标题： 基于部分对称性的注意力分解（PSEAD）：生物系统中等变变换器的群论框架 显示英文标题

标题： Partial Symmetry Enforced Attention Decomposition (PSEAD): A Group-Theoretic Framework for Equivariant Transformers in Biological Systems

摘要： 这项研究介绍了部分对称性强制注意分解理论（PSEAD），这是一种新的、严格的群论框架，旨在无缝地将局部对称性意识整合到Transformer模型中自注意力机制的核心架构中。 我们形式化了生物数据窗口上的局部排列子群作用的概念，并证明在这些作用下，注意力机制自然分解为正交不可约成分的直和。 关键的是，这些成分与作用排列子群的不可约表示内在对齐，从而为解耦对称和非对称特征提供了强大的数学基础。 我们展示了PSEAD具有显著的优势。 这些优势包括对表现出类似部分对称性的新型生物基序的增强泛化能力，通过允许直接可视化和分析不同对称通道的注意力贡献，实现前所未有的可解释性，以及通过将表征能力集中在相关的对称子空间上，获得显著的计算效率提升。 除了静态数据分析，我们将PSEAD的应用扩展到强化学习范式中的动态生物过程，展示了其在复杂环境中加速发现和优化生物学上有意义策略的潜力，例如蛋白质折叠和药物发现。 这项工作为新一代生物信息学驱动的、具有对称性意识的人工智能模型奠定了基础。 显示英文摘要

摘要： This research introduces the Theory of Partial Symmetry Enforced Attention Decomposition (PSEAD), a new and rigorous group-theoretic framework designed to seamlessly integrate local symmetry awareness into the core architecture of self-attention mechanisms within Transformer models. We formalize the concept of local permutation subgroup actions on windows of biological data, proving that under such actions, the attention mechanism naturally decomposes into a direct sum of orthogonal irreducible components. Critically, these components are intrinsically aligned with the irreducible representations of the acting permutation subgroup, thereby providing a powerful mathematical basis for disentangling symmetric and asymmetric features. We show that PSEAD offers substantial advantages. These include enhanced generalization capabilities to novel biological motifs exhibiting similar partial symmetries, unprecedented interpretability by allowing direct visualization and analysis of attention contributions from different symmetry channels, and significant computational efficiency gains by focusing representational capacity on relevant symmetric subspaces. Beyond static data analysis, we extend PSEAD's applicability to dynamic biological processes within reinforcement learning paradigms, showcasing its potential to accelerate the discovery and optimization of biologically meaningful policies in complex environments like protein folding and drug discovery. This work lays the groundwork for a new generation of biologically informed, symmetry-aware artificial intelligence models.