We present an interpretable deep learning model that enhances the prediction of cohesive energy in transition metal alloys (TMAs) by incorporating cohesion theory into a graph neural network (GNN) framework. The model not only predicts the total cohesive energy-an indicator of crystal stability-but also disentangles its various contributing factors and underlying physical parameters. The physics insights extracted from the model clarify the stability trends of transition metal surfaces across the periodic table. Furthermore, by applying the model to single-atom alloys (SAAs), a class of catalytically significant next-generation TMAs, we analyze and explain the relative stability of monomer/dimer (in-plane symmetry breaking) and top-/sub-layer (out-of-plane symmetry breaking) configurations. These two types of symmetry breaking lead to distinct thermodynamic preferences in SAAs, governed by localized effects (e.g. d-orbital coupling) and delocalized effects (e.g. wavefunction renormalization). The model is thus positioned as a powerful tool for understanding and strategically designing TMAs, enabling the tailored development of materials with improved stability for advanced applications in catalysis and materials science.