Why Gradient Descent Works in Enormous Dimensions?
burny_tech · x · 2026-09-02
The post explains a core puzzle in deep learning (including LLM training): why gradient descent doesn't get stuck in poor local minima within high-dimensional, non-convex loss landscapes.
- Saddle Points Dominate: In high-dimensional non-convex landscapes, the vast majority of critical points are saddle points rather than local minima. As dimensionality grows, this becomes increasingly true.
- Escape Mechanism: The optimization process is more likely to pass through and escape saddle-like regions rather than getting trapped in rare local minima.
This insight references the paper "Identifying and attacking the saddle point problem in high-dimensional non-convex optimization," providing a theoretical basis for training large-scale neural networks.
Related event: Why Gradient Descent Works in High-Dimensional Non-Convex Landscapes(2 posts)→
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