SwarmPNM: A Single-Trajectory Adaptive Optimizer with Positive–Negative Momentum and PSO-Inspired Attraction

SwarmPNM combines an adaptive second-moment estimate and positive–negative gradient momentum with attraction towards the lowest-loss weights stored along a single training trajectory. The attraction is inspired by particle swarm optimization, but the method does not maintain a particle population. We specify the update, analyze the attraction locally under Hessian assumptions and obtain a conditional regret bound for an auxiliary strongly convex projected-gradient model with controlled perturbations. Experiments cover 15 analytic test functions, molecular classification with MolCLR-pretrained GIN and GCN encoders on the blood–brain barrier penetration (BBBP), beta-secretase-1 inhibitor (BACE) and human immunodeficiency virus replication-inhibition (HIV) datasets, and nuclear cross-section regression with a multilayer perceptron. SwarmPNM attains the highest mean ROC–AUC in five of six molecular dataset–encoder combinations. In the four-library nuclear comparison, it has the lowest mean absolute error and the highest coefficient of determination; a separate three-seed nuclear experiment under a different protocol favors AdamW. Repeated-run, sensitivity and ablation studies establish that the contribution of attraction depends on the task and tuning, with the learning rate having the largest observed influence in the analytic sensitivity tests. We also report the additional computational cost relative to AdamW. The auxiliary theory does not establish convergence of the complete nonconvex optimizer.