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