Information Entropy Invariance: Enhancing Length Extrapolation in Attention Mechanisms

Improving the length extrapolation capabilities of Large Language Models (LLMs) remains a critical challenge in natural language processing. Many recent efforts have focused on modifying the scaled dot-product attention mechanism, and often introduce scaled temperatures without rigorous theoretical justification. To fill this gap, we introduce a novel approach based on information entropy invariance. We propose two new scaled temperatures to enhance length extrapolation. First, a training-free method InfoScale is designed for dot-product attention, and preserves focus on original tokens during length extrapolation by ensuring information entropy remains consistent. Second, we theoretically analyze the impact of scaling (CosScale) on cosine attention. Experimental data demonstrates that combining InfoScale and CosScale achieves state-of-the-art performance on the GAU-{\alpha} model with a context window extended to 64 times the training length, and outperforms seven existing methods. Our analysis reveals that significantly increasing CosScale approximates windowed attention, and highlights the significance of attention score dilution as a key challenge in long-range context handling. The code and data are available at https://github.com/HT-NEKO/InfoScale.