Characterization of Gaussian Universality Breakdown in High-Dimensional Empirical Risk Minimization
arXiv:2604.03146v2 Announce Type: replace-cross Abstract: We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min-Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min-max characterization of key statistics, enabling approximation of the mean $\mu_{\hat{\theta}}$ and covariance $C_{\hat{\theta}}$ of the ERM estimator $\hat{\theta}$. Specifically, under a concentration assumption on the data matrix and standard regularity conditions on the loss and regularizer, we show that
This research is part of a continuous effort to improve the theoretical understanding and practical application of high-dimensional machine learning models, driven by the increasing complexity of AI systems.
Understanding the theoretical underpinnings of high-dimensional AI models, especially concerning non-Gaussian data, is crucial for developing more robust, reliable, and efficient algorithms.
This theoretical advancement could lead to more accurate predictions and better-tuned regularizers in various high-dimensional machine learning applications, particularly those dealing with complex, real-world data distributions.
- · AI researchers
- · Generative AI developers
- · Companies with complex datasets
- · Developers relying on simplistic model assumptions
Improved performance and stability for AI models trained on diverse, non-Gaussian datasets.
Reduced need for extensive hyperparameter tuning due to better theoretical guidance, accelerating AI development.
Enhanced AI capabilities in domains like scientific discovery and finance where data often deviates significantly from Gaussian assumptions.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG