{"type":"rich","version":"1.0","provider_name":"Transistor","provider_url":"https://transistor.fm","author_name":"Daily Paper Cast","title":"Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization","html":"","width":"100%","height":180,"duration":1294,"description":"\n 🤗 Upvotes: 20 | cs.AI, cs.CL\n\n Authors:\n Ermo Hua, Che Jiang, Xingtai Lv, Kaiyan Zhang, Ning Ding, Youbang Sun, Biqing Qi, Yuchen Fan, Xue Kai Zhu, Bowen Zhou\n\n Title:\n Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization\n\n Arxiv:\n http://arxiv.org/abs/2412.17739v1\n\n Abstract:\n 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.\n ","thumbnail_url":"https://img.transistorcdn.com/8lOVNnuwhrA3rxrDMv7Osu4j_t1-jORooO6NfGcQhcw/rs:fill:0:0:1/w:400/h:400/q:60/mb:500000/aHR0cHM6Ly9pbWct/dXBsb2FkLXByb2R1/Y3Rpb24udHJhbnNp/c3Rvci5mbS81Zjg1/YzRhODczMDU4MmE4/OGMwN2FiNDlmYzI2/MDliMi5qcGVn.webp","thumbnail_width":300,"thumbnail_height":300}