# Compositional Processing Emerges in Neural Networks Solving Math Problems

arXiv: https://arxiv.org/abs/2105.08961 · HTML: https://mlsanity.com/paper/2105.08961/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 20 references that are in the map.
- First posted on arXiv 19 May 2021.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Syntactic Structure from Deep Learning](https://mlsanity.com/paper/2004.10827/) (2020)
- [Enhancing the Transformer with Explicit Relational Encoding for Math Problem Solving](https://mlsanity.com/paper/1910.06611/) (2019)

## Built on by (most cited first, 11 of 11)

- [Does CLIP Bind Concepts? Probing Compositionality in Large Image Models](https://mlsanity.com/paper/2212.10537/) (2022)
- [Pointer Value Retrieval: A new benchmark for understanding the limits of neural network generalization](https://mlsanity.com/paper/2107.12580/) (2021)
- [Limits of Transformer Language Models on Learning to Compose Algorithms](https://mlsanity.com/paper/2402.05785/) (2024)
- [Are Representations Built from the Ground Up? An Empirical Examination of Local Composition in Language Models](https://mlsanity.com/paper/2210.03575/) (2022)
- [Skews in the Phenomenon Space Hinder Generalization in Text-to-Image Generation](https://mlsanity.com/paper/2403.16394/) (2024)
- [From Frege to chatGPT: Compositionality in language, cognition, and deep neural networks](https://mlsanity.com/paper/2405.15164/) (2024)
- [Recursive Neural Networks with Bottlenecks Diagnose (Non-)Compositionality](https://mlsanity.com/paper/2301.13714/) (2023)
- [Semantic Representations of Mathematical Expressions in a Continuous Vector Space](https://mlsanity.com/paper/2211.08142/) (2022)
- [Representational Homomorphism Predicts and Improves Compositional Generalization In Transformer Language Model](https://mlsanity.com/paper/2601.18858/) (2026)
- [An Application of Pseudo-Log-Likelihoods to Natural Language Scoring](https://mlsanity.com/paper/2201.09377/) (2022)
- [Solving Reasoning Tasks with a Slot Transformer](https://mlsanity.com/paper/2210.11394/) (2022)

## Abstract (arXiv)

A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations (e.g., auditory speech), and use this knowledge to guide the composition of simpler meanings into complex wholes. Recent progress in artificial neural networks has shown that when large models are trained on enough linguistic data, grammatical structure emerges in their representations. We extend this work to the domain of mathematical reasoning, where it is possible to formulate precise hypotheses about how meanings (e.g., the quantities corresponding to numerals) should be composed according to structured rules (e.g., order of operations). Our work shows that neural networks are not only able to infer something about the structured relationships implicit in their training data, but can also deploy this knowledge to guide the composition of individual meanings into composite wholes.