The network doesn't detect matches, but the model definitely works on similarities. Words are mapped in a hyperspace, with the idea that that space can mathematically retain conceptual similarity as spatial representation.

Words are transformed in a mathematical representation that is able (or at least tries) to retain semantic information of words.

But different meanings of the different words belongs to the words themselves and are defined by the language, model cannot modify them.

Anyway we are talking about details here. We could kill the audience of boredom

Edit. I asked gpt-4 to summarize the concepts. I believe it did a decent job. I hope it helps:

1. Embedding Space:

   • Initially, every token is mapped to a point (or vector) in a high-dimensional space via embeddings. This space is typically called the "embedding space."
   • The dimensionality of this space is determined by the size of the embeddings. For many Transformer models, this is often several hundred dimensions, e.g., 768 for some versions of GPT and BERT.

2. Positional Encodings:

   • These are vectors added to the embeddings to provide positional context. They share the same dimensionality as the embedding vectors, so they exist within the same high-dimensional space.

3. Transformations Through Layers:

   • As tokens' representations (vectors) pass through Transformer layers, they undergo a series of linear and non-linear transformations. These include matrix multiplications, additions, and the application of functions like softmax.
   • At each layer, the vectors are "moved" within this high-dimensional space. When we say "moved," we mean they are transformed, resulting in a change in their coordinates in the vector space.
   • The self-attention mechanism allows a token's representation to be influenced by other tokens' representations, effectively "pulling" or "pushing" it in various directions in the space based on the context.

4. Nature of the Vector Space:

   • This space is abstract and high-dimensional, making it hard to visualize directly. However, in this space, the "distance" and "direction" between vectors can have semantic meaning. Vectors close to each other can be seen as semantically similar or related.
   • The exact nature and structure of this space are learned during training. The model adjusts the parameters (like weights in the attention mechanisms and feed-forward networks) to ensure that semantically or syntactically related concepts are positioned appropriately relative to each other in this space.

5. Output Space:

   • The final layer of the model transforms the token representations into an output space corresponding to the vocabulary size. This is a probability distribution over all possible tokens for the next word prediction.

In essence, the entire process of token representation within the Transformer model can be seen as continuous transformations within a vector space. The space itself can be considered a learned representation where relative positions and directions hold semantic and syntactic significance. The model's training process essentially shapes this space in a way that facilitates accurate and coherent language understanding and generation.