247 citations · 967 across the 25 of their papers we have counts for
26 papers
Information Geometry of Wasserstein Statistics on Shapes and Affine Deformations
Shun-ichi Amari, Takeru Matsuda
Information geometry and Wasserstein geometry are two main structures introduced in a manifold of probability distributions, and they capture its different characteristics. We stud…
Deep Learning in Random Neural Fields: Numerical Experiments via Neural Tangent Kernel
Kaito Watanabe, Kotaro Sakamoto, Ryo Karakida +2
A biological neural network in the cortex forms a neural field. Neurons in the field have their own receptive fields, and connection weights between two neurons are random but high…
Wasserstein Statistics in One-dimensional Location-Scale Model
Shun-ichi Amari, Takeru Matsuda
Wasserstein geometry and information geometry are two important structures to be introduced in a manifold of probability distributions. Wasserstein geometry is defined by using the…
When Does Preconditioning Help or Hurt Generalization?
Shun-ichi Amari, Jimmy Ba, Roger Grosse +5
While second order optimizers such as natural gradient descent (NGD) often speed up optimization, their effect on generalization has been called into question. This work presents a…
Wasserstein statistics in 1D location-scale model
Shun-ichi Amari
Wasserstein geometry and information geometry are two important structures introduced in a manifold of probability distributions. The former is defined by using the transportation…
Any Target Function Exists in a Neighborhood of Any Sufficiently Wide Random Network: A Geometrical Perspective
Shun-ichi Amari
It is known that any target function is realized in a sufficiently small neighborhood of any randomly connected deep network, provided the width (the number of neurons in a layer)…