Position Interpolation: Extending Context Window Sizes in Large Language Models

In this blog post, we will delve into the paper Position Interpolation for Large Language Models, which proposes a novel method to extend the context window sizes of large language models (LLMs) such as LLaMA.

Introduction

The paper introduces a technique called Position Interpolation (PI) to enable LLMs to handle longer context windows without the need for training from scratch. The researchers found that directly fine-tuning an existing LLM with a longer context window is inefficient and slow. Instead, they propose down-scaling the position indices to match the original context window size, using interpolation rather than extrapolation. This approach allows for the accommodation of more input tokens without causing catastrophic attention scores.

Positional Encodings in Transformers

Positional encodings are a crucial component of Transformer models. They provide a sense of order to the input tokens, allowing the model to understand the position of each token in the sequence. Without positional encodings, all input tokens would be processed independently, and the model would lose the ability to understand the sequence’s order.

There are several types of positional encodings used in Transformer models:

1. Fixed Positional Encodings: These are pre-computed vectors that are added to the input embeddings. The original Transformer model uses sinusoidal positional encodings, which are generated using a specific formula involving sine and cosine functions.
2. Learned Positional Encodings: These are vectors that are learned during training. They start as random vectors and are updated via backpropagation, just like the model’s weights.
3. Rotary Positional Encodings (RoPE): Introduced in the LLaMA model, these are a type of learned positional encodings that are applied via a rotation operation rather than addition. This allows the model to preserve the magnitude of the input embeddings while still incorporating positional information.

Rotary Positional Encodings in LLaMA

LLaMA uses Rotary Positional Encodings (RoPE) to incorporate positional information into the input embeddings. Unlike traditional positional encodings, which are added to the input embeddings, RoPE are applied via a rotation operation. This allows the model to preserve the magnitude of the input embeddings while still incorporating positional information.

The rotation operation is a complex multiplication in the Fourier space, which can be thought of as a rotation in a high-dimensional space. This rotation changes the direction of the input embeddings based on their positions, allowing the model to distinguish between tokens at different positions.

Position Interpolation

The paper proposes Position Interpolation (PI) as a method to extend the context window size of LLMs. The idea is to down-scale the position indices to match the original context window size. For instance, if we have a model with a context window size of 512 tokens, and we want to extend it to 1024 tokens, we calculate the corresponding position in the 512-token window for each position in the 1024-token window using interpolation.

This approach allows the model to accommodate more input tokens without causing catastrophic attention scores. It’s like tricking the model into thinking it’s still working with a 512-token window, while it’s actually processing a 1024-token window.

For example, consider a story of 1024 tokens long. Without PI, the model would have to process the story in two chunks of 512 tokens each, potentially losing context between the two chunks. With PI, the model can process the entire 1024-token story at once, maintaining the context across the entire story.

Summary

Position Interpolation is a promising technique to extend the capabilities of large language models, allowing them to handle longer contexts more efficiently and effectively. By interpolating the position indices, the model can process longer sequences without having to see new position embeddings that it hasn’t seen during training. This can help maintain the model’s performance while enabling it to handle longer contexts.

I hope this blog post provides a comprehensive overview of Position Interpolation and its significance in the context of large language models. If you have any questions or comments, feel free to leave them below!