no code implementations • 26 Apr 2022 • Yasuhiko Asao, Ryotaro Sakamoto, Shiro Takagi
We give a proof that, under relatively mild conditions, fully-connected feed-forward deep random neural networks converge to a Gaussian mixture distribution as only the width of the last hidden layer goes to infinity.
no code implementations • 6 Sep 2021 • Yasuhiko Asao, Jumpei Nagase, Ryotaro Sakamoto, Shiro Takagi
By considering this weighted graph as a pseudo-metric space, we construct a Vietoris-Rips complex with a parameter $\varepsilon$ by a well-known process of algebraic topology.
no code implementations • 25 Nov 2020 • Chi-Yun Hsu, Zhaorong Jin, Ryotaro Sakamoto
For a non-endoscopic cohomological cuspidal automorphic representation of $\mathrm{GSp}_4 \times \mathrm{GL}_2$, assumed to be $p$-ordinary, we construct an Euler system for the Galois representation associated to it.
Number Theory
