arXiv Machine Learning October 8, 2026 By Ruoyu Zhao, Yuting Chen, Jinheng Zhang, Zhehao Zou, Tong Che

Shared Gaussianization: What Gaussian Regularizers Certify About Contrastive Learning, and What They Miss

Read the original on arXiv Machine Learning →

The paper introduces Shared Gaussianization (SG), a characteristic‑function test that evaluates Gaussianity of the average of two normalized views scaled by an independent χ_d radius. SG detects both misalignment and non‑uniformity in contrastive learning, vanishing exactly at aligned, uniform minimizers of population InfoNCE, and provides a sharp, dimension‑free bound on InfoNCE excess. The study also explores how SG behaves under different kernels, alignment weights, batch sizes, and latent‑variable models, revealing optimization gaps and the impact of nuisance channels.

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