37 citations
13 papers
Platonic Projection Structures: Operator-Induced Observability in Representation Learning
Kazuo Ishii, Bishnu Prasad Gautam, Jieling Wu +2
We characterize observability in representation learning through Platonic Projection Structures (PPS), an operator-theoretic framework for analyzing representation accessibility un…
Shape of Growth Rate Distribution Determines the Type of Non-Gibrat's Property
Atushi Ishikawa, Shouji Fujimoto, Takayuki Mizuno
In this study, the authors examine exhaustive business data on Japanese firms, which cover nearly all companies in the mid- and large-scale ranges in terms of firm size, to reach s…
Non-Gibrat's law in the middle scale region
Masashi Tomoyose, Shouji Fujimoto, Atushi Ishikawa
By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, w…
The uniqueness of company size distribution function from tent-shaped growth rate distribution
Atushi Ishikawa
We report the proof that the extension of Gibrat's law in the middle scale region is unique and the probability distribution function (pdf) is also uniquely derived from the extend…
Annual change of Pareto index dynamically deduced from the law of detailed quasi-balance
Atushi Ishikawa
Employing data on the assessed value of land in 1983 -- 2005 Japan, we investigate the dynamical behavior in the high scale region of non-equilibrium systems. From the detailed qua…
Derivation of the distribution from extended Gibrat's law
Atushi Ishikawa
Employing profits data of Japanese companies in 2002 and 2003, we identify the non-Gibrat's law which holds in the middle profits region. From the law of detailed balance in all re…