# Anisotropic Representations Improve Planning in JEPA World Models

arXiv: https://arxiv.org/abs/2609.37441 · HTML: https://mlsanity.com/paper/2609.37441/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 15 of 15)

- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [When Does LeJEPA Learn a World Model?](https://mlsanity.com/paper/2605.26379/) (2026)
- [Predictive but Not Plannable: RC-aux for Latent World Models](https://mlsanity.com/paper/2605.07278/) (2026)
- [Fast LeWorldModel](https://mlsanity.com/paper/2606.26217/) (2026)
- [Rectified LpJEPA: Joint-Embedding Predictive Architectures with Sparse and Maximum-Entropy Representations](https://mlsanity.com/paper/2602.01456/) (2026)
- [KerJEPA: Kernel Discrepancies for Euclidean Self-Supervised Learning](https://mlsanity.com/paper/2512.19605/) (2025)
- [World Model Control by Trajectory Reachability Metrics](https://mlsanity.com/paper/2605.22164/) (2026)
- [LpWM: A Case for Sparse Representations in World Models](https://mlsanity.com/paper/2608.22764/) (2026)
- [Decision-Metric Alignment in Latent World Models: Diagnostics and Action-Conditioned Objectives for MPC Planning](https://mlsanity.com/paper/2608.18746/) (2026)
- [Radial-VCReg: More Informative Representation Learning Through Radial Gaussianization](https://mlsanity.com/paper/2602.14272/) (2026)
- [Temporally Centered SIGReg Improves LeWorldModel Representations for Robot Policy Learning](https://mlsanity.com/paper/2607.26924/) (2026)
- [SCALE: State-Calibrated Latent Embeddings for JEPA Planning in the Right Geometry](https://mlsanity.com/paper/2608.16287/) (2026)
- [Beyond Isotropy in JEPAs: Hamiltonian Geometry and Symplectic Prediction](https://mlsanity.com/paper/2605.20107/) (2026)

## Abstract (arXiv)

Latent world models learn action-conditioned dynamics in representation space and often score candidate actions by Euclidean distance to a goal representation. Joint training typically regularizes the representation to prevent collapse, but the resulting representation geometry also determines how terminal errors are weighted during planning. We show that accurate prediction and noncollapsed representations do not guarantee a task-aligned latent planning cost: isotropic Gaussian regularization can induce a geometry that ranks feasible outcomes differently from the task cost. To address this mismatch, we introduce AnisoWM with LambdaReg, which replaces the fixed isotropic Gaussian target with a learnable diagonal covariance under fixed-trace and anisotropy constraints. The prediction objective, predictor architecture, and Euclidean planner remain unchanged; the target is used only during training. Our analysis characterizes the prediction-driven allocation of target variance, its dependence on the training distribution, and the conditions under which the induced metric reduces planning regret. Across four visual control environments, AnisoWM improves planning success over LeWorldModel in all four. Its latent planning cost also shows better agreement with task outcomes. Project website: https://rkdrn79.github.io/AnisoWM-page/