Slice Selection Matters: Structured and Adaptive Directions for Sliced Latent Regularization

Sliced latent regularization typically uses random projections to pursue Gaussian-target matching, but these directions can conceal discrepancies along directions populated by the encoder. We investigate deterministic rotation and propose a simple radial-adaptive augmentation to better fulfill the regularization objective. For $D$-dimensional latents, we append $K$ normalized minibatch vectors to $D$ random or rotating base directions, selecting vectors whose lengths are unusually small or large relative to the isotropic Gaussian target. Recomputed at each training step, this construction requires no additional learned parameters or inner optimization and supports both sliced Wasserstein-$2$ and Epps–Pulley losses. Across autoencoding and JEPA-style self-supervision on MNIST and ImageNet-100, matched-budget controls replace the $K$ adaptive directions with $K$ random directions, separating augmentation from base schedule and slice count. Over ten matched seeds, radial-adaptive augmentation lowers mean held-out latent-direction Kolmogorov–Smirnov discrepancy in all 16 comparisons spanning datasets, objectives, losses, and base schedules. Additional evaluation with disjoint samples preserves these mean improvements. Deterministic rotation alone has no universal advantage, whereas adaptation benefits both base schedules. A residual directional gap remains, so improved projected agreement does not establish complete Gaussian matching. We therefore recommend radial-adaptive augmentation as a simple complement to sliced Gaussian regularization when improved target matching is the goal, together with evaluation using both random and latent directions.