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The elementary excitations in metallic glasses (MGs), i.e., $β$ processes that involve hopping between nearby sub-basins, underlie many unusual properties of the amorphous alloys. A high-efficacy prediction of the propensity for those activated processes from solely the atomic positions, however, has remained a daunting challenge. Recently, employing well-designed site environment descriptors and machine learning (ML), notable progress has been made in predicting the propensity for stress-activated $β$ processes (i.e., shear transformations) from the static structure. However, the complex tensorial stress field and direction-dependent activation would induce non-trivial noises in the data, limiting the accuracy of the structure-property mapping learned. Here, we focus on the thermally activated elementary excitations and generate high-quality data in several Cu-Zr MGs, allowing quantitative mapping of the potential energy landscape. After fingerprinting the atomic environment with short- and medium-range interstice distribution, ML can identify the atoms with strong resistance or high compliance to thermal activation, at an unprecedented accuracy over ML models for stress-driven activation events. Interestingly, a quantitative "between-task" transferring test reveals that our learnt model can also generalize to predict the propensity of shear transformation. Our dataset is potentially useful for benchmarking future ML models on structure-property relationships in MGs.