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Updated: Jun 18, 2025

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
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Arithmetic with language models: From memorization to computation.

Davide Maltoni1, Matteo Ferrara1

  • 1Department of Computer Science and Engineering, University of Bologna, Italy.

Neural Networks : the Official Journal of the International Neural Network Society
|July 28, 2024
PubMed
Summary
This summary is machine-generated.

Large language models can perform arithmetic computations, like binary addition and multiplication, by generalizing beyond their training data. These models function as Encoding-Regression-Decoding machines for computational tasks.

Keywords:
AI explainabilityArithmeticInterpretabilityLanguage modelsProbing

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Area of Science:

  • Artificial Intelligence
  • Computational Linguistics
  • Machine Learning

Background:

  • Recent large language models (LLMs) demonstrate emergent computational abilities.
  • Understanding these capabilities is crucial for improving LLM performance and applications.

Purpose of the Study:

  • Investigate how LLMs trained on next-token prediction perform arithmetic computations.
  • Analyze the generalization capabilities of LLMs beyond their training data for mathematical tasks.

Main Methods:

  • Trained a lightweight language model on binary addition and multiplication tasks.
  • Conducted experiments to assess extrapolation capabilities and internal processing.
  • Utilized binary arithmetic as a testbed due to its small vocabulary and discontinuities.

Main Results:

  • Successfully trained a language model to perform binary addition and multiplication.
  • Demonstrated that the language model can generalize arithmetic computations to novel data.
  • Evidence suggests a computational process involving encoding, regression, and decoding within the model.

Conclusions:

  • Language models can be trained to perform arithmetic computations with generalization.
  • The model appears to operate as an Encoding-Regression-Decoding system for these tasks.
  • Computation occurs in a value space after mapping input tokens to internal representations.