Analyzing Transformer Dynamics as Movement through Embedding Space

Transformer language models exhibit intelligent behaviors such as understanding natural language, recognizing patterns, acquiring knowledge, reasoning, planning, reflecting and using tools. This paper explores how their underlying mechanics give rise to intelligent behaviors. We adopt a systems approach to analyze Transformers in detail and develop a mathematical framework that frames their dynamics as movement through embedding space. This novel perspective provides a principled way of thinking about the problem and reveals important insights related to the emergence of intelligence: 1. At its core the Transformer is a Embedding Space walker, mapping intelligent behavior to trajectories in this vector space. 2. At each step of the walk, it composes context into a single composite vector whose location in Embedding Space defines the next step. 3. No learning actually occurs during decoding; in-context learning and generalization are simply the result of different contexts composing into different vectors. 4. Ultimately the knowledge, intelligence and skills exhibited by the model are embodied in the organization of vectors in Embedding Space rather than in specific neurons or layers. These abilities are properties of this organization. 5. Attention's contribution boils down to the association-bias it lends to vector composition and which influences the aforementioned organization. However, more investigation is needed to ascertain its significance. 6. The entire model is composed from two principal operations: data independent filtering and data dependent aggregation. This generalization unifies Transformers with other sequence models and across modalities. Building upon this foundation we formalize and test a semantic space theory which posits that embedding vectors represent semantic concepts and find some evidence of its validity.