# Arbitrary-Length Generalization for Addition in a Tiny Transformer

arXiv: https://arxiv.org/abs/2406.00075 · HTML: https://mlsanity.com/paper/2406.00075/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 6 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 5 of 5)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Investigating the Limitations of Transformers with Simple Arithmetic Tasks](https://mlsanity.com/paper/2102.13019/) (2021)
- [Teaching Arithmetic to Small Transformers](https://mlsanity.com/paper/2307.03381/) (2023)
- [Transformers Can Do Arithmetic with the Right Embeddings](https://mlsanity.com/paper/2405.17399/) (2024)

## Abstract (arXiv)

This paper introduces a novel training methodology that enables a Transformer model to generalize the addition of two-digit numbers to numbers with unseen lengths of digits. The proposed approach employs an autoregressive generation technique, processing from right to left, which mimics a common manual method for adding large numbers. To the best of my knowledge, this methodology has not been previously explored in the literature. All results are reproducible, and the corresponding R code is available at github.com/AGPatriota/ALGA-R/.