QQWorld: Quantile-Quantile Matching for World Model Regularization

2026/07/30 by Zhoushun Yu, Xiaoyu Hu, Xiangyu Xu
Computer Science · #cs.LG #cs.AI #cs.CV #cs.MM #cs.RO

paper · pdf

arxiv created 2026/07/30 · arxiv updated 2026/07/31

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.

Citations

• LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels
• Interpreting Physics in Video World Models
• Chimère Ω — blueprint for a physico-cognitively inspired local-first LLM runtime
• V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning
• Learning from Reward-Free Offline Data: A Case for Planning with Latent Dynamics Models
• DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning
• OGBench: Benchmarking Offline Goal-Conditioned RL
• Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distances
• VICReg: Variance-Invariance-Covariance Regularization for\n Self-Supervised Learning
• Dream to Control: Learning Behaviors by Latent Imagination
• Closed-form Expressions for Maximum Mean Discrepancy with Applications\n to Wasserstein Auto-Encoders
• Learning Latent Dynamics for Planning from Pixels
• DeepMind Control Suite
• On Wasserstein Two Sample Testing and Related Families of Nonparametric\n Tests
• An analysis of variance test for normality (complete samples)
• Table for Estimating the Goodness of Fit of Empirical Distributions

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