Weak-SIGReg: Covariance Regularization for Stable Deep Learning

• URL: http://arxiv.org/abs/2603.05924v1
• Date: Fri, 06 Mar 2026 05:32:40 GMT
• Title: Weak-SIGReg: Covariance Regularization for Stable Deep Learning
• Abstract summary: This work adopts Sketched Isotropic Gaussian Regularization ( SIGReg), recently introduced in the LeJEPA self-supervised framework, and repurposes it as a general optimization stabilizer for supervised learning.<n>Inspired by interacting particle systems, representation collapse is viewed as drift; SIGReg constrains the representation density towards an isotropic Gaussian, mitigating this drift.<n> Empirically, SIGReg recovers the training of a ViT on CIFAR-100 from a collapsed 20.73% to 72.02% accuracy without architectural hacks and significantly improves the convergence of deep vanillas trained with pure SGD. Code is available at
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Modern neural network optimization relies heavily on architectural priorssuch as Batch Normalization and Residual connectionsto stabilize training dynamics. Without these, or in low-data regimes with aggressive augmentation, low-bias architectures like Vision Transformers (ViTs) often suffer from optimization collapse. This work adopts Sketched Isotropic Gaussian Regularization (SIGReg), recently introduced in the LeJEPA self-supervised framework, and repurposes it as a general optimization stabilizer for supervised learning. While the original formulation targets the full characteristic function, a computationally efficient variant is derived, Weak-SIGReg, which targets the covariance matrix via random sketching. Inspired by interacting particle systems, representation collapse is viewed as stochastic drift; SIGReg constrains the representation density towards an isotropic Gaussian, mitigating this drift. Empirically, SIGReg recovers the training of a ViT on CIFAR-100 from a collapsed 20.73\% to 72.02\% accuracy without architectural hacks and significantly improves the convergence of deep vanilla MLPs trained with pure SGD. Code is available at \href{https://github.com/kreasof-ai/sigreg}{github.com/kreasof-ai/sigreg}.

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