Gradient Descent with Large Step Size Restores Symmetry in Deep Linear Networks with Multi-Pathway
arXiv:2606.05219v1 Announce Type: new Abstract: Recent analyses of multi-pathway Deep Linear Networks use Gradient Flow to predict a "winner-takes-all" specialization in which path symmetry breaks and each feature concentrates in a single pathway. In this work, we show that discrete Gradient Descent (GD) with a large step size tells a different story. We prove that single-path solutions are sharp minima, whereas distributing signals across pathways reduces sharpness by a factor that decreases with both the number of pathways and depth. Consequently, while early training reproduces the depth-dr
This research provides a new theoretical understanding of deep linear network training dynamics, which is crucial as AI models become more complex and their training processes more opaque.
A strategic reader should care because a deeper understanding of how gradient descent impacts network symmetry can lead to more efficient, robust, and predictable AI model development, impacting capabilities and resource allocation.
The understanding of deep linear network training shifts from 'winner-takes-all' specialization with gradient flow to a more symmetrical signal distribution with large-step discrete gradient descent, challenging previous assumptions.
- · AI researchers
- · Deep learning practitioners
- · Hardware manufacturers for AI (indirectly)
- · Developers relying solely on gradient flow assumptions
- · Inefficient AI training methodologies
This research suggests that varying step sizes in gradient descent can profoundly alter the learned representations within deep neural networks.
Improved theoretical understanding could lead to more optimized training algorithms, resulting in faster and more energy-efficient AI model development.
These algorithmic advancements might reduce the computational resources required for specific AI tasks, potentially broadening access to advanced AI development.
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Read at arXiv cs.LG