QQWorld: Quantile-Quantile Matching for World Model Regularization
Authors: Zhoushun Yu, Xiaoyu Hu, Xiangyu Xu
Organizations: Xi’an Jiaotong University
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.
A representation that scrambles the true degrees of freedom of the world cannot support reliable planning or compositional generalization. We prove that LeJEPA (alignment plus Gaussian regularization) linearly recovers the world's latent variables from nonlinear observations, a property known as linear identifiability, in a broad class of worlds where latents evolve under stationary, additive-noise transitions. Our main result is that among all such worlds, the Gaussian is the unique latent distribution for which this guarantee holds. The forward direction rests on a spectral decomposition in which each degree of nonlinearity is strictly penalized by alignment, making the linear map the optimum; the converse rules out every non-Gaussian alternative. We further prove an approximate identifiability result where the guarantee degrades gracefully, and show that linear, orthogonal identifiability enables optimal latent-space planning. We validate the theory with experiments ranging from 2D examples to 1024-dimensional latents, including distributional ablations and pixel-based robotic control. Our theory turns an empirically successful recipe into a mathematical guarantee, providing the foundation for building World Models that provably recover the structure of the world.
Joint-Embedding Predictive Architectures (JEPAs) provide a simpleframework for learning world models by predicting future latent representations.However, JEPA training is subject to a bias-variance tradeoff.Without sufficient structural constraints, excessive representationalvariance causes the model to collapse to trivial solutions.The recent LeWorldModel (LeWM) shows that this issue can be alleviated bysimply constraining latent embeddings with an isotropic Gaussian prior.However, latent representations inherently lie on low-dimensional manifoldswithin a high-dimensional ambient space, and enforcing an isotropic Gaussianprior directly in this ambient space introduces an overly strong bias.In this work, we propose ame, which seeks a favorable operatingpoint on the bias-variance frontier by applying Gaussian constraints inmultiple random subspaces rather than in the originalembedding space.This design relaxes the global constraint while preserving itsanti-collapse effect, leading to a better balance between trainingstability and representation flexibility.Extensive experiments across fourcontinuous-control environments demonstrate that consistentlyoutperforms LeWM with very clear margins.Our method is simple yet effective, and serves as a strong baseline for future JEPA-based world model research.fdefinedeeemodeThe code is available at https://github.com/intcomp/Sub-JEPA.
Latent world models have become increasingly popular as a method to predict and plan in latent space rather than pixel space. Recent architectures, such as LeWorldModel (LeWM), jointly train the encoder and predictor using regularization techniques like SIGReg to prevent representation collapse. Even with such regularization preventing representation collapse, we identify a new world model failure mode of physical representation laziness, particularly noted in highly dynamic environments. For these lazy cases, the learned latent states do not collapse but nonetheless fail to represent key physical properties, causing ubiquitous downstream planning failure. To resolve this issue, we propose training-time auxiliary supervision with a lightweight "Fourier auxiliary head", which enforces physically-informed structuring of the latent space with no additional inference-time cost and can be generalized to any environment. Experimentally, we show that the auxiliary head substantially improves planning success rates in dynamic environments where the baseline LeWM exhibits physical representation laziness. It also leads to modest improvements in other environments, even when the baseline does not exhibit physical representation laziness. We further observe superior planning performance being accompanied by higher latent space correlations with key physical properties, indicating both the ability of our method to physically structure latent states and the potential planning-side benefit to the learned representation being physically structured. We also see in low-data regimes, auxiliary supervision is particularly impactful in increasing success rate. These findings support the use of our Fourier auxiliary head method to improve both overall success rate and data efficiency, while avoiding representation laziness in latent world models.