Stable Training of EPiC-GAN for High-Energy Physics Jet Generation via Exponential Moving Average and Distribution-Aware Checkpointing

Generative models offer a promising route to accelerating Monte Carlo simulation in high-energy physics (HEP). We present a systematic study of generative models for top-quark jet synthesis on the JetNet-30 benchmark, progressing from a flat MLP WGAN-GP baseline to a faithful reimplementation of EPiC-GAN. We identify and document a training instability inherent to point-cloud GANs trained with LSGAN: the generator loss does not correlate with distribution quality, causing the generator to oscillate between reproducing particle-level features and jet multiplicity across training checkpoints — a phenomenon we term checkpoint oscillation. We propose two complementary fixes: (1) Exponential Moving Average (EMA) of generator weights with decay τ = 0.999, which eliminates oscillation by smoothing the weight trajectory, and (2) distribution-aware checkpointing, which selects the best model by the sum of Wasserstein distances over all target observables including multiplicity. Our final model achieves W1_eta = 9.6e-4, W1_phi = 1.0e-3, W1_pT = 3.6e-4, multiplicity W1 = 0.038, and W1_M = 2.49e-3 on the JetNet-30 top-quark test set, with particle-level W1P = 0.93e-3 exceeding the published EPiC-GAN (2.1e-3). All results are from a single training seed without error bars.