Traveling Words: A Geometric Interpretation of Transformers

Introduction to the Geometric Perspective of Transformers

The transformative impact of the transformer architecture in AI has been immense, influencing areas like NLP, computer vision (CV), and robotics. However, as with many complex models, understanding their internal workings remains a challenge. In this context, a novel geometric perspective is introduced that sheds light on the inner workings of the transformer mechanism.

Layer Normalization in Transformers

The discussion begins with the concept of layer normalization, which is a crucial step in the transformer architecture. The paper presents new insights that show how layer normalization effectively confines input features into the surface of a hyper-sphere. By imposing this geometric constraint, the transformer model achieves normalized and consistent feature representation across different layers. This constraint is proven to be vital for maintaining stable attention focusing and avoiding issues with attention scattering over irrelevant keys. Once seen through this geometric lens, the transformer operations of iterative refinement and contextual embedding generation appear seamlessly related.

Analyzing Transformer Components Geometrically

The analysis proceeds with a detailed geometric dissection of the transformer components. Understanding the role of matrices like W QK and WV O enables intuitive grasping of attention operations as geometric transformations on the hyper-sphere. This geometric interpretation extends to probing the model, revealing subject-specific behavior of the attention heads and the nuanced interaction between queries and keys at different transformer layers. The paper also explores the geometric roles of W E (the embedding matrix) and how layer normalization influences the model's output probabilities, drawing parallels with the von Mises-Fisher distribution.

Experimental Findings

The final model insights are supplemented by experimental probing, which utilized a pre-trained 124M parameter GPT-2 model. The experiments investigated the effect of layer normalization on embeddings, attention heads' behavior with common nouns, singular value decomposition (SVD) of key transformer matrices, and finally, visualizations of the iterative refinement process across layers of the transformer. These analyses support the proposed geometric interpretation and offer intriguing indications of the nature of the transformations occurring at both shallow and deep transformer layers.

Conclusion and Interpretation

The paper concludes by echoing the proposed interpretation of transformers as geometric processes, interlinking all the pieces in a unified view that sees words as particles traveling across a hyper-spherical surface. Here, the transformer model sculpts the trajectory of these particles, altering their meaning at every step to reflect the journey from one word to the next. This geometric viewpoint not only provides a more intuitive understanding of transformers but also establishes a basis for future exploration and analysis of these models.