The Expressibility of Polynomial based Attention Scheme

📄 arXiv: 2310.20051v1 📥 PDF

作者: Zhao Song, Guangyi Xu, Junze Yin

分类: cs.LG

发布日期: 2023-10-30

备注: arXiv admin note: substantial text overlap with arXiv:2310.11685

💡 一句话要点

提出多项式注意力机制以解决长文本处理的复杂性问题

🎯 匹配领域: 支柱九：具身大模型 (Embodied Foundation Models)

关键词: 多项式注意力 长文本处理 变换器架构 语言模型 特征区分 机器学习 自然语言处理

📋 核心要点

  1. 现有的变换器架构在处理长文本时面临二次复杂度的挑战，限制了大型语言模型的有效性。
  2. 本文提出了一种多项式注意力机制，通过理论分析高阶多项式的表达能力，解决了现有方法的不足。
  3. 实验结果表明，高阶多项式注意力网络能够有效区分特征值差异显著的数据集，提升了模型的表现。

📝 摘要（中文）

大型语言模型（LLMs）在多个领域显著提升了生产力和决策过程，但其在处理长文本时面临二次复杂度的挑战。本文对多项式注意力机制的表达能力进行了理论分析，构建了两个数据集，展示了高阶多项式在区分数据集方面的优势。研究表明，高阶多项式能够有效放大特征值，从而更好地捕捉复杂的语言关联，为注意力机制的设计提供了理论依据。

🔬 方法详解

问题定义：本文旨在解决变换器架构在处理长文本时的二次复杂度问题，现有方法在训练和推理时效率低下。

核心思路：通过引入多项式函数替代传统的softmax，提升注意力机制的计算效率，并分析高阶多项式的表达能力。

技术框架：研究构建了两个数据集$ ext{D}_0$和$ ext{D}_1$，并通过单层多项式注意力网络进行实验，分析不同阶数多项式的表现。

关键创新：提出了多项式注意力机制的理论分析，揭示了高阶多项式在特征区分上的优势，提供了对现有注意力机制的改进思路。

关键设计：通过设计不同阶数的多项式，研究其在特征放大和数据集区分能力上的表现，强调高阶多项式在捕捉复杂语言关系中的重要性。

📊 实验亮点

实验结果显示，使用高阶多项式的注意力网络在区分特征值差异显著的数据集上表现优异，相较于低阶多项式，模型的区分能力显著提升，验证了理论分析的有效性。

🎯 应用场景

该研究的多项式注意力机制可广泛应用于自然语言处理、机器翻译和文本生成等领域，提升模型在长文本处理中的效率和准确性。未来，随着模型规模的扩大，该方法可能在更多实际应用中发挥重要作用。

📄 摘要（原文）

Large language models (LLMs) have significantly improved various aspects of our daily lives. These models have impacted numerous domains, from healthcare to education, enhancing productivity, decision-making processes, and accessibility. As a result, they have influenced and, to some extent, reshaped people's lifestyles. However, the quadratic complexity of attention in transformer architectures poses a challenge when scaling up these models for processing long textual contexts. This issue makes it impractical to train very large models on lengthy texts or use them efficiently during inference. While a recent study by [KMZ23] introduced a technique that replaces the softmax with a polynomial function and polynomial sketching to speed up attention mechanisms, the theoretical understandings of this new approach are not yet well understood. In this paper, we offer a theoretical analysis of the expressive capabilities of polynomial attention. Our study reveals a disparity in the ability of high-degree and low-degree polynomial attention. Specifically, we construct two carefully designed datasets, namely $\mathcal{D}_0$ and $\mathcal{D}_1$, where $\mathcal{D}_1$ includes a feature with a significantly larger value compared to $\mathcal{D}_0$. We demonstrate that with a sufficiently high degree $β$, a single-layer polynomial attention network can distinguish between $\mathcal{D}_0$ and $\mathcal{D}_1$. However, with a low degree $β$, the network cannot effectively separate the two datasets. This analysis underscores the greater effectiveness of high-degree polynomials in amplifying large values and distinguishing between datasets. Our analysis offers insight into the representational capacity of polynomial attention and provides a rationale for incorporating higher-degree polynomials in attention mechanisms to capture intricate linguistic correlations.