# Beyond Gaussian Worlds: Latent Geometry Matters for JEPAs

arXiv: https://arxiv.org/abs/2609.21656 · HTML: https://mlsanity.com/paper/2609.21656/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 18 Sep 2026.

## Builds on (most cited first, 16 of 16)

- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Contrastive and Non-Contrastive Self-Supervised Learning Recover Global and Local Spectral Embedding Methods](https://mlsanity.com/paper/2205.11508/) (2022)
- [EdgeNeXt: Efficiently Amalgamated CNN-Transformer Architecture for Mobile Vision Applications](https://mlsanity.com/paper/2206.10589/) (2022)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [Explorations in Homeomorphic Variational Auto-Encoding](https://mlsanity.com/paper/1807.04689/) (2018)
- [When Does LeJEPA Learn a World Model?](https://mlsanity.com/paper/2605.26379/) (2026)
- [KerJEPA: Kernel Discrepancies for Euclidean Self-Supervised Learning](https://mlsanity.com/paper/2512.19605/) (2025)
- [Exact heat kernel on a hypersphere and its applications in kernel SVM](https://mlsanity.com/paper/1702.01373/) (2017)
- [SPHERE-JEPA: Spherical Prediction with Homogeneous Embeddings](https://mlsanity.com/paper/2605.26900/) (2026)
- [Expanding SPHERE-JEPA: A Family of Statistical Regularizers for the Hypersphere](https://mlsanity.com/paper/2606.17603/) (2026)

## Built on by (most cited first, 1 of 1)

- [Shared Gaussianization: What Gaussian Regularizers Certify About Contrastive Learning, and What They Miss](https://mlsanity.com/paper/2610.10299/) (2026)

## Abstract (arXiv)

Recent Joint-Embedding Predictive Architectures (JEPAs) prevent representation collapse by constraining learned representations to follow a prescribed target distribution, such as an isotropic Gaussian or the uniform distribution on a hypersphere. Klindt et al. (2026) showed that, under their Euclidean assumptions, matching a Gaussian target can recover Gaussian latent variables up to a linear transformation, and that the Gaussian is the unique distribution with this guarantee. We extend their analysis to latent variables supported on embedded Riemannian manifolds and derive conditions on the latent geometry and positive-pair dynamics under which alignment and exact distribution matching guarantee linear recovery. In particular, when the latent variables are uniformly distributed on a sphere and the representations are matched to the same spherical distribution, every optimal representation recovers the latent state up to an orthogonal transformation. This shows that Gaussian uniqueness is not a universal property of distribution-matched JEPAs: non-Euclidean latent geometries can admit other linearly recoverable distributions. We further derive an approximate-recovery bound that is strictly tighter for the spherical world than for the Gaussian world. Experiments on Gaussian, spherical, and toroidal latent spaces show that geometrically compatible targets yield better linear recovery when optimization succeeds, whereas mismatched targets distort the latent structure. This advantage persists in high-dimensional Clifford-torus worlds.