Step 3: Applying the Softmax Function in Self-Attention

This section details the crucial role of the softmax function in the self-attention mechanism, specifically after the scaled dot product of query and key matrices.

Why Softmax is Used in Self-Attention

Following the computation and scaling of the dot product between the query ($Q$) and key ($K$) matrices, the resulting similarity scores are unnormalized. These scores can span any range of values, making them unsuitable for direct interpretation as attention weights.

The softmax function is applied to each row of this score matrix to address this. Its primary purpose is to transform these unnormalized similarity scores into a probability distribution.

How Softmax Works in Self-Attention

The softmax function has two key properties when applied to the attention scores:

1. Normalization: It converts each score into a value between 0 and 1.
2. Summation to One: It ensures that the sum of all values within each row of the resulting matrix equals 1.

These properties allow the model to interpret the output as attention weights. Each weight signifies the relative importance or focus that a particular word (represented by a row) should place on every other word in the sequence (represented by the columns) for the current context.

Formula

The attention weights are calculated by applying the softmax function to the scaled dot product of the query and key matrices:

$$ \text{Attention Weights} = \text{softmax}\left(\frac{Q \cdot K^T}{\sqrt{d_k}}\right) $$

Where:

• $Q$ is the Query matrix.
• $K^T$ is the transpose of the Key matrix.
• $d_k$ is the dimension of the key vectors.
• $\sqrt{d_k}$ is the scaling factor.

Example: Interpreting Attention Scores

Consider the simple sentence: "I am good."

Let's assume that after the scaled dot product and softmax function, the attention weights for the word "I" are as follows:

• "I": 0.90
• "am": 0.07
• "good": 0.03

Interpretation:

These weights indicate the following distribution of attention for the word "I":

• "I" focuses 90% on itself.
• "I" focuses 7% on the word "am".
• "I" focuses 3% on the word "good".

This single row in the attention matrix represents how the word "I" "attends" to every other word (including itself) in the sentence to gather contextual information. This process is independently repeated for every word ("am", "good") in the sentence, resulting in a complete attention score matrix.

Conclusion

The softmax function is indispensable in the self-attention mechanism. It normalizes the raw similarity scores into a coherent probability distribution, enabling the model to compute meaningful attention weights. These weights are critical for the Transformer model to effectively capture contextual relationships between words and understand the nuances of language.

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Interview Questions

• What is the purpose of using the softmax function in self-attention?
• How does softmax convert similarity scores into attention weights?
• Why must the attention weights sum to 1?
• What would happen if we didn’t apply softmax after the scaled dot product?
• In the context of Transformers, how is softmax applied to the attention score matrix?
• Can you explain the relationship between softmax and context-awareness in self-attention?
• How does softmax handle very large or very small input scores?
• Why is softmax applied row-wise in the attention score matrix?
• How does softmax contribute to differentiability in the Transformer model?
• In a sentence like “I am good,” what do softmax attention weights represent for each word?