I assume that if you want to reduce the space between the (numbered) chapter header and the following section header, you also want to reduce the space between the lines that contain the chapter number and the chapter header.
Here's a solution that doesn't use any packages (other than etoolbox, which allows the "patching" of existing macros).
Note that this solution does not affect the amount of whitespace above the chapter header.
\documentclass[12pt,a4paper]{report}
\usepackage{etoolbox} % for "\patchcmd" macro
\makeatletter
% No extra space between chapter number and chapter header lines:
\patchcmd{\@makechapterhead} {\vskip 20}{\vskip 0} {}{}
% Reduce extra space between chapter header and section header lines by 50%:
\patchcmd{\@makechapterhead} {\vskip 40}{\vskip 20}{}{}
\patchcmd{\@makeschapterhead}{\vskip 40}{\vskip 20}{}{} % for unnumbered chapters
\makeatother
\begin{document}
\setcounter{chapter}{1} % just for this example
\chapter{Background}
\section{Recurrent Neural Networks}
\end{document}

titlespacingcommand from thetitlesecpackage. (See this answer: https://tex.stackexchange.com/a/53341/134144) – leandriis Dec 27 '17 at 23:50\titlespacing\chapter{0pt}{50pt}{20pt}, where0ptand50ptare the default<left>and<before>separations (used intitlesec). – Werner Dec 28 '17 at 01:27