Teaching Transformers Modular Arithmetic at Scale
Keywords: transformers, modular arithmetic, math
TL;DR: We make several improvements that enable transformers to do modular arithmetic with large moduli (up to 3329) and many terms (up to 256)
Abstract: Modular addition is, on its face, a simple operation: given $N$ elements in $\mathbb{Z}_q$, compute their sum modulo $q$. Yet, scalable machine learning solutions to this problem remain elusive: prior work trains ML models that sum $N \le 6$ elements mod $q \le 1000$. Promising applications of ML models for cryptanalysis$\textemdash$which often involve modular arithmetic with large $N$ and $q$$\textemdash$motivate reconsideration of this problem. This work proposes three changes to the modular addition model training pipeline: more diverse training data, an angular embedding, and a custom loss function. With these changes, we demonstrate success with our approach for $N = 256, q = 3329$, a case which is interesting for cryptographic applications, and a significant increase in $N$ and $q$ over prior work. These techniques also generalize to other modular arithmetic problems, motivating future work.
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 4677
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