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Statistical Mechanics and Artificial Neural Networks: Principles, Models, and Applications
Artificial neural networks can be seen as high-dimensional mathematical functions, and understanding the geometric properties of their loss landscapes (i. e., the high-dimensional space on which one wishes to find extrema or saddles) can provide valuable insights into their optimization behavior, generalization abilities, and overall performance.
Visualizing high-dimensional loss landscapes with Hessian directions
We show that saddle points in the original space are rarely correctly identified as such in expected lower-dimensional representations if random projections are used.
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