# Benchmarking Compositionality with Formal Languages

arXiv: https://arxiv.org/abs/2208.08195 · HTML: https://mlsanity.com/paper/2208.08195/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 17 Aug 2022.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Compositionality decomposed: how do neural networks generalise?](https://mlsanity.com/paper/1908.08351/) (2019)
- [On the Practical Computational Power of Finite Precision RNNs for Language Recognition](https://mlsanity.com/paper/1805.04908/) (2018)
- [A Benchmark for Systematic Generalization in Grounded Language Understanding](https://mlsanity.com/paper/2003.05161/) (2020)
- [Measuring Compositionality in Representation Learning](https://mlsanity.com/paper/1902.07181/) (2019)
- [RNNs can generate bounded hierarchical languages with optimal memory](https://mlsanity.com/paper/2010.07515/) (2020)
- [The paradox of the compositionality of natural language: a neural machine translation case study](https://mlsanity.com/paper/2108.05885/) (2021)
- [LSTM Networks Can Perform Dynamic Counting](https://mlsanity.com/paper/1906.03648/) (2019)
- [Examining the Inductive Bias of Neural Language Models with Artificial Languages](https://mlsanity.com/paper/2106.01044/) (2021)
- [Jump to better conclusions: SCAN both left and right](https://mlsanity.com/paper/1809.04640/) (2018)
- [Unobserved Local Structures Make Compositional Generalization Hard](https://mlsanity.com/paper/2201.05899/) (2022)
- [Exact Hard Monotonic Attention for Character-Level Transduction](https://mlsanity.com/paper/1905.06319/) (2019)
- [On the Practical Ability of Recurrent Neural Networks to Recognize Hierarchical Languages](https://mlsanity.com/paper/2011.03965/) (2020)
- [A Roadmap towards Machine Intelligence](https://mlsanity.com/paper/1511.08130/) (2015)
- [Subregular Complexity and Deep Learning](https://mlsanity.com/paper/1705.05940/) (2017)
- [Multi-Element Long Distance Dependencies: Using SPk Languages to Explore the Characteristics of Long-Distance Dependencies](https://mlsanity.com/paper/1907.06048/) (2019)

## Built on by (most cited first, 12 of 12)

- [What Algorithms can Transformers Learn? A Study in Length Generalization](https://mlsanity.com/paper/2310.16028/) (2023)
- [Mechanistically analyzing the effects of fine-tuning on procedurally defined tasks](https://mlsanity.com/paper/2311.12786/) (2023)
- [Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task](https://mlsanity.com/paper/2310.09336/) (2023)
- [A Percolation Model of Emergence: Analyzing Transformers Trained on a Formal Language](https://mlsanity.com/paper/2408.12578/) (2024)
- [A Survey on Compositional Learning of AI Models: Theoretical and Experimental Practices](https://mlsanity.com/paper/2406.08787/) (2024)
- [The Validity of Evaluation Results: Assessing Concurrence Across Compositionality Benchmarks](https://mlsanity.com/paper/2310.17514/) (2023)
- [Mechanistic evaluation of Transformers and state space models](https://mlsanity.com/paper/2505.15105/) (2025)
- [Vocabulary for Universal Approximation: A Linguistic Perspective of Mapping Compositions](https://mlsanity.com/paper/2305.12205/) (2023)
- [Swing-by Dynamics in Concept Learning and Compositional Generalization](https://mlsanity.com/paper/2410.08309/) (2024)
- [Provable Benefits of In-Tool Learning for Large Language Models](https://mlsanity.com/paper/2508.20755/) (2025)
- [Randomly Sampled Language Reasoning Problems Elucidate Limitations of In-Context Learning](https://mlsanity.com/paper/2501.02825/) (2025)
- [Compositionality Emerges in a Narrow Depth-Connectivity Regime: Architecture Constraints and Solution Manifolds](https://mlsanity.com/paper/2606.19941/) (2026)

## Abstract (arXiv)

Recombining known primitive concepts into larger novel combinations is a quintessentially human cognitive capability. Whether large neural models in NLP can acquire this ability while learning from data is an open question. In this paper, we investigate this problem from the perspective of formal languages. We use deterministic finite-state transducers to make an unbounded number of datasets with controllable properties governing compositionality. By randomly sampling over many transducers, we explore which of their properties contribute to learnability of a compositional relation by a neural network. We find that the models either learn the relations completely or not at all. The key is transition coverage, setting a soft learnability limit at 400 examples per transition.