Self-attention mechanism in PyTorch - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of scaled dot-product attention calculation

Given the following PyTorch code snippet implementing scaled dot-product attention, what is the output tensor?

PyTorch

import torch
import torch.nn.functional as F

query = torch.tensor([[1., 0., 0.]])  # shape (1, 3)
key = torch.tensor([[1., 0., 0.], [0., 1., 0.]])  # shape (2, 3)
value = torch.tensor([[1., 2.], [3., 4.]])  # shape (2, 2)

# Compute attention scores
scores = torch.matmul(query, key.T) / (3 ** 0.5)
weights = F.softmax(scores, dim=-1)
output = torch.matmul(weights, value)
print(output)

A [[1.9999, 2.9999]]

B [[3.0, 4.0]]

C [[1.718, 2.718]]

D [[1.5, 2.5]]

💡 Hint

Recall that softmax normalizes scores to probabilities, and output is weighted sum of values.

The query matches perfectly with the first key vector, so the attention weight for the first key is near 1, and near 0 for the second. The output is close to the first value vector [1., 2.]. After scaling and softmax, the output is approximately [[1.718, 2.718]].

❓ Model Choice

intermediate

Choosing the correct self-attention output shape

In a self-attention layer, if the input tensor has shape (batch_size=4, seq_len=10, embedding_dim=64), what will be the shape of the output tensor after applying multi-head self-attention with 8 heads and the same embedding dimension?

A (4, 10, 512)

B (4, 10, 64)

C (4, 8, 10, 8)

D (4, 64, 10)

💡 Hint

Multi-head attention splits embedding_dim into heads but concatenates back to original embedding_dim.

Multi-head attention splits the embedding dimension into 8 heads of size 8 each (64/8=8), processes attention in parallel, then concatenates back to shape (batch_size, seq_len, embedding_dim), which is (4, 10, 64).

❓ Hyperparameter

advanced

Effect of increasing number of attention heads

What is the most likely effect of increasing the number of attention heads in a multi-head self-attention model while keeping the total embedding dimension fixed?

A The model's total capacity increases linearly with the number of heads.

B The model becomes unable to learn because the embedding dimension is fixed.

C The embedding dimension per head increases, improving feature representation.

D Each head attends to a smaller subspace, potentially capturing more diverse features.

💡 Hint

Think about how embedding dimension is split among heads.

Increasing heads splits the fixed embedding dimension into smaller parts per head, allowing each head to focus on different aspects of the input, improving diversity of attention.

🔧 Debug

advanced

Identifying error in self-attention implementation

Consider this PyTorch code snippet for self-attention. What error will it raise when executed?

PyTorch

import torch
import torch.nn.functional as F

query = torch.randn(2, 5, 16)
key = torch.randn(2, 5, 16)
value = torch.randn(2, 5, 16)

scores = torch.matmul(query, key) / (16 ** 0.5)
weights = F.softmax(scores, dim=-1)
output = torch.matmul(weights, value)
print(output.shape)

A RuntimeError due to shape mismatch in torch.matmul(query, key)

B RuntimeError due to shape mismatch in torch.matmul(weights, value)

C No error, prints torch.Size([2, 5, 16])

D SyntaxError due to missing colon

💡 Hint

Check the dimensions of query and key for matrix multiplication.

query has shape (2,5,16) and key has shape (2,5,16). torch.matmul expects the last two dims to be compatible. Here, 16 != 5, so it raises RuntimeError.

🧠 Conceptual

expert

Why use scaled dot-product in self-attention?

Why do self-attention mechanisms scale the dot product of query and key vectors by the square root of their dimension?

A To prevent the dot products from growing too large, which can cause softmax gradients to vanish.

B To increase the magnitude of dot products, making attention weights sharper.

C To normalize the query and key vectors to unit length before dot product.

D To reduce computational cost by scaling down the vectors.

💡 Hint

Think about how large dot products affect softmax.

Without scaling, large dot products can push softmax into regions with very small gradients, making training harder. Scaling by sqrt(dim) keeps values in a range that stabilizes gradients.