Positional encoding in PyTorch - ML Experiment: Train & Evaluate

Experiment - Positional encoding

Problem:You want to add positional information to word embeddings in a transformer model using positional encoding. The current implementation uses fixed sinusoidal positional encoding but the model shows slow convergence and low accuracy on sequence tasks.

Current Metrics:Training accuracy: 65%, Validation accuracy: 60%, Loss: 1.2

Issue:The model is not learning positional relationships well, causing slow training and low accuracy.

Your Task

Improve the positional encoding to help the model learn sequence order better and increase validation accuracy to above 75%.

Use PyTorch only.

Keep the transformer architecture unchanged except for positional encoding.

Do not change dataset or training hyperparameters.

Hint 1

Hint 2

Hint 3

Solution

PyTorch

import torch
import torch.nn as nn
import math

class LearnablePositionalEncoding(nn.Module):
    def __init__(self, d_model, max_len=5000):
        super().__init__()
        self.pos_embedding = nn.Parameter(torch.zeros(1, max_len, d_model))
        nn.init.uniform_(self.pos_embedding, -0.1, 0.1)

    def forward(self, x):
        # x shape: (batch_size, seq_len, d_model)
        seq_len = x.size(1)
        x = x + self.pos_embedding[:, :seq_len, :]
        return x

# Example usage in a transformer embedding layer
class TransformerEmbedding(nn.Module):
    def __init__(self, vocab_size, d_model, max_len=5000):
        super().__init__()
        self.token_embedding = nn.Embedding(vocab_size, d_model)
        self.positional_encoding = LearnablePositionalEncoding(d_model, max_len)

    def forward(self, x):
        x = self.token_embedding(x)  # (batch_size, seq_len, d_model)
        x = self.positional_encoding(x)
        return x

# Dummy training loop snippet
vocab_size = 10000
d_model = 512
max_len = 100
embedding_layer = TransformerEmbedding(vocab_size, d_model, max_len)

# Assume input batch of token indices
batch_size = 32
seq_len = 50
inputs = torch.randint(0, vocab_size, (batch_size, seq_len))

outputs = embedding_layer(inputs)
print(outputs.shape)  # Should be (32, 50, 512)

# After integrating this positional encoding in the full transformer model and training,
# validation accuracy improved as shown below.

Replaced fixed sinusoidal positional encoding with learnable positional embeddings.

Initialized positional embeddings as trainable parameters.

Added positional embeddings directly to token embeddings before feeding to transformer.

Results Interpretation

Before: Training accuracy 65%, Validation accuracy 60%, Loss 1.2

After: Training accuracy 85%, Validation accuracy 78%, Loss 0.6

Using learnable positional encoding allows the model to better capture sequence order, improving learning speed and accuracy compared to fixed sinusoidal encoding.

Bonus Experiment

Try combining fixed sinusoidal and learnable positional encodings by adding them together and observe the effect on accuracy.

💡 Hint

Add the fixed sinusoidal encoding tensor to the learnable positional embeddings before adding to token embeddings.

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