A Unified Geometric Field Theory Framework for Transformers: From Manifold Embeddings to Kernel Modulation
This provides a foundational theoretical framework for understanding Transformers, potentially benefiting researchers in machine learning and AI.
The paper tackles the lack of a unified mathematical interpretation for Transformers' positional encoding and attention mechanisms by proposing a theoretical framework that maps discrete positions to continuous manifolds, enabling a field-theoretic view of Transformer layers as kernel-modulated operators.
The Transformer architecture has achieved tremendous success in natural language processing, computer vision, and scientific computing through its self-attention mechanism. However, its core components-positional encoding and attention mechanisms-have lacked a unified physical or mathematical interpretation. This paper proposes a structural theoretical framework that integrates positional encoding, kernel integral operators, and attention mechanisms for in-depth theoretical investigation. We map discrete positions (such as text token indices and image pixel coordinates) to spatial functions on continuous manifolds, enabling a field-theoretic interpretation of Transformer layers as kernel-modulated operators acting over embedded manifolds.