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- W3149313975 abstract "By using the viewpoint of modern computational algebraic geometry, we explore properties of the optimization landscapes of deep linear neural network models. After providing clarification on the various definitions of flat minima, we show that the geometrically flat minima, which are merely artifacts of residual continuous symmetries of the deep linear networks, can be straightforwardly removed by a generalized L2-regularization. Then, we establish upper bounds on the number of isolated stationary points of these networks with the help of algebraic geometry. Combining these upper bounds with a method in numerical algebraic geometry, we find all stationary points for modest depth and matrix size. We demonstrate that, in the presence of the non-zero regularization, deep linear networks can indeed possess local minima which are not global minima. Finally, we show that even though the number of stationary points increases as the number of neurons (regularization parameters) increases (decreases), higher index saddles are surprisingly rare." @default.
- W3149313975 created "2021-04-13" @default.
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- W3149313975 date "2021-01-01" @default.
- W3149313975 modified "2023-09-23" @default.
- W3149313975 title "The Loss Surface Of Deep Linear Networks Viewed Through The Algebraic Geometry Lens" @default.
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- W3149313975 doi "https://doi.org/10.1109/tpami.2021.3071289" @default.
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