QQWorld: Quantile-Quantile Matching for World Model Regularization

Hugging Face Daily Papers Papers
world-models regularization quantile-matching reinforcement-learning control-environments

Summary

This paper proposes QQWorld, a quantile-quantile matching objective that replaces the Epps-Pulley objective in LeWorldModel for better regularization of latent distributions, improving planning success in control environments.

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.
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Source: https://huggingface.co/papers/2607.28415

Abstract

Latentworldmodelsenableefficientplanningbypredictingfuturestatesinacompactrepresentationspace,buttheirperformancedependscriticallyonthequalityofthelearnedlatentdistribution.LeWorldModel(LeWM)regularizesitslatentstowardanisotropicGaussianusingtheEpps-Pulley(EP)objective.WeshowthatthecorrectivegradientsofEPrapidlyvanishforisolatedtailsamples,leavingheavy-taileddeviationsinsufficientlycontrolled.Toaddressthislimitation,weproposeQQWorld,whichreplacesEPwithaquantile-quantilematchingobjectivethatdirectlyalignsprojectedlatentsampleswithrank-matchedGaussianquantiles,therebymaintainingeffectivecorrectivegradientsinthetails.Wefurtherdevelopcross-batchQQ,whichenlargestheeffectiverankingpoolusingdetachedsamplesfrompreviousbatches,andcharacterizeitsbias-variancetrade-off.Acrossfourcontrolenvironments,QQWorldeffectivelyimprovestheaverageplanningsuccessrateofLeWM,whileconsistentlyyieldingbetterGaussianalignmentandthinnerlatenttails.

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