Roman Sarapin

activity

20212026

most citedLocal solubility for a family of quadrics over a split quadric surface

1 citations · 1 across the 4 of their papers we have counts for

collaborators

4 papers

cs.LG2026

Randomly initialized autoencoders: fixed points and edge-of-chaos

Leonid Berlyand, Roman Sarapin, Yitzchak Shmalo +2

In this paper we study autoencoders, a special class of deep neural nets (DNNs) whose performance can be characterized via their fixed points. This perspective naturally raises que…

math-ph2024

Limiting eigenvalue distribution of the general deformed Ginibre ensemble

Roman Sarapin

Consider the $n \times n$ matrix $X_{n} = A_{n} + H_{n}$ , where $A_{n}$ is a $n \times n$ matrix (either deterministic or random) and $H_{n}$ is a $n \times n$ matrix independent from $A_{n}$ drawn f…

math.NT2022★ 1 cited

Local solubility for a family of quadrics over a split quadric surface

Tim Browning, Julian Lyczak, Roman Sarapin

We study the density of everywhere locally soluble diagonal quadric surfaces, parameterised by rational points that lie on a split quadric surface.

math.NT2021

Quartic del Pezzo surfaces with a Brauer group of order 4

Julian Lyczak, Roman Sarapin

We study arithmetic properties of del Pezzo surfaces of degree 4 for which the Brauer group has the largest possible order using different fibrations into curves. We show that if s…