In the context of input embedding in a Transformer, a vector representation means that each word (or subword/token) from the input sequence is mapped to a fixed-length numerical vector—typically a high-dimensional dense vector.
Here’s a breakdown:
🔹 What is a Vector Representation?
A vector is simply an array of numbers (like [0.1, -0.3, 0.7, ..., 0.05]) that represents the semantic meaning of a token in a form that a neural network can understand.
- For example, if the embedding size is 512, each token is mapped to a 512-dimensional vector.
- This vector captures various linguistic properties (like syntax and semantics) learned during training.
🔹 Why Use It?
- Machine learning models can’t work with raw text (e.g., “apple”). They need numerical input.
- Embedding layers learn to assign similar vectors to semantically similar words, so “cat” and “dog” might have vectors that are closer to each other than to “car” or “computer”.
🔹 How Is It Done?
- A lookup table (called the embedding matrix) is initialized with random values and learned during training.
- Each token’s index is used to fetch its corresponding vector from this table.
Example:
Suppose the sentence is:
Input: ["I", "am", "a", "student"]
After tokenization and embedding:
"I" → [0.12, -0.45, 0.63, ..., 0.08]
"am" → [0.03, 0.91, -0.25, ..., -0.12]
...
These are then passed into the Transformer layers.
Q. From this page, embedding size is 512, means ?
When we say embedding size is 512, it means that each input token is represented by a vector of 512 numbers (dimensions) after the embedding layer.
Let’s break this down:
✅ What it means
- You have a vocabulary (say 50,000 tokens) → words, subwords, or characters.
- The embedding layer maps each token in that vocabulary to a 512-dimensional dense vector.
So:
- “cat” → [0.12, -0.33, 0.78, …, 0.05] → vector length = 512
- “dog” → [-0.41, 0.29, 0.55, …, -0.27] → vector length = 512
Even though “cat” and “dog” are very different words, after embedding they become points in a 512-dimensional space, and their relative positions (distance, angle) can capture meaningful relationships.
✅ Why 512?
- It’s a design choice—large enough to capture complex patterns, but small enough to train efficiently.
- Vaswani et al. (2017) chose 512 as a balance between performance and computation.
- Other models like BERT or GPT often use 768, 1024, or even 4096 depending on their scale.
✅ Summary
Embedding size = 512 → every token gets represented as a vector with 512 numerical values.
Q. Is, each token has its own separate 512-dimensional vector ?
✅ Yes — each token has its own separate 512-dimensional vector.
Let me explain clearly:
🔹 What happens in the embedding layer?
- You have a vocabulary of tokens, say 50,000 tokens.
- You set embedding size = 512.
The embedding layer creates a lookup table (embedding matrix) of size: 50,000 tokens×512 dimensions
So, it’s essentially a matrix of shape (50000, 512):
- Row 1 → embedding vector for token 1 (512 numbers)
- Row 2 → embedding vector for token 2 (512 numbers)
- …
- Row 50000 → embedding vector for token 50000 (512 numbers)
🔹 When you pass in a sequence
For example:
Input sequence: ["I", "am", "a", "student"]
Let’s say:
- “I” → token ID 12
- “am” → token ID 45
- “a” → token ID 78
- “student” → token ID 3000
The embedding layer:
- Looks up row 12 → 512-dimensional vector
- Looks up row 45 → 512-dimensional vector
- Looks up row 78 → 512-dimensional vector
- Looks up row 3000 → 512-dimensional vector
So, the sequence becomes a matrix of shape (4 tokens, 512 dimensions).
🔹 Important point:
✅ Each token has its own unique 512-dim vector,
✅ These vectors are learned and adjusted during training,
✅ Similar tokens may end up with similar vectors.
🔹 Example in simple form
| Token | 512-dimensional vector (example values) |
|---|---|
| “I” | [0.1, -0.3, 0.7, …, 0.05] |
| “am” | [0.03, 0.91, -0.25, …, -0.12] |
| “a” | [-0.15, 0.44, 0.62, …, 0.09] |
| “student” | [0.55, -0.67, 0.11, …, 0.33] |
Q. How embeddings are initialized and updated,
Great! Here’s a clear explanation on how embeddings are initialized and updated during model training:
🌟 1. How embeddings are initialized
At the start of training, the embedding layer is typically initialized with random numbers.
Specifically:
- The embedding matrix (shape:
vocab_size × embedding_dim) is filled with small random values, often drawn from:- Uniform distribution (e.g.,
U(-0.1, 0.1)), or - Normal distribution (e.g.,
N(0, 0.01)).
- Uniform distribution (e.g.,
Why random?
- Because we have no prior knowledge about the meaning of tokens before training.
- The model will learn the best values by itself during training.
🌟 2. How embeddings are updated
The embeddings are updated during backpropagation like any other model parameters.
Here’s the process:
1️⃣ Forward pass
- Input tokens → embedding layer → downstream layers → compute predictions → compute loss.
2️⃣ Backward pass
- Compute gradient of the loss with respect to each embedding vector.
- Example: If “student” appears in the input and contributes to the prediction error, the gradient of the loss will flow back to its embedding vector.
3️⃣ Parameter update
- The optimizer (e.g., Adam, SGD) adjusts the embedding matrix using the gradients: new embedding=old embedding−learning rate×gradient\text{new embedding} = \text{old embedding} – \text{learning rate} \times \text{gradient}
This happens for only the tokens present in the batch, not for all tokens.
🌟 3. Summary
| Step | What happens |
|---|---|
| Initialization | Random small values assigned to each embedding vector. |
| Forward pass | Lookup embeddings → pass through model → compute output. |
| Backward pass | Compute gradients of loss w.r.t. embeddings. |
| Update | Adjust only the embeddings used in the batch, via optimizer. |
🌟 Bonus: Pretrained embeddings
Sometimes we don’t start from random — we initialize with pretrained embeddings like:
- Word2Vec
- GloVe
- FastText
These are loaded into the embedding layer as initial values, and can be:
- Frozen → fixed during training.
- Fine-tuned → further updated with gradients.
🔧 Example in PyTorch
embedding = nn.Embedding(vocab_size, embedding_dim)
# Initialized randomly by default
optimizer = torch.optim.Adam(embedding.parameters(), lr=0.001)
# During training, optimizer updates embedding weights via backprop