arXiv:2606.28486v1 Announce Type: cross Abstract: The emergence of low-dimensional structures in the spectra of neural network weight matrices is a common empirical feature of trained models, but the dynamical origin of this phenomenon during learning remains an open problem. We formulate neural network training as the stochastic evolution of an initially random matrix ensemble, driven by stochastic gradient descent (SGD) updates that reshape the spectral bulk while amplifying signal strength. This induces a Baik-Ben Arous-P\'ech\'e (BBP) transition during training, where isolated eigenvalues
This paper offers a theoretical framework for understanding the internal dynamics of neural network training, which is becoming increasingly critical as AI models scale and their complexity grows.
A deeper theoretical understanding of neural network training can lead to more efficient, stable, and interpretable AI systems, accelerating progress in the field.
This research provides insights into why neural networks develop specific spectral properties, potentially allowing for more targeted design and training methodologies.
- · AI researchers
- · Machine learning engineers
- · Deep learning hardware developers
- · AI development relying solely on empirical trial and error
Improved understanding of neural network learning dynamics leads to more efficient algorithm design.
Optimized algorithms reduce the computational resources needed for training advanced AI models.
Lower compute requirements democratize access to leading-edge AI development, fostering innovation across more diverse actors.
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