Arithmetic with Language Models: from Memorization to Computation

• URL: http://arxiv.org/abs/2308.01154v4
• Date: Fri, 2 Aug 2024 12:39:17 GMT
• Title: Arithmetic with Language Models: from Memorization to Computation
• Authors: Davide Maltoni, Matteo Ferrara,
• Abstract summary: This work investigates how a language model, trained to predict the next token, can perform arithmetic computations generalizing beyond training data. We successfully trained a light language model to learn these tasks and ran a number of experiments to investigate the extrapolation capabilities and internal information processing.
• Score: 3.077668143048211
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A better understanding of the emergent computation and problem-solving capabilities of recent large language models is of paramount importance to further improve them and broaden their applicability. This work investigates how a language model, trained to predict the next token, can perform arithmetic computations generalizing beyond training data. Binary addition and multiplication constitute a good testbed for this purpose, since they require a very small vocabulary and exhibit relevant input/output discontinuities making smooth input interpolation ineffective for novel data. We successfully trained a light language model to learn these tasks and ran a number of experiments to investigate the extrapolation capabilities and internal information processing. Our findings support the hypothesis that the language model works as an Encoding-Regression-Decoding machine where the computation takes place in the value space once the input token representation is mapped to an appropriate internal representation.

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