Sketched Linear Contrastive Learning: Approximation, Optimization, and Statistical Scaling
Scaling laws describe how learning performance varies with model size, data size, and compute. While recent theoretical work has established scaling laws for sketched linear regression, much less is understood for contrastive representation learning. In this paper, we study a sketched linear model for contrastive learning under a paired Gaussian latent-variable setup. The learner observes only sketched views of two correlated variables and trains a bilinear contrastive score by full-batch empirical gradient descent. We analyze a Gaussian-negative quadratic contrastive surrogate under aligned power-law spectra and a contrastive source condition, where we derive a risk decomposition into ir...
| Authors | Ziyan Chen, Zhongzhu Zhou, Ding-Xuan Zhou |
|---|---|
| Primary category | cs.LG |
| Published | 25 June 2026 |
| Last updated at source | 22 July 2026 |
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