Modeling short-range interactions in highly disordered materials remains challenging due to the immense configuration space and the disruption of local symmetry in truncated theoretical models. Here, we propose a symmetry-preserving local representation framework that strictly enforces topological continuity and translational invariance via boundary passivation. Applied to high-entropy alloys, this approach autonomously unravels the nonlinear ligand effects modulating local reactivity and accurately captures coverage-dependent many-body interactions without explicit periodic expansion. By resolving the conflict between localized chemical environments and extended periodic boundaries, this framework not only reduces computational complexity by an order of magnitude but also provides a physically transparent paradigm for deciphering short-range order in complex condensed matter systems.