QQWorld：分位数-分位数匹配用于世界模型正则化

摘要

潜在世界模型通过在紧凑的表征空间中预测未来状态来实现高效规划，但其性能关键取决于所学潜变量分布的质量。LeWorldModel（LeWM）利用Epps-Pulley（EP）目标将其潜变量正则化为各向同性高斯分布。我们表明，EP的修正梯度对于孤立的尾部样本会迅速消失，导致重尾偏差得不到充分控制。为解决这一局限性，我们提出QQWorld，用分位数-分位数匹配目标替代EP，直接将对齐后的投影潜变量样本与秩匹配的高斯分位数进行匹配，从而在尾部保持有效的修正梯度。我们进一步开发了跨批次QQ方法，利用先前批次的分离样本扩大有效排序池，并刻画了其偏差-方差权衡。在四个控制环境中，QQWorld有效提升了LeWM的平均规划成功率，同时持续获得更好的高斯对齐和更薄的潜变量尾部。

English

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.