arXiv:2202.08832v3 Announce Type: replace-cross Abstract: We study a general class of optimization problems with decision variable $\boldsymbol{\Theta} \in \mathbb{R}^{p \times k}$ and cost function which is the sum of $n$ terms, each dependent on $\boldsymbol{\Theta}$ through the $k$-dimensional projection $\boldsymbol{\Theta}^\top \boldsymbol{x}_i$, where $\boldsymbol{x}_i$, $i \leq n$ are i.i.d. random vectors. This setting is general enough to include examples of current interest in statistical physics, high-dimensional statistics, and statistical learning theory. We consider the proportio
This publication represents ongoing research in the foundational mathematics of machine learning, a field experiencing rapid development and widespread application across various scientific disciplines.
Understanding the universality of empirical risk minimization provides deeper theoretical guarantees and insights into the performance and limitations of many AI algorithms, influencing future development directions.
While not an immediate shift, this research contributes to the fundamental mathematical understanding of how AI models learn, potentially leading to more robust, efficient, and generalizable AI systems over time.
- · AI researchers
- · Machine learning developers
- · Academic institutions
- · Overly simplistic black-box AI approaches
Improved theoretical foundations for current and future AI models.
Development of more generalized and less data-hungry AI algorithms due to deeper understanding of learning principles.
Accelerated progress in fields heavily reliant on statistical learning, fostering new scientific discoveries.
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