# Compositionality decomposed: how do neural networks generalise?

arXiv: https://arxiv.org/abs/1908.08351 · HTML: https://mlsanity.com/paper/1908.08351/

## Key facts

- Cited by 265 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2019.

## Built on by (most cited first, 30 of 265)

- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Socratic Models: Composing Zero-Shot Multimodal Reasoning with Language](https://mlsanity.com/paper/2204.00598/) (2022)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [SugarCrepe: Fixing Hackable Benchmarks for Vision-Language Compositionality](https://mlsanity.com/paper/2306.14610/) (2023)
- [Large Language Models as General Pattern Machines](https://mlsanity.com/paper/2307.04721/) (2023)
- [CREPE: Can Vision-Language Foundation Models Reason Compositionally?](https://mlsanity.com/paper/2212.07796/) (2022)
- [A Survey of Zero-shot Generalisation in Deep Reinforcement Learning](https://mlsanity.com/paper/2111.09794/) (2021)
- [How much do language models copy from their training data? Evaluating linguistic novelty in text generation using RAVEN](https://mlsanity.com/paper/2111.09509/) (2021)
- [The Devil is in the Detail: Simple Tricks Improve Systematic Generalization of Transformers](https://mlsanity.com/paper/2108.12284/) (2021)
- [Unveiling Transformers with LEGO: a synthetic reasoning task](https://mlsanity.com/paper/2206.04301/) (2022)
- [State-of-the-art generalisation research in NLP: A taxonomy and review](https://mlsanity.com/paper/2210.03050/) (2022)
- [Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task](https://mlsanity.com/paper/2310.09336/) (2023)
- [Survey of Low-Resource Machine Translation](https://mlsanity.com/paper/2109.00486/) (2021)
- [A Theory of Emergent In-Context Learning as Implicit Structure Induction](https://mlsanity.com/paper/2303.07971/) (2023)
- [Transformers Can Achieve Length Generalization But Not Robustly](https://mlsanity.com/paper/2402.09371/) (2024)
- [Modular Deep Learning](https://mlsanity.com/paper/2302.11529/) (2023)
- [Can Wikipedia Help Offline Reinforcement Learning?](https://mlsanity.com/paper/2201.12122/) (2022)
- [No "Zero-Shot" Without Exponential Data: Pretraining Concept Frequency Determines Multimodal Model Performance](https://mlsanity.com/paper/2404.04125/) (2024)
- [Generalization on the Unseen, Logic Reasoning and Degree Curriculum](https://mlsanity.com/paper/2301.13105/) (2023)
- [Making Transformers Solve Compositional Tasks](https://mlsanity.com/paper/2108.04378/) (2021)
- [Learning to Compose Soft Prompts for Compositional Zero-Shot Learning](https://mlsanity.com/paper/2204.03574/) (2022)
- [The Neural Data Router: Adaptive Control Flow in Transformers Improves Systematic Generalization](https://mlsanity.com/paper/2110.07732/) (2021)
- [ConceptMix: A Compositional Image Generation Benchmark with Controllable Difficulty](https://mlsanity.com/paper/2408.14339/) (2024)
- [The paradox of the compositionality of natural language: a neural machine translation case study](https://mlsanity.com/paper/2108.05885/) (2021)
- [Linear Spaces of Meanings: Compositional Structures in Vision-Language Models](https://mlsanity.com/paper/2302.14383/) (2023)
- [Break It Down: Evidence for Structural Compositionality in Neural Networks](https://mlsanity.com/paper/2301.10884/) (2023)
- [A Benchmark for Compositional Visual Reasoning](https://mlsanity.com/paper/2206.05379/) (2022)
- [Can language models handle recursively nested grammatical structures? A case study on comparing models and humans](https://mlsanity.com/paper/2210.15303/) (2022)
- [Disentangling Syntax and Semantics in the Brain with Deep Networks](https://mlsanity.com/paper/2103.01620/) (2021)

## Abstract (arXiv)

Despite a multitude of empirical studies, little consensus exists on whether neural networks are able to generalise compositionally, a controversy that, in part, stems from a lack of agreement about what it means for a neural model to be compositional. As a response to this controversy, we present a set of tests that provide a bridge between, on the one hand, the vast amount of linguistic and philosophical theory about compositionality of language and, on the other, the successful neural models of language. We collect different interpretations of compositionality and translate them into five theoretically grounded tests for models that are formulated on a task-independent level. In particular, we provide tests to investigate (i) if models systematically recombine known parts and rules (ii) if models can extend their predictions beyond the length they have seen in the training data (iii) if models' composition operations are local or global (iv) if models' predictions are robust to synonym substitutions and (v) if models favour rules or exceptions during training. To demonstrate the usefulness of this evaluation paradigm, we instantiate these five tests on a highly compositional data set which we dub PCFG SET and apply the resulting tests to three popular sequence-to-sequence models: a recurrent, a convolution-based and a transformer model. We provide an in-depth analysis of the results, which uncover the strengths and weaknesses of these three architectures and point to potential areas of improvement.