The cross-modal encoder takes atomic embeddings of surfaces and vector embeddings of adsorbates as inputs to predict the GMAE. It comprises cross-attention layer(s), self-attention layer(s), and an energy block (Fig. and). The adsorption energy primarily arises from the interaction between the catalyst surface and the adsorbate, while the resulting surface atomic displacements also influence it . Therefore, the cross-attention layer is assigned to capture the complex relationships between the adsorbate and all surface atoms, while the selfattention layer is expected to learn the interactions between atoms within the surface caused by adsorption (e.g., atomic displacements). In the first cross-attention layer (Fig. ), the concatenated matrix of adsorbate vector embeddings and surface graph embeddings is employed as the query matrix, while the concatenated matrix of atomic embeddings and depth embeddings serves as the key and value matrices. Each atomic depth vector describes the relative position (e.g., top-layer or bottom-layer) of an atom within the surface (Methods). In the self-attention layer, the stacked matrix of atom embeddings, surface graph embeddings, and adsorbate vector embeddings are set to the input query, key, and value. The aggregated output of the final selfattention layer is concatenated with the output of the last cross-attention layer, and passed into the energy block to predict the GMAE. The detailed algorithm of the cross-modal encoder is described in the Methods. AdsGT layers (c) with an edge-wise attention mechanism. d t ij and e t ij are the distance and embedding of t-th edge between atom i and j. z i is the atomic number of atom i. h l i is the atomic embedding of atom i at l-th AdsGT layer. LN and BN represent layer normalization and batch normalization, respectively.