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This work aims to develop a comprehensive mathematical theory explaining the structure and operations of the Transformer architecture.

A Mathematical Explanation of Transformers

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This work aims to develop a comprehensive mathematical theory explaining the structure and operations of the Transformer architecture.
Proposes a continuous framework interpreting the Transformer as a discretization of a structured integro-differential equation.
Characterizes self-attention as a nonlocal integral operator and layer normalization as a projection to a time-dependent constraint.
Embeds Transformer operations in continuous domains for token indices and feature dimensions.
The new mathematical interpretation offers a unified foundation for understanding core components of Transformers.
Enhances theoretical insight and suggests new directions for architecture design and analysis.
Bridges the gap between deep learning architectures and continuous mathematical modeling.

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Novel framework interprets Transformer using integro-differential equations, enhancing understanding and design.

Tai et al. (2026) studied this question.

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