Positional encodings are a crucial component of transformer models, enabling them to understand the order of tokens in a sequence. Since transformers lack built-in mechanisms to process sequential data, positional encodings inject information about the position of each token, allowing the model to capture the structure of the input. In this blog post, we’ll explore three popular types of positional encodings: **Absolute Positional Encoding**, **Relative Positional Encoding**, and **Rotary Positional Encoding**. We’ll also discuss their differences, sample outputs, and why they matter.
Why Positional Encodings Matter
Transformers process input sequences in parallel, unlike recurrent neural networks (RNNs) that process tokens sequentially. While this parallelism improves efficiency, it also means transformers have no inherent understanding of token order. Positional encodings address this by adding information about the position of each token to the input embeddings. This allows the model to distinguish between tokens based on their order in the sequence.
Types of Positional Encodings
1. Absolute Positional Encoding
Absolute Positional Encoding assigns a unique representation to each position in the sequence using sine and cosine functions. The encoding is added to the input embeddings, providing the model with information about the absolute position of each token.
Key Features:
- Uses sine and cosine functions with varying frequencies across feature dimensions.
- Each feature dimension captures a different scale of positional information.
- Fixed and deterministic (not learned).
Sample Output:
For a sequence of length 100 and 5 feature dimensions, the encoding has a shape of `[100, 5]`. When visualized, it shows a sinusoidal pattern, with lower dimensions having lower frequencies and higher dimensions having higher frequencies.
Why It’s Important:
- Provides a unique representation for each position.
- Captures multi-scale positional information through varying frequencies.
2. Relative Positional Encoding
Relative Positional Encoding focuses on the distances between tokens rather than their absolute positions. It uses learned embeddings to represent relative positions, making it more flexible than fixed encodings.
Key Features:
- Encodes the relative distances between tokens.
- Uses learned embeddings (e.g., via `nn.Embedding`).
- Applied dynamically based on the relative positions of tokens.
Sample Output:
For a sequence of length 100 and 5 feature dimensions, the encoding has a shape of `[100, 5]`. Unlike Absolute Encoding, it does not show a clear sinusoidal pattern but instead reflects the learned representations of relative positions.
Note on Relative Positional Encoding:
Relative positional encodings can have a high range of values, which may lead to training instability. To address this, it is recommended to normalize the relative positions or scale the learned embeddings to a smaller range (e.g.,
[-1, 1]). Additionally, applying layer normalization can help stabilize the training process and ensure better convergence.Why It’s Important:
- Captures the relative order of tokens, which is often more important than absolute positions.
- Learned embeddings allow the model to adapt to the task.
3. Rotary Positional Encoding
Rotary Positional Encoding applies a rotation matrix to the input embeddings based on their positions. This method modifies the embeddings directly, preserving their norm while encoding positional information.
Key Features:
- Uses rotation matrices to encode positions.
- Each feature dimension is rotated differently based on its index.
- Preserves the norm of the embeddings.
Sample Output:
For a sequence of length 100 and 5 feature dimensions, the encoding has a shape of `[100, 5]`. The output shows a unique rotation pattern for each feature dimension, reflecting the rotation-based approach.
Why It’s Important:
- Preserves the relative distances between embeddings better than Absolute Encoding.
- Elegant and theoretically appealing due to its rotation mechanism.
Sample Outputs and Unique Values
We have visualized the produced positional encoding values. Do they all give unique values for each feature? The answer is as below
Relative shape: torch.Size([100, 5]) unique: 500 | Learned embeddings are less likely to repeat values.
Rotary shape: torch.Size([100, 5]) unique: 298 | Rotation operation and periodic functions lead to repeated values.
1. **Absolute vs. Rotary**:
- Both use sinusoidal functions to encode positions, but Rotary Encoding applies a rotation matrix, making it more elegant and theoretically appealing.
- Absolute Encoding is fixed, while Rotary Encoding modifies the embeddings directly.
2. **Relative Encoding**:
- Focuses on the distances between tokens rather than their absolute positions.
- Uses learned embeddings, making it more flexible but computationally heavier.
3. **Why Different Encodings for Each Feature Dimension?**
- Varying encodings across feature dimensions allow the model to capture multi-scale positional information.
- This increases the expressiveness of the model and avoids redundancy.
4. **Unique Values are different for eac encoding? (expected 500? (seq * F))**:
- The number of unique values depends on the encoding method. Absolute and Rotary encodings may have fewer unique values due to the periodic nature of sine and cosine functions, while Relative Encoding typically has more unique values due to learned embeddings.
Conclusion
Positional encodings are a fundamental part of transformer models, enabling them to process sequential data effectively. Absolute, Relative, and Rotary encodings each have their strengths and trade-offs, making them suitable for different tasks. Understanding these encodings and their properties can help you choose the right approach for your specific use case.
Whether you’re working on language modeling, machine translation, time series or any other sequence-based task, positional encodings play a critical role in ensuring your model understands the order of tokens. By experimenting with these encodings and analyzing their outputs, you can gain deeper insights into how they work and how to leverage them effectively.
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