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LeJEPA addresses this by enforcing an isotropic Gaussian target on the embeddings via Sketched Isotropic Gaussian Regularization (SIGReg). This target is in tension with the manifold hypothesis, which expects embeddings to concentrate on a low-dimensional subset of the ambient space. We propose \\emph{UR-JEPA}, which targets a uniformly $n$-rectifiable measure of local tangent dimension $n$ at small scales, realized through a Gaussian-kernel smoothed Carleson-type square function $\\mathcal{L}^{\\text{CGLT}}$, with a complementary Jones $\\beta$-number formulation. On Inet10, UR-JEPA($\\mathcal{L}^{\\text{CGLT}}$) attains $0.9141 \\pm 0.0014$ for a $+0.83$\\,pp gain over LeJEPA($\\mathcal{L}^{\\text{SIGReg}}$) with $\\sim 30\\%$ lower seed standard deviation; on matched-recipe Galaxy10~SDSS, a single-seed ImageNet-$100$ run, and","title":"UR-JEPA: Uniform Rectifiability as a Regularizer for Joint-Embedding Predictive Architectures","url":"https://arxiv.org/abs/2606.01443","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.01443v1 Announce Type: cross \nAbstract: A central difficulty in training Joint-Embedding Predictive Architectures (JEPAs) is preventing representation collapse. LeJEPA addresses this by enforcing an isotropic Gaussian target on the embeddings via Sketched Isotropic Gaussian Regularization (SIGReg). This target is in tension with the manifold hypothesis, which expects embeddings to concentrate on a low-dimensional subset of the ambient space. We propose \\emph{UR-JEPA}, which targets a uniformly $n$-rectifiable measure of local tangent dimension $n$ at small scales, realized through a Gaussian-kernel smoothed Carleson-type square function $\\mathcal{L}^{\\text{CGLT}}$, with a complementary Jones $\\beta$-number formulation. 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