Any Target Function Exists in a Neighborhood of Any Sufficiently Wide Random Network: A Geometrical Perspective.

Neural Computation
Shun-Ichi Amari

Abstract

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) is sufficiently large. There are sophisticated analytical theories and discussions concerning this striking fact, but rigorous theories are very complicated. We give an elementary geometrical proof by using a simple model for the purpose of elucidating its structure. We show that high-dimensional geometry plays a magical role. When we project a high-dimensional sphere of radius 1 to a low-dimensional subspace, the uniform distribution over the sphere shrinks to a gaussian distribution with negligibly small variances and covariances.

References

Mar 19, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Shun-ichi AmariNaoki Masuda
Apr 20, 2016·The Journal of Physical Chemistry. B·Ekin Dogus CubukAndrea J Liu
Jul 12, 2018·IEEE Transactions on Neural Networks and Learning Systems·Jiangcheng ZhuChao Xu
Nov 18, 2018·Journal of the National Comprehensive Cancer Network : JNCCN·Parijatham S Thomas
Jun 23, 2019·Neural Networks : the Official Journal of the International Neural Network Society·Charles B Delahunt, J Nathan Kutz
Oct 3, 2019·Journal of Neural Engineering·Ameya C NanivadekarLee E Fisher

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Dental press journal of orthodontics
Glaucia Cristina Rodrigues NascimentoDavid Normando
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Kaiichiro OtaToshio Aoyagi
Journal of the American Statistical Association
Simon N VandekarRussell T Shinohara
© 2022 Meta ULC. All rights reserved