arXiv:2506.13139v3 Announce Type: replace-cross Abstract: Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down. In particular, the proportional regime where the data dimension, sample size, and number of model parameters are all large and comparable, gives rise to novel and sometimes counterintuitive behaviors. This paper extends traditional Random Matrix Theory (RMT) beyond eigenvalue-based analysis of linear models to address the challenges posed by nonli
The increasing complexity and scale of modern AI models, particularly deep neural networks, are consistently pushing the boundaries of traditional statistical understanding, necessitating new theoretical frameworks like expanded Random Matrix Theory.
This research provides fundamental theoretical tools to better understand, predict, and potentially optimize the behavior of high-dimensional, overparameterized AI models, moving beyond empirical trial-and-error.
Our ability to develop more robust, efficient, and theoretically grounded AI systems will improve significantly as the mathematical underpinnings of complex models become clearer.
- · AI Researchers
- · Deep Learning Engineers
- · High-Performance Computing (HPC) providers
- · Developers unable to leverage advanced theoretical insights
- · Classical statistical modeling approaches
More efficient and trustworthy AI model development through a deeper understanding of their properties.
Reduced computational costs and faster innovation in AI due to more directed research and development efforts.
Accelerated deployment of advanced AI applications across various sectors, impacting productivity and competitive landscapes.
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