@inproceedings{kang-etal-2026-beyond,
title = "Beyond Append-Only Decoding: A Recursive Edit-Based Encoder for Arithmetic Length Generalization",
author = "Kang, Bong Gyun and
Ahn, Junyong and
Byeon, Jieun and
Yoon, Sungroh",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.1920/",
pages = "43731--43750",
ISBN = "979-8-89176-459-0",
abstract = "Algorithmic reasoning{---}internalizing a procedure from small examples and applying it at arbitrary scale{---}is a hallmark of human intelligence: a child who learns arithmetic on a few digits can, given time and paper, evaluate expressions of unbounded length. Modern language models cannot: Qwen3.5-27B, despite 100k-token reasoning contexts, degrades to below 10{\%} accuracy on 30-digit multiplication. Departing from reasoning-through-scale, we introduce RACE (Recursive Arithmetic Control Encoder), a 3.6M-parameter Transformer trained from scratch that generalizes far better by recursively decomposing problems while keeping its working memory bounded. Two mechanisms drive this: token-level editing, which erases intermediate scratchwork, and self-calling, which recurses on subproblems. Within a single model, RACE improves multiplication length generalization 4.7 times over the Arithmetic Transformer and, for the first time, achieves length generalization on subtraction and division ({\texttimes}47.1 and {\texttimes}17.6), while also solving nested, multi-operator expressions. Code is available at https://github.com/Pusheen-cat/RACE{\_}2026."
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<abstract>Algorithmic reasoning—internalizing a procedure from small examples and applying it at arbitrary scale—is a hallmark of human intelligence: a child who learns arithmetic on a few digits can, given time and paper, evaluate expressions of unbounded length. Modern language models cannot: Qwen3.5-27B, despite 100k-token reasoning contexts, degrades to below 10% accuracy on 30-digit multiplication. Departing from reasoning-through-scale, we introduce RACE (Recursive Arithmetic Control Encoder), a 3.6M-parameter Transformer trained from scratch that generalizes far better by recursively decomposing problems while keeping its working memory bounded. Two mechanisms drive this: token-level editing, which erases intermediate scratchwork, and self-calling, which recurses on subproblems. Within a single model, RACE improves multiplication length generalization 4.7 times over the Arithmetic Transformer and, for the first time, achieves length generalization on subtraction and division (×47.1 and ×17.6), while also solving nested, multi-operator expressions. Code is available at https://github.com/Pusheen-cat/RACE_2026.</abstract>
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%0 Conference Proceedings
%T Beyond Append-Only Decoding: A Recursive Edit-Based Encoder for Arithmetic Length Generalization
%A Kang, Bong Gyun
%A Ahn, Junyong
%A Byeon, Jieun
%A Yoon, Sungroh
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F kang-etal-2026-beyond
%X Algorithmic reasoning—internalizing a procedure from small examples and applying it at arbitrary scale—is a hallmark of human intelligence: a child who learns arithmetic on a few digits can, given time and paper, evaluate expressions of unbounded length. Modern language models cannot: Qwen3.5-27B, despite 100k-token reasoning contexts, degrades to below 10% accuracy on 30-digit multiplication. Departing from reasoning-through-scale, we introduce RACE (Recursive Arithmetic Control Encoder), a 3.6M-parameter Transformer trained from scratch that generalizes far better by recursively decomposing problems while keeping its working memory bounded. Two mechanisms drive this: token-level editing, which erases intermediate scratchwork, and self-calling, which recurses on subproblems. Within a single model, RACE improves multiplication length generalization 4.7 times over the Arithmetic Transformer and, for the first time, achieves length generalization on subtraction and division (×47.1 and ×17.6), while also solving nested, multi-operator expressions. Code is available at https://github.com/Pusheen-cat/RACE_2026.
%U https://aclanthology.org/2026.emnlp-main.1920/
%P 43731-43750
Markdown (Informal)
[Beyond Append-Only Decoding: A Recursive Edit-Based Encoder for Arithmetic Length Generalization](https://aclanthology.org/2026.emnlp-main.1920/) (Kang et al., EMNLP 2026)
ACL