傅立葉位置嵌入：增強注意力的週期擴展以實現長度泛化

摘要

通過改進旋轉位置嵌入（RoPE）來擴展語言模型（LMs）的上下文長度已成為一種趨勢。雖然現有的研究主要解決了注意機制內RoPE的局限性，但本文在LMs的幾乎所有部分提供了分析，揭示了它們對基於RoPE的注意力在長度泛化方面的不利影響。利用離散信號處理理論，我們展示RoPE通過隱式實現非均勻離散傅立葉變換來實現週期性注意力。然而，這種周期性受到以下因素造成的頻譜損傷的影響：1）在注意力之外的線性層和激活函數；2）由時域截斷帶來的訓練不足的頻率成分。基於我們的觀察，我們提出了傅立葉位置嵌入（FoPE），它增強了注意力的頻域特性，從而改善了其週期擴展和長度泛化。FoPE構建傅立葉級數並清除破壞性頻率成分，增加了模型對頻譜損傷的韌性。在各種模型規模上進行的實驗顯示，在不同上下文窗口中，與RoPE和ALiBi相比，FoPE在針在一堆乾草任務中能夠保持更穩定的困惑度和更一致的準確性。幾項分析和消融進一步支持我們的方法和理論建模。

English

Extending the context length of Language Models (LMs) by improving Rotary Position Embedding (RoPE) has become a trend. While existing works mainly address RoPE's limitations within attention mechanism, this paper provides an analysis across nearly all parts of LMs, uncovering their adverse effects on length generalization for RoPE-based attention. Using Discrete Signal Processing theory, we show that RoPE enables periodic attention by implicitly achieving Non-Uniform Discrete Fourier Transform. However, this periodicity is undermined by the spectral damage caused by: 1) linear layers and activation functions outside of attention; 2) insufficiently trained frequency components brought by time-domain truncation. Building on our observations, we propose Fourier Position Embedding (FoPE), which enhances attention's frequency-domain properties to improve both its periodic extension and length generalization. FoPE constructs Fourier Series and zero-outs the destructive frequency components, increasing model robustness against the spectrum damage. Experiments across various model scales show that, within varying context windows, FoPE can maintain a more stable perplexity and a more consistent accuracy in a needle-in-haystack task compared to RoPE and ALiBi. Several analyses and ablations bring further support to our method and theoretical modeling.

傅立葉位置嵌入：增強注意力的週期擴展以實現長度泛化

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

摘要

Summary

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