QQWorld: Quantile-Quantile Matching for World Model Regularization

🤗 Upvotes: 24 | cs.LG, cs.AI, cs.CV, cs.MM, cs.RO

Authors:
Zhoushun Yu, Xiaoyu Hu, Xiangyu Xu

Title:
QQWorld: Quantile-Quantile Matching for World Model Regularization

Arxiv:
http://arxiv.org/abs/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.