This paper introduces a novel rigorous group-theoretic framework, Partial Symmetry Enhanced Attention Decomposition Theory (PSEAD), designed to seamlessly integrate local symmetry awareness into the core architecture of the self-attention mechanism in the Transformer model. We formalize the notion of local permutation subgroup actions on windows of biological data and demonstrate that under such actions, the attention mechanism naturally decomposes into a direct sum of orthogonal indefinite components. Importantly, these components are intrinsically aligned with the indefinite representation of the permutation subgroups on which they operate, providing a powerful mathematical foundation for separating symmetric and asymmetric features. PSEAD offers improved generalization capabilities (for novel biological motifs exhibiting similar partial symmetries), unprecedented interpretability by allowing direct visualization and analysis of attention contributions in different symmetry channels, and substantial computational efficiency gains by concentrating representational power on the relevant symmetry subspace. Beyond static data analysis, we extend the applicability of PSEAD to dynamic biological processes within the reinforcement learning paradigm, demonstrating the potential to accelerate the discovery and optimization of biologically meaningful policies in complex environments such as protein folding and drug discovery. This study lays the foundation for a new generation of biologically informed, symmetry-aware artificial intelligence models.
