Learning Position with Positional Encoding

Transformers have revolutionized natural language processing, but their parallel processing nature necessitates a mechanism to retain sequential information. This is where positional encoding comes into play.

Why Do Transformers Need Positional Encoding?

Traditional Recurrent Neural Networks (RNNs) process sequences word by word, inherently capturing the order of words. For instance, in the sentence "I am good," an RNN processes "I," then "am," and finally "good," allowing it to learn contextual meaning over time through this sequential flow.

Transformers, on the other hand, process input sequences in parallel. This parallelism significantly boosts training speed and enables the capture of long-range dependencies. However, because all tokens are processed simultaneously, Transformers lack an inherent understanding of word order.

To bridge this gap, Transformers utilize positional encoding to inject crucial word order information into the model.

What Is Positional Encoding?

Positional encoding is a technique that adds information about the position of tokens within a sequence to their corresponding word embeddings. This ensures that the Transformer can differentiate between words based on their location in a sentence, even when processed in parallel.

The positional encoding is generated as a matrix that has the same shape as the word embedding matrix. This positional encoding matrix is then added element-wise to the word embeddings before they are fed into the Transformer's encoder.

Example: Understanding Positional Encoding

Let's consider the sentence: "I am good"

Assume an embedding dimension of 4. This means each word is represented by a vector of size 4. The input for this sentence, before positional encoding, would be an embedding matrix of shape [3 x 4], where:

• 3 represents the number of words in the sentence.
• 4 represents the embedding dimension (the size of each word vector).

This [3 x 4] embedding matrix only contains semantic information about the words. To incorporate positional information, we generate a positional encoding matrix of the same shape [3 x 4].

By adding the positional encoding matrix element-wise to the embedding matrix, the resulting matrix contains:

• The word's semantic meaning: Provided by the original word embeddings.
• The word's position in the sentence: Provided by the positional encoding.

This combined representation allows the Transformer to understand not just what a word means, but also where it appears in the sequence.

How Is the Positional Encoding Matrix Computed?

The authors of the Transformer paper, "Attention Is All You Need," proposed a sinusoidal positional encoding function. This function generates unique and continuous encodings for each position and dimension, allowing the model to generalize to sequences longer than those encountered during training.

The formulas for calculating the positional encoding are:

• For even indices (2i): $$ PE(pos, 2i) = \sin\left(\frac{pos}{10000^{2i/d}}\right) $$

• For odd indices (2i+1): $$ PE(pos, 2i+1) = \cos\left(\frac{pos}{10000^{2i/d}}\right) $$

Where:

• pos: The position of the word in the sentence (e.g., 0 for the first word, 1 for the second, etc.).
• i: The dimension index within the embedding vector.
• d: The total embedding dimension (the size of the word embedding vector).

This approach ensures that each position has a unique encoding, and the relative positions can be easily learned by the model through linear transformations of these encodings.

Example Calculation

For the sentence "I am good", the positions are:

• "I" → position 0
• "am" → position 1
• "good" → position 2

Using the sinusoidal formulas, we would calculate the sine and cosine values for each position and each dimension of the embedding vector. These values would fill the [3 x 4] positional encoding matrix. This matrix is then added element-wise to the [3 x 4] word embedding matrix.

Integration into the Encoder

After computing the positional encoding matrix and adding it to the word embedding matrix, the resulting combined matrix serves as the input to the Transformer's encoder. This unified representation allows the encoder to process not only the semantic content of the words but also their relative and absolute positions within the sequence.

This step is visually represented in the Transformer architecture diagrams, typically occurring right before the input enters the first encoder block.

Conclusion

Positional encoding is a critical component that empowers Transformers to understand and leverage word order without relying on recurrent processing. By embedding positional information alongside word semantics, it significantly enhances the model's comprehension of sentence structure and contextual meaning.

When combined with the multi-head attention mechanism, positional encodings enable Transformers to effectively capture complex linguistic patterns in natural language processing tasks.

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Interview Questions

• Why do Transformers require positional encoding?
• How does positional encoding differ from word embeddings?
• What problem does positional encoding solve in Transformers?
• Describe the formula used for sinusoidal positional encoding.
• What are the benefits of using sinusoidal functions for position encoding?
• How does positional encoding help in capturing word order?
• Can Transformers understand sequences without positional encoding?
• How is positional encoding integrated into the encoder block?
• What is the shape of the positional encoding matrix relative to embeddings?
• How does positional encoding support generalization to longer sequences?