Sub-JEPA: Subspace Gaussian Regularization for Stable End-to-End World Models
Authors: Kai Zhao, Dongliang Nie, Yuchen Lin, Zhehan Luo, Yixiao Gu, Deng-Ping Fan, Dan Zeng
Organizations: 1Shanghai University · 2The University of Manchester · 3Nankai University
Abstract
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.
Joint-Embedding Predictive Architectures (JEPAs) learn compact latent world models by predicting future embeddings, but no single coordinate of the latent is designated to encode task progression. We carve the JEPA latent into two orthogonal subspaces with disjoint roles: a low-dimensional progression subspace shaped by a cosine-margin triplet loss, and a high-dimensional content subspace regularised by the existing SIGReg objective of LeWM. We prove that the two anti-collapse forces act on disjoint coordinates, so they compose additively rather than competing on the same dimensions. Our method, SD-JEPA improves over the LeWM baseline on the majority of its control benchmarks at matched compute, and outperforms the strongest non-LeWM JEPA baseline on Push-T; a subspace-ablation falsifier confirms the split is the load-bearing ingredient. Beyond planning, the resulting 1-D angular progression coordinate functions as a scene-aware compass on the latent. It advances with task progress, regresses when the agent backtracks, and under controlled perturbations both spikes and relocalises to a semantically appropriate new task-phase sector, separating the moment of surprise from its meaning in a way that prediction-error scalars cannot.
We propose PhyLatent, a dynamics-relevant training objective for JointEmbedding Predictive Architecture (JEPA) world models. Our key observation is that preventing global latent collapse does not ensure that a representation preserves physical states and action consequences. We identify three failure modes in JEPA world models: physical invariance collapse, physical identifiability collapse, and counterfactual dynamics collapse. PhyLatent addresses them through three training pathways: physical invariance, physical identifiability, and counterfactual dynamics, implemented with physical state grounding, future representation alignment, static visual invariance, counterfactual branch separation, and latent denoising. On OGBench-Cube, PhyLatent reduces the three failure rates from 15.60%, 6.71%, and 8.41% to 7.53%, 0.95%, and 4.62%, respectively, and improves model predictive control (MPC) success from 70.0% to 78.1%. With the same architecture and planner, it further improves success from 81.0% to 98.0% on TwoRooms and remains competitive on Reacher and PushT. These results show that global non-collapse alone is insufficient for learning a reliable JEPA worldmodel state space.
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.