# Machine learning for modular multiplication

arXiv: https://arxiv.org/abs/2402.19254 · HTML: https://mlsanity.com/paper/2402.19254/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 14 references that are in the map.
- First posted on arXiv 29 Feb 2024.

## Builds on (most cited first, 9 of 9)

- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Grokking modular arithmetic](https://mlsanity.com/paper/2301.02679/) (2023)
- [Length Generalization in Arithmetic Transformers](https://mlsanity.com/paper/2306.15400/) (2023)
- [Linear algebra with transformers](https://mlsanity.com/paper/2112.01898/) (2021)
- [Positional Description Matters for Transformers Arithmetic](https://mlsanity.com/paper/2311.14737/) (2023)
- [SALSA: Attacking Lattice Cryptography with Transformers](https://mlsanity.com/paper/2207.04785/) (2022)
- [SALSA PICANTE: a machine learning attack on LWE with binary secrets](https://mlsanity.com/paper/2303.04178/) (2023)
- [Gradient Descent Fails to Learn High-frequency Functions and Modular Arithmetic](https://mlsanity.com/paper/2310.12660/) (2023)

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

- [Formal Mathematical Reasoning: A New Frontier in AI](https://mlsanity.com/paper/2412.16075/) (2024)
- [Making Hard Problems Easier with Custom Data Distributions and Loss Regularization: A Case Study in Modular Arithmetic](https://mlsanity.com/paper/2410.03569/) (2024)

## Abstract (arXiv)

Motivated by cryptographic applications, we investigate two machine learning approaches to modular multiplication: namely circular regression and a sequence-to-sequence transformer model. The limited success of both methods demonstrated in our results gives evidence for the hardness of tasks involving modular multiplication upon which cryptosystems are based.