# Modelling the development of counting with memory-augmented neural networks

arXiv: https://arxiv.org/abs/2105.10577 · HTML: https://mlsanity.com/paper/2105.10577/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 21 May 2021.

## Builds on (most cited first, 8 of 8)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Measuring abstract reasoning in neural networks](https://mlsanity.com/paper/1807.04225/) (2018)
- [Representation Learning by Learning to Count](https://mlsanity.com/paper/1708.06734/) (2017)
- [Imitating Interactive Intelligence](https://mlsanity.com/paper/2012.05672/) (2020)
- [Human few-shot learning of compositional instructions](https://mlsanity.com/paper/1901.04587/) (2019)
- [Emergent Symbols through Binding in External Memory](https://mlsanity.com/paper/2012.14601/) (2020)
- [Learning Representations that Support Extrapolation](https://mlsanity.com/paper/2007.05059/) (2020)

## Built on by (most cited first, 4 of 4)

- [The Relational Bottleneck as an Inductive Bias for Efficient Abstraction](https://mlsanity.com/paper/2309.06629/) (2023)
- [Sequential Enumeration in Large Language Models](https://mlsanity.com/paper/2512.04727/) (2025)
- [Beyond Transformers for Function Learning](https://mlsanity.com/paper/2304.09979/) (2023)
- [A Vision Toward Energy-Efficient Domain-Specific Artificial Intelligence Models and Agents](https://mlsanity.com/paper/2510.22052/) (2025)

## Abstract (arXiv)

Learning to count is an important example of the broader human capacity for systematic generalization, and the development of counting is often characterized by an inflection point when children rapidly acquire proficiency with the procedures that support this ability. We aimed to model this process by training a reinforcement learning agent to select N items from a binary vector when instructed (known as the give-N task). We found that a memory-augmented modular network architecture based on the recently proposed Emergent Symbol Binding Network (ESBN) exhibited an inflection during learning that resembled human development. This model was also capable of systematic extrapolation outside the range of its training set - for example, trained only to select between 1 and 10 items, it could succeed at selecting 11 to 15 items as long as it could make use of an arbitrary count sequence of at least that length. The close parallels to child development and the capacity for extrapolation suggest that our model could shed light on the emergence of systematicity in humans.