Measuring Compositionality in Representation Learning (1902.07181v2)

Abstract: 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.

• The paper introduces TRE, a method that quantitatively reconstructs learned representations from primitive elements to assess compositional structure.
• The paper finds a strong link between compositionality, information compression, and human judgment, validating its approach in neural and linguistic contexts.
• The paper demonstrates that enforcing compositional constraints can reduce representation divergence and improve generalization in machine learning models.

Insights into Measuring Compositionality in Representation Learning

The paper "Measuring Compositionality in Representation Learning" by Jacob Andreas investigates the emergent compositional structures in representation learning algorithms. These algorithms often utilize embeddings or codes to represent input data. When data possesses inherent compositional structures, such as objects made of parts or procedures derived from subroutines, an important consideration is whether such structures manifest in the learned representations. Unlike linguistic models that come with extensive toolsets for compositionality analysis, machine learning lacks general-purpose metrics for such assessments across diverse representation spaces. This paper addresses this gap by proposing a novel method: the Tree Reconstruction Error (TRE).

Summary of Contributions

The paper primarily contributes by defining a framework to measure how well representations approximate compositional structures derived from known primitives. It utilizes an oracle setting, where the data's compositional structure is pre-defined and the task is to evaluate its reflection in model outputs. TRE quantitatively assesses this by attempting to approximate a true representation with a constructed model derived from inferred primitives. It does so by optimizing a set of parameters to find a composition of primitive elements that closely matches the outputs of the original model.

Empirical and Formal Findings

1. Framework and Methodology: The central contribution is TRE, a formal and automatable method for evaluating compositional structures in learned representations. The TRE method seeks to find an optimal set of hidden primitives that, when composed, can reconstruct the outputs of a representation model. The quality of this reconstruction reflects the model's compositional alignment with the input data's structure.
2. Implications for Learning Dynamics: The research demonstrates a significant relationship between compositionality and representation learning dynamics. Utilizing the information bottleneck theory, it is observed that during the compression stage of learning, models tend to discard irrelevant information while isolating essential attributes, reflecting compositional representation. This was evidenced by a correlation between mutual information and TRE measurements in a few-shot classification task.
3. Human Judgments: TRE was applied to assess the compositionality of word embeddings against human judgment metrics. There was a reasonable correlation between TRE measures and human evaluations of noun--noun compound compositionality, validating the method’s applicability in linguistic contexts.
4. Similarity and Generalization: The paper further explores the constraints compositionality imposes on representation similarity and generalization. It provides a formal proposition showing TRE imposes an upper bound on derivation edit distances, illustrating compositionality's role in limiting divergence among learned representations.
5. Communication Games: In experiments with emergent communication protocols, the research underscores that compositional language protocols contribute to improved generalization. However, the relationship is not straightforward, as non-compositional strategies also achieved comparable performance, highlighting compositionality's nuanced role in enhancing model generalization.

Implications and Future Directions

The implications of this research are multifaceted. Practically, TRE provides a rigorous, formalized approach to evaluating compositional structures in representation learning, which could enhance the development and tuning of machine learning models, especially in tasks involving complex input structures. Theoretically, it provokes further investigation into how compositionality naturally arises and impacts learning and generalization in neural networks. A promising direction is the potential extension of TRE to unsupervised settings, possibly integrating grammar induction techniques to uncover latent structure without oracle guidance. The method's adaptability to a variety of tasks makes it a potent tool for future research in AI and representation learning.

The paper succeeds in setting the groundwork for a deeper understanding of how compositionality can be quantified and leveraged in machine learning contexts, bridging a crucial gap in the capabilities of current methodological tools.