EqTrajectory: enhancing pedestrian trajectory prediction with convolutional neural network—inspired equivariant learning

Ensuring equivariance to Euclidean transformations is crucial for pedestrian trajectory prediction. However, EGNNs have limited generalization in node-level nonlinear expressions and often rely on stacking networks to extract motion patterns, restricting their ability to capture complex features. To address these challenges, we propose the equivariant trajectory prediction model, EqTrajectory. EqTrajectory learns equivariant features under Euclidean transformations by employing an equivariant multilayer perceptron attention mechanism for temporal characteristics and an equivariant agent aggregation mechanism for spatial characteristics. Inspired by learnable activation functions, we developed a dynamic nonlinear equivariant function that adaptively adjusts nonlinearity strength, enhancing the model’s capacity to learn complex features. In addition, a hybrid invariant pattern learning module alternates between graph attention networks and traditional GNNs to extract more representative invariant patterns. EqTrajectory demonstrated superior performance across four-scenario particle dynamics, molecular dynamics, 3D human skeleton motion, and pedestrian trajectory prediction, achieving 3.9% final displacement error and 1.8% average displacement error improvements in pedestrian trajectory prediction, a 14.3% enhancement in molecular dynamics, and a 1.17% increase in Human 3.6M skeleton action prediction, showcasing its broad applicability and effectiveness in complex dynamic systems.