QQWorld: Quantile-Quantile Matching for World Model Regularization

QQWorld: Quantile-Quantile Matching for World Model Regularization

|Authors: Zhoushun Yu, Xiaoyu Hu, Xiangyu Xu

|Venue: arXiv preprint | Year: 2026

|arXiv: 2607.28415v1

Abstract

Latent world models enable efficient planning by predicting future states in a compact representation space, but their performance depends critically on the quality of the learned latent distribution. LeWorldModel (LeWM) regularizes its latents toward an isotropic Gaussian using the Epps-Pulley (EP) objective. We show that the corrective gradients of EP rapidly vanish for isolated tail samples, leaving heavy-tailed deviations insufficiently controlled. To address this limitation, we propose QQWorld, which replaces EP with a quantile-quantile matching objective that directly aligns projected latent samples with rank-matched Gaussian quantiles, thereby maintaining effective corrective gradients in the tails. We further develop cross-batch QQ, which enlarges the effective ranking pool using detached samples from previous batches, and characterize its bias-variance trade-off. Across four control environments, QQWorld effectively improves the average planning success rate of LeWM, while consistently yielding better Gaussian alignment and thinner latent tails.

Key Contributions

• Latent world models enable efficient planning by predicting future states in a compact representa…
• LeWorldModel (LeWM) regularizes its latents toward an isotropic Gaussian using the Epps-Pulley (E…
• We show that the corrective gradients of EP rapidly vanish for isolated tail samples, leaving hea…
• To address this limitation, we propose QQWorld, which replaces EP with a quantile-quantile matchi…
• We further develop cross-batch QQ, which enlarges the effective ranking pool using detached sampl…

Topics

• reinforcement-learning
• planning
• control

Code & Data

No code repository linked in paper metadata.

BibTeX

@article{Yu2026_260728415v1,
  title     = {QQWorld: Quantile-Quantile Matching for World Model Regularization},
  author    = {Zhoushun Yu and Xiaoyu Hu and Xiangyu Xu},
  year      = {2026},
  eprint    = {2607.28415v1},
  archivePrefix = {arXiv},
  primaryClass  = {cs.LG},
  url       = {https://arxiv.org/abs/2607.28415v1}
}