Hacker News: Pre-Trained Large Language Models Use Fourier Features to Compute Addition

Feb 6, 2025

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Source URL: https://arxiv.org/abs/2406.03445
Source: Hacker News
Title: Pre-Trained Large Language Models Use Fourier Features to Compute Addition

Feedly Summary: Comments

AI Summary and Description: Yes

Short Summary: The paper discusses how pre-trained large language models (LLMs) utilize Fourier features to enhance their arithmetic capabilities, specifically focusing on addition. It provides insights into the mechanisms that enable these models to perform mathematical reasoning more effectively through the use of both low-frequency and high-frequency features in their architecture.

Detailed Description:
This research presents a significant advancement in understanding how pre-trained LLMs execute basic arithmetic operations, particularly addition. Key findings from the paper include:

– **Fourier Features Usage**: The study highlights that LLMs leverage Fourier features, which enables them to represent numerical values in a sparse frequency domain.

– **Layer Functionality**:
– **MLP Layers**: These layers primarily utilize low-frequency features to approximate the magnitude of addition.
– **Attention Layers**: They use high-frequency features to perform modular operations, such as determining if a sum is even or odd.

– **Importance of Pre-training**: The results indicate that pre-training plays a critical role; models trained from scratch exhibit reduced accuracy because they do not adequately utilize the full range of features available in the pre-trained models.

– **Rescuing Performance**: By incorporating pre-trained token embeddings into a model that was initialized randomly, the performance on addition tasks significantly improves, underlining the necessity of pre-trained representations for effective learning.

Overall, this research not only sheds light on the mathematical reasoning capabilities of LLMs but also offers a fundamental understanding of how their architectural components work together to tackle algorithmic tasks. This can have broader implications for AI practitioners focused on enhancing LLM deployed in varied applications, especially where mathematical accuracy is critical.

Key Insights for Professionals:
– Understanding the underlying mechanisms of LLMs like Fourier features can help in designing more efficient models for tasks requiring mathematical reasoning.
– Pre-training strategies should be a fundamental consideration in AI model development, particularly for operations where precision is paramount.
– The findings can guide future research and improvements in the mathematical capabilities of AI systems, contributing to the fields of AI security and compliance by potentially minimizing errors in critical computational tasks.

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