem BID25 . Beyond this, it is our hope that this line of research opens up two different kinds of new work: better understanding of existing machine learning models, by providing a new set of tools for understanding their representational capacity; and better understanding of problems, by better understanding the kinds of data distributions and loss functions that give rise to compositionalor non-compositional representations of observations.
This paper proposes a simple procedure for evaluating compositional structure in learned representations, and uses the procedure to explore the role of compositionality in four learning problems.
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