Definition
- Token Embedding Matrix (
wte): This matrix is a learned representation where each row corresponds to a unique token (word or subword) in the model’s vocabulary. The columns represent the features or dimensions of the embedding space. This matrix is typically learned during the training process of the model.
Structure and Dimensions
- Dimensions: If the vocabulary size of the model is VV and the embedding dimension is CC, then the token embedding matrix will have the dimensions V×CV×C. For instance, if there are 50,000 tokens in the vocabulary and each embedding is 768-dimensional, the matrix size will be 50,000 x 768.
- Content: Each row in this matrix is a vector representing a token. The vector is not human-readable and generally doesn’t have an interpretable meaning in conventional terms. It’s a high-dimensional representation that the model learns to associate with the semantics and usage patterns of the token.
How It Works
- Lookup Process: During the forward pass, the model receives a sequence of token indices as input. These indices are used to “look up” or retrieve the corresponding embedding vectors from the token embedding matrix. This process is often referred to as an embedding lookup.
- Example: Suppose the word “hello” is represented by index 423 in the vocabulary. The model will access the 423rd row of the token embedding matrix to fetch the embedding vector for “hello”.
Importance
- Semantic Representation: The embeddings capture semantic and syntactic aspects of the tokens. Tokens that are used in similar contexts tend to have closer embeddings in the vector space, a property useful for many language tasks.
- Training: Initially, these embeddings are random but learn to capture meaningful representations through the backpropagation of error gradients during training.
Visualization (Conceptual)
Here’s a simplified conceptual view of what a part of a token embedding matrix might look like:
+---------+------------------+------------------+-----+------------------+
| TokenID | Feature_1 | Feature_2 | ... | Feature_C |
+---------+------------------+------------------+-----+------------------+
| 1 | 0.786 | -1.234 | ... | 0.045 |
| 2 | -0.560 | 0.990 | ... | -0.112 |
| ... | ... | ... | ... | ... |
| 423 | 0.158 | 0.732 | ... | -0.903 |
| ... | ... | ... | ... | ... |
| V | -0.369 | 0.209 | ... | 1.334 |
+---------+------------------+------------------+-----+------------------+
In this table, each row under “Feature_1” to “Feature_C” is the embedding of the token identified by “TokenID”.
Usage
The embeddings are used as the first transformation step in models to convert categorical token information into a form that the subsequent layers (like attention layers in GPT-2) can process effectively.
Would you like to delve into how these embeddings are used in training, or perhaps explore more about positional embeddings or other components of the model?