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07/24/2023
Information Geometry of Wasserstein Statistics on Shapes and Affine Deformations
Information geometry and Wasserstein geometry are two main structures in...
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02/10/2022
Deep Learning in Random Neural Fields: Numerical Experiments via Neural Tangent Kernel
A biological neural network in the cortex forms a neural field. Neurons ...
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07/21/2020
Wasserstein Statistics in One-dimensional Location-Scale Model
Wasserstein geometry and information geometry are two important structur...
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06/18/2020
When Does Preconditioning Help or Hurt Generalization?
While second order optimizers such as natural gradient descent (NGD) oft...
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03/06/2020
Wasserstein statistics in 1D location-scale model
Wasserstein geometry and information geometry are two important structur...
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01/20/2020
Any Target Function Exists in a Neighborhood of Any Sufficiently Wide Random Network: A Geometrical Perspective
It is known that any target function is realized in a sufficiently small...
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10/14/2019
Pathological spectra of the Fisher information metric and its variants in deep neural networks
The Fisher information matrix (FIM) plays an essential role in statistic...
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06/07/2019
The Normalization Method for Alleviating Pathological Sharpness in Wide Neural Networks
Normalization methods play an important role in enhancing the performanc...
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10/18/2018
Interpolating between Optimal Transport and MMD using Sinkhorn Divergences
Comparing probability distributions is a fundamental problem in data sci...
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08/22/2018
Fisher Information and Natural Gradient Learning of Random Deep Networks
A deep neural network is a hierarchical nonlinear model transforming inp...
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08/22/2018
Statistical Neurodynamics of Deep Networks: Geometry of Signal Spaces
Statistical neurodynamics studies macroscopic behaviors of randomly conn...
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06/04/2018
Universal Statistics of Fisher Information in Deep Neural Networks: Mean Field Approach
This study analyzes the Fisher information matrix (FIM) by applying mean...
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10/09/2014