Canonical Joint Energy-Based Model on CIFAR-10: failure modes and practical indistinguishability of Predictor-Corrector and SGLD samplers

Abstract

Joint Energy-Based Models (JEM) unify classification and generation within a single network and support out-of-distribution (OOD) detection. Canonical JEM training relies on stochastic gradient Langevin dynamics (SGLD); a theoretically motivated alternative, the Predictor-Corrector (PC) sampler, has not previously undergone a systematic replication test on the canonical model. We reproduce canonical JEM on WideResNet-28-10 without normalisation layers on two independent runs and test whether PC retains its theoretical advantage without an annealed noise schedule, across three protocols: PC replacing SGLD throughout the roughly 130 training epochs; cold-start generation (FID); and refinement-style multi-OOD detection (AUROC). The reconstruction reaches 92.88% test accuracy and buffer-FID 44.46 (canonical: 92.9% and 38.40). We document two failure modes: catastrophic late-training divergence via the canonical outlier-buffer mechanism (both SGLD runs and, with the same signature, both PC runs), and run-dependent SVHN OOD-discrimination dynamics. No method-level advantage of PC over SGLD is observed on any protocol: at inference the absolute AUROC difference stays below 0.007 across all ten checkpoint-OOD pairs and the FID difference below 0.5; on the training protocol a hierarchical seed-by-image bootstrap gives a 95% confidence interval on the macro-averaged AUROC difference that contains zero, while a seed-level equivalence test with two runs per method cannot establish formal equivalence. The data are consistent both with equivalence and with a small directional effect. This practical indistinguishability is theoretically expected: under fixed noise the PC predictor step degenerates by construction, so its guarantees do not transfer to canonical JEM.