# Compositional learning of functions in humans and machines

arXiv: https://arxiv.org/abs/2403.12201 · HTML: https://mlsanity.com/paper/2403.12201/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 19 references that are in the map.
- First posted on arXiv 18 Mar 2024.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [A Benchmark for Systematic Generalization in Grounded Language Understanding](https://mlsanity.com/paper/2003.05161/) (2020)
- [Modeling rapid language learning by distilling Bayesian priors into artificial neural networks](https://mlsanity.com/paper/2305.14701/) (2023)
- [Memorize or generalize? Searching for a compositional RNN in a haystack](https://mlsanity.com/paper/1802.06467/) (2018)
- [Jump to better conclusions: SCAN both left and right](https://mlsanity.com/paper/1809.04640/) (2018)
- [Compositional diversity in visual concept learning](https://mlsanity.com/paper/2305.19374/) (2023)

## Built on by (most cited first, 2 of 2)

- [How Do Language Models Compose Functions?](https://mlsanity.com/paper/2510.01685/) (2025)
- [Extracting Memorized Training Data via Decomposition](https://mlsanity.com/paper/2409.12367/) (2024)

## Abstract (arXiv)

The ability to learn and compose functions is foundational to efficient learning and reasoning in humans, enabling flexible generalizations such as creating new dishes from known cooking processes. Beyond sequential chaining of functions, existing linguistics literature indicates that humans can grasp more complex compositions with interacting functions, where output production depends on context changes induced by different function orderings. Extending the investigation into the visual domain, we developed a function learning paradigm to explore the capacity of humans and neural network models in learning and reasoning with compositional functions under varied interaction conditions. Following brief training on individual functions, human participants were assessed on composing two learned functions, in ways covering four main interaction types, including instances in which the application of the first function creates or removes the context for applying the second function. Our findings indicate that humans can make zero-shot generalizations on novel visual function compositions across interaction conditions, demonstrating sensitivity to contextual changes. A comparison with a neural network model on the same task reveals that, through the meta-learning for compositionality (MLC) approach, a standard sequence-to-sequence Transformer can mimic human generalization patterns in composing functions.