Elucidating the intricate relationship between the structure and dynamics in the context of the glass transition has been a persistent challenge. Machine learning (ML) has emerged as a pivotal tool, offering novel pathways to predict dynamic behaviors from structural descriptors. Notably, recent research has highlighted that the distance between the initial particle positions between the equilibrium positions substantially enhances the prediction of glassy dynamics. However, these methodologies have been limited in their ability to capture the directional aspects of these deviations from the equilibrium positions, which are crucial for a comprehensive understanding of the complex particle interactions within the cage dynamics. Therefore, this paper introduces a novel structural parameter: the vectorial displacement of particles from their initial configuration to their equilibrium positions. Recognizing the inadequacy of current ML models in effectively handling such vectorial parameters, we have developed an Equivariance-Constrained Invariant Graph Neural Network (EIGNN). This innovative model not only bolsters the descriptive capacity of conventional rotation-invariant models but also streamlines the computational demands associated with rotation-equivariant graph neural networks. Our rigorous experimental validation on 3D glassy system from GlassBench dataset has yielded compelling evidence that the EIGNN model significantly enhance the correlation between structural representation and dynamic properties.