VISReg: Variance-Invariance-Sketching Regularization for JEPA training

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 $β$-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 a $3$-seed EuroSAT remote-sensing run, the two methods lie in the same peak-accuracy band at convergence, with UR-JEPA retaining its lower-seed-variance signature. On EuroSAT the in-domain pair is competitive at $96.0$ to $96.1\%$ with large remote-sensing foundation-model transfer at a $25\times$ smaller backbone. The distinction is geometric: direct visualization of the projector output distribution shows that on all four datasets UR--JEPA($\mathcal{L}^{\text{CGLT}}$) produces a global PCA spectrum with a $4$ to $5$ order-of-magnitude drop at index $\sim 20$ to $25$ out of $D = 32$, while LeJEPA's spectrum is near-flat (top-to-bottom ratio at most $3.6$). Per-dimension marginals are simultaneously near-Gaussian for both methods (mean Shapiro-Wilk $W \in [0.992, 0.996]$) as a Diaconis-Freedman consequence. At matched accuracy the two regularizers therefore yield structurally distinct projected representations.

Despite recent advances, self-supervised learning (SSL) models and Joint-Embedding Predictive Architectures (JEPAs) remain susceptible to learning spurious biases in the dataset. These techniques rely on regularization, which prevents representation collapse by enforcing a global target distribution such as a multivariate Gaussian or a uniform distribution on the sphere. However, these global constraints are insufficient to prevent bias entanglement, as task-irrelevant features can still segregate the latent space into distinct sub-regions. While recent approaches like Entangling and Disentangling (EnD) and Fair Supervised Contrastive Learning (FSCL) empirically debias the latent space, we show that they act as partial approximations of conditional distribution matching. To enforce this matching explicitly, we propose Unbiased Open World Regularization (UOWReg), an encoder-only framework. We show that this shift from a global to a conditional objective guarantees statistical independence between the learned representations and the targeted attributes, regardless of the chosen target distribution. We empirically validate this framework across both Gaussian and spherical latent spaces, using statistical measures to enforce these target distributions. While conditional matching successfully mitigates bias with both distributions, we demonstrate that enforcing conditional uniformity on the sphere yields a lower linearprobing classification error. Empirically, UOWReg reduces Equalized Odds violations on the CelebA benchmark while maintaining competitive classification accuracy compared to existing encoder-only baselines. Furthermore, we introduce the Synthetic Engraving Task-a novel setting in which a dominant macro-structure masks a fine-grained micro-signature. We show that UOWReg effectively prevents the subpopulation collapse observed in standard SSL, successfully isolating micro-signatures even when heavily entangled with the global structure.

In Self-Supervised Learning (SSL), preventing representation collapse by explicitly enforcing a uniform distribution on the unit hypersphere has proven to be effective. However, current frameworks typically rely on sliced statistical regularizers such as SIGReg (used in LeJEPA) and SUSReg (used in SPHERE-JEPA), which approximate this continuous objective via Monte Carlo sampling along random 1D directions. This stochasticity injects projection variance into the training gradients, destabilizing optimization, and hindering convergence. In this work, we first show that analytically integrating out these random projections natively yields a deterministic Maximum Mean Discrepancy (MMD), bypassing the variance of sliced methods. Motivated by this equivalence, we formulate full-dimensional objectives for MMD, Kernel Stein Discrepancy (KSD), and Kullback-Leibler (KL) divergence directly on the sphere to enforce a uniform distribution. To prevent spatial bias, we equip these tests with rotationally invariant kernels constructed via spectral theory, systematically evaluating two canonical families: smooth exponential decay (Heat) and strict frequency cutoff (Bandlimited) filters. Empirically, removing projection-induced noise results in more stable optimization, faster convergence, and consistent improvements over stochastic sliced regularizers on ImageNet and Galaxy10. Furthermore, we reveal that the choice of the statistical test shapes the geometry of the learned latent space: MMD and KSD favor locally clustered organization suitable for object-centric domains, whereas the continuous KDE-based KL divergence promotes fine-grained instance separation, yielding the strongest results on unclustered procedural texture retrieval.