Measuring Compositionality in Representation Learning

By Jacob Andreas. 2019

169 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Cultural Studies, Representation & Self-Supervised Learning

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Citations in the corpus

Compositionality Decomposed: How do Neural Networks Generalise? (2019, methodology): “, 2019; McCoy, Linzen, Dunbar, & Smolensky, 2019; Soulos, McCoy, Linzen, & Smolensky, 2019; Weiss, Goldberg, & Yahav, 2018a) or studies that evaluate compositionality only based on models’ representations (Andreas, 2019).”
On the Binding Problem in Artificial Neural Networks (2020, background): “A similar belief also underlies the interest in compositionality for understanding and encouraging productivity, systematicity, and efficient inference in neural networks (Santoro et al., 2018b; Hupkes et al., 2020; Andreas, 2019).”
Measuring Compositional Generalization: A Comprehensive Method on Realistic Data (2019, background): “Andreas (2019) discusses measuring the compositionality of a trained representation, e.g. of a learned embedding.”
Learning by Abstraction: The Neural State Machine (2019, background): “Others have argued for the importance of incorporating strong inductive biases into neural architectures [14, 10, 6, 8], and indeed, there is a growing body of research that seeks to introduce different forms of structural priors inspired by computer architectures [29, 80, 40] or theory of…”
Linguistic generalization and compositionality in modern artificial neural networks (2019, result): “Similar conclusions were drawn by Andreas [62] from a very different experiment.”
How to Reuse and Compose Knowledge for a Lifetime of Tasks: A Survey on Continual Learning and Functional Composition (2022, background): “An initial study quantified the compositionality of a model as the ability to approximate its output on compositional inputs by combining representational primitives (Andreas, 2019).”
A Benchmark for Systematic Generalization in Grounded Language Understanding (2020, methodology): “We further test a baseline multi-modal model representative of contemporary deep neural architectures, as well as a recent method proposed to address compositional generalization in the original SCAN dataset (GECA, Andreas, 2019).”
Compositionality and Generalization In Emergent Languages (2020, background): “This in turn requires measures of how compositional an emergent language is (Andreas, 2019).”
Locality and compositionality in zero-shot learning (2019, methodology): “• δ ( · , · ) is a distance function, chosen to be cosine similarity as in Andreas (2019).”
Compositional Visual Generation with Energy Based Models (2020, background): “Compositionality has been incorporated in representation learning (see [1] for a summary) and generative modeling.”
Emergent Communication of Generalizations (2021, methodology): “Lastly, our method ACRe builds off of the TRE metric developed by Andreas [1], and we describe this relationship in Section 7.”
Discovering the Compositional Structure of Vector Representations with Role Learning Networks (2019, background): “Most closely related are the approaches of [2], [5], and [1], who also propose methods for uncovering symbolic structure in vector representations, and [14] and [20], which also seek to understand neural networks by extracting more interpretable symbolic models that approximate their behavior.”
Learning Compositional Representations for Few-Shot Recognition (2018, methodology): “Following the formalism proposed in [3], on the base dataset Sbase, we augment the category labels yi ∈ Cbase of the examples xi, with information about their structure in the form of derivations D(xi), defined over a set of primitives D0.”
Are Neural Nets Modular? Inspecting Functional Modularity Through Differentiable Weight Masks (2020, background): “Andreas (2019) introduced a direct measure of compositionality by reconstructing NN representations from a set of primitive representations and a learned composition function.”