Positional encoding in PyTorch - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a positional encoding tensor of zeros with shape (max_len, d_model).

PyTorch

pos_encoding = torch.zeros([1], d_model)

Drag options to blanks, or click blank then click option'

Aseq_len

Bd_model

Cbatch_size

Dmax_len

Attempts:

3 left

💡 Hint

Common Mistakes

Using d_model as the first dimension instead of max_len.

Confusing batch size with sequence length.

We create a positional encoding tensor with shape (max_len, d_model) to hold positional information for each position up to max_len.

2fill in blank

medium

Complete the code to compute the position indices tensor for max_len positions.

PyTorch

position = torch.arange([1]).unsqueeze(1)

Drag options to blanks, or click blank then click option'

Ad_model

Bbatch_size

Cmax_len

Dseq_len

Attempts:

3 left

💡 Hint

Common Mistakes

Using d_model instead of max_len for position range.

Not unsqueezing to get a column vector.

We use torch.arange(max_len) to get position indices from 0 to max_len-1, then unsqueeze to make it a column vector.

3fill in blank

hard

Fix the error in the code to compute the angle rates for positional encoding.

PyTorch

angle_rates = 1 / torch.pow(10000, (2 * ([1] // 2)) / d_model)

Drag options to blanks, or click blank then click option'

Ai

Bpos

Cdim

Dposition

Attempts:

3 left

💡 Hint

Common Mistakes

Using position instead of dimension index.

Using undefined variable pos.

The variable i represents the dimension index used to calculate the angle rates for each dimension.

4fill in blank

hard

Fill both blanks to assign sine to even indices and cosine to odd indices in the positional encoding.

PyTorch

pos_encoding[:, [1]] = torch.sin(angle_rads[:, [2]])

Drag options to blanks, or click blank then click option'

A::2

B1::2

C0::2

D2::2

Attempts:

3 left

💡 Hint

Common Mistakes

Using odd indices for sine instead of even.

Mismatching slices between pos_encoding and angle_rads.

Even indices start at 0 and step by 2, so 0::2 selects even dims for sine. The angle_rads uses the same indexing.

5fill in blank

hard

Complete the code to assign cosine to odd indices in the positional encoding.

PyTorch

pos_encoding[:, [1]] = torch.cos(angle_rads[:, [2]])

Drag options to blanks, or click blank then click option'

A::2

B1::2

C0::2

D2::2

Attempts:

3 left

💡 Hint

Common Mistakes

Using even indices (0::2 or ::2) for cosine.

Mismatching slices between pos_encoding and angle_rads.

Odd indices start at 1 and step by 2, so 1::2 selects odd dims for cosine. Use the same slice for angle_rads.

Practice

1. What is the main purpose of positional encoding in transformer models?

easy

A. To increase the number of layers in the model

B. To reduce the size of the input data

C. To add information about the order of tokens in a sequence

D. To normalize the input embeddings

Solution

1. Step 1: Understand the role of positional encoding

   Positional encoding adds information about the position of each token in the input sequence, which helps the model understand order. The other options relate to unrelated tasks such as increasing the number of layers, reducing input size, or normalizing embeddings.

2. Final Answer:

   To add information about the order of tokens in a sequence -> Option C

3. Quick Check:

   Positional encoding = order info [OK]

Hint: Positional encoding = position info added to embeddings [OK]

Common Mistakes:

• Thinking positional encoding reduces data size
• Confusing positional encoding with normalization
• Assuming it increases model layers

2. Which of the following is the correct way to compute the positional encoding for position pos and dimension i using sine and cosine functions in PyTorch?

easy

A. pos_enc[pos, i] = sin(pos * 10000^(i/d_model))

B. pos_enc[pos, 2*i] = sin(pos / 10000^(2*i/d_model)); pos_enc[pos, 2*i+1] = cos(pos / 10000^(2*i/d_model))

C. pos_enc[pos, i] = cos(pos / 10000^(i/d_model))

D. pos_enc[pos, 2*i] = cos(pos / 10000^(2*i/d_model)); pos_enc[pos, 2*i+1] = sin(pos / 10000^(2*i/d_model))

Solution

1. Step 1: Recall the positional encoding formula

   Positional encoding uses sine for even indices and cosine for odd indices with the formula: pos_enc[pos, 2*i] = sin(pos / 10000^(2*i/d_model)); pos_enc[pos, 2*i+1] = cos(pos / 10000^(2*i/d_model)).

2. Final Answer:

   pos_enc[pos, 2*i] = sin(pos / 10000^(2*i/d_model)); pos_enc[pos, 2*i+1] = cos(pos / 10000^(2*i/d_model)) -> Option B

3. Quick Check:

   Sine even, cosine odd = pos_enc[pos, 2*i] = sin(pos / 10000^(2*i/d_model)); pos_enc[pos, 2*i+1] = cos(pos / 10000^(2*i/d_model)) [OK]

Hint: Sine for even dims, cosine for odd dims in positional encoding [OK]

Common Mistakes:

• Swapping sine and cosine roles
• Using multiplication instead of division in exponent
• Applying sine or cosine to all dimensions only

3. Given the following PyTorch code snippet for positional encoding, what is the shape of the output tensor pos_encoding?

import torch
import math

def get_positional_encoding(seq_len, d_model):
    pos_encoding = torch.zeros(seq_len, d_model)
    for pos in range(seq_len):
        for i in range(0, d_model, 2):
            pos_encoding[pos, i] = math.sin(pos / (10000 ** (i / d_model)))
            if i + 1 < d_model:
                pos_encoding[pos, i + 1] = math.cos(pos / (10000 ** (i / d_model)))
    return pos_encoding

pos_encoding = get_positional_encoding(50, 512)

medium

A. [50, 512]

B. [512, 50]

C. [50, 256]

D. [512, 512]

Solution

1. Step 1: Analyze function input parameters and output shape

   The function takes seq_len=50 and d_model=512, creating a tensor of zeros with shape (50, 512). The loops fill values in this tensor without changing its shape, so output shape remains (50, 512).

2. Final Answer:

   [50, 512] -> Option A

3. Quick Check:

   Output shape = (seq_len, d_model) = [50, 512] [OK]

Hint: Output shape matches (sequence length, embedding dim) [OK]

Common Mistakes:

• Confusing dimensions order
• Thinking output is half the embedding size
• Assuming square matrix output

4. Identify the error in this PyTorch positional encoding code and select the fix:

import torch
import math

def positional_encoding(seq_len, d_model):
    pos_enc = torch.zeros(seq_len, d_model)
    for pos in range(seq_len):
        for i in range(d_model):
            pos_enc[pos, i] = math.sin(pos / 10000 ** (i / d_model))
    return pos_enc

pos_enc = positional_encoding(10, 16)

medium

A. Use sine for even indices and cosine for odd indices instead of sine only

B. Change math.sin to torch.sin for GPU compatibility

C. Initialize pos_enc with ones instead of zeros

D. Remove the inner loop and use vectorized operations

Solution

1. Step 1: Review positional encoding formula and identify fix

   Positional encoding uses sine for even dimensions and cosine for odd dimensions, but code uses sine only. Use sine for even indices and cosine for odd indices instead of sine only correctly fixes this.

2. Final Answer:

   Use sine for even indices and cosine for odd indices instead of sine only -> Option A

3. Quick Check:

   Sine and cosine alternate = Use sine for even indices and cosine for odd indices instead of sine only [OK]

Hint: Positional encoding alternates sine and cosine per dimension [OK]

Common Mistakes:

• Using sine only for all dimensions
• Ignoring cosine for odd indices
• Thinking initialization value causes error

5. You want to add positional encoding to a batch of input embeddings with shape (batch_size, seq_len, d_model) in PyTorch. Which approach correctly applies positional encoding to each sequence in the batch?

hard

A. Create a positional encoding tensor of shape (batch_size, d_model) and multiply element-wise with input embeddings

B. Create a positional encoding tensor of shape (seq_len,) and add it to input embeddings directly

C. Create a positional encoding tensor of shape (batch_size, seq_len, 1) and concatenate it to input embeddings

D. Create a positional encoding tensor of shape (seq_len, d_model) and add it to input embeddings using broadcasting

Solution

1. Step 1: Understand input and positional encoding shapes

   Input embeddings have shape (batch_size, seq_len, d_model). Positional encoding is per position and dimension, so shape (seq_len, d_model) fits. Adding it broadcasts over batch dimension correctly.

2. Final Answer:

   Create a positional encoding tensor of shape (seq_len, d_model) and add it to input embeddings using broadcasting -> Option D

3. Quick Check:

   Broadcast positional encoding over batch = Create a positional encoding tensor of shape (seq_len, d_model) and add it to input embeddings using broadcasting [OK]

Hint: Broadcast positional encoding (seq_len, d_model) over batch [OK]

Common Mistakes:

• Using positional encoding without seq_len dimension
• Multiplying instead of adding positional encoding
• Concatenating positional encoding incorrectly