arXiv:2607.07845v1 Announce Type: new Abstract: The Hessian of the training loss governs the local geometry of the loss landscape, yet despite existing explanations for its largest eigenvalues, the origin of the vast multitude of vanishingly small eigenvalues remains elusive. We argue that the bulk consists of the weakly lifted pseudo-Goldstone modes of the continuous symmetries of the network parametrization. In deep linear networks these symmetries are exact: they generate flat directions and hence exact zero modes, whose eigenvectors we construct explicitly. Introducing a ReLU nonlinearity
The paper contributes to foundational AI research, specifically in understanding the optimization landscapes of neural networks, which is an ongoing area of active academic inquiry.
Understanding the loss landscape's geometry is crucial for developing more robust, efficient, and theoretically sound AI models, directly impacting future AI capabilities and training methodologies.
This research offers a potential theoretical underpinning for previously unexplained phenomena in neural network optimization (small Hessian eigenvalues), suggesting new avenues for algorithm design.
- · AI researchers
- · Machine learning framework developers
- · Academia
- · Dogmatic rule-of-thumb optimization methods
Improved theoretical understanding of neural network training dynamics through the lens of approximate symmetries and pseudo-Goldstone modes.
Development of novel optimization algorithms that explicitly account for or exploit these approximate symmetries to improve training stability or speed.
Potential for new methods to reliably find better minima in the loss landscape, leading to more performant and generalizable AI models across various applications.
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Read at arXiv cs.LG