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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.05924 |
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| _version_ | 1866911492601806848 |
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| author | Akbar, Habibullah |
| author_facet | Akbar, Habibullah |
| contents | 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}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05924 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weak-SIGReg: Covariance Regularization for Stable Deep Learning Akbar, Habibullah Machine Learning 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}. |
| title | Weak-SIGReg: Covariance Regularization for Stable Deep Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.05924 |