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Teaching Arithmetic to Small Transformers (arxiv.org)
3 points by famouswaffles on Jul 10, 2023 | hide | past | pdf | 1 comment on HN

In plain words: Small transformers trained from scratch can learn addition, multiplication, and square roots, and how the training examples are formatted matters a lot. Giving the model worked-out intermediate steps raised accuracy while also needing fewer examples and converging faster than plain question-answer pairs.

Abstract

Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token prediction objective. This study investigates how small transformers, trained from random initialization, can efficiently learn arithmetic operations such as addition, multiplication, and elementary functions like square root, using the next-token prediction objective. We first demonstrate that conventional training data is not the most effective for arithmetic learning, and simple formatting changes can significantly improve accuracy. This leads to sharp phase transitions as a function of training data scale, which, in some cases, can be explained through connections to low-rank matrix completion. Building on prior work, we then train on chain-of-thought style data that includes intermediate step results. Even in the complete absence of pretraining, this approach significantly and simultaneously improves accuracy, sample complexity, and convergence speed. We also study the interplay between arithmetic and text data during training and examine the effects of few-shot prompting, pretraining, and model scale. Additionally, we discuss length generalization challenges. Our work highlights the importance of high-quality, instructive data that considers the particular characteristics of the next-word prediction objective for rapidly eliciting arithmetic capabilities.

Nayoung Lee, Kartik Sreenivasan, Jason D. Lee, Kangwook Lee, Dimitris Papailiopoulos
arXiv:2307.03381 · cs.LG · submitted Jul 7, 2023
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Also discussed: Jul 2023 (3 points, 0 comments)

There's also RWKV able to perform arithmetic to 100% with a tweak of the dataset https://twitter.com/BlinkDL_AI/status/1677593798531223552