\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}

\tikzstyle{neuron}=[draw,circle,minimum size=12pt,inner sep=0pt, fill=white]
\tikzstyle{stateTransition}=[very thick]
\tikzstyle{learned}=[text=red]
\tikzstyle{input}=[draw,fill=red!50,circle,minimum size=10pt,inner sep=0pt]

\begin{document}
    \newcommand\n{6}
    \newcommand\xs{3}
    \begin{tikzpicture}
        \foreach \y in {1,...,\n}{
            \foreach \x in {1,...,\n}{
                \node (N-\y-\x)[neuron] at (0.55*\y + \x, 0.75*\y) {};
            }
        }

        \foreach \x in {1,...,\xs}{
            \node (x-\x)[input] at (3+\x, -1) {$x_\x$};
        }

        \foreach \y in {1,...,\n}{
            \foreach \x in {1,...,\n}{
                \foreach \t in {1,...,\xs}{
                    \draw[thin, dashed, black!50] (x-\t) -- (N-\y-\x) node [midway,above=-0.06cm,sloped] {};
                }
            }
        }

        \foreach \y in {1,...,\n}{
            \foreach \x in {1,...,\n}{
                \node (N-\y-\x)[neuron] at (0.55*\y + \x, 0.75*\y) {};
            }
        }

        % Make it look more like a board
        \draw[very thick, dashed, black!50] (N-1-1) -- (N-1-2)
                                                    -- (N-1-3)
                                                    -- (N-1-4)
                                                    -- (N-1-5)
                                                    -- (N-1-6)
                                                    -- (N-2-6)
                                                    -- (N-3-6)
                                                    -- (N-4-6)
                                                    -- (N-5-6)
                                                    -- (N-6-6)
                                                    -- (N-6-5)
                                                    -- (N-6-4)
                                                    -- (N-6-3)
                                                    -- (N-6-2)
                                                    -- (N-6-1)
                                                    -- (N-5-1)
                                                    -- (N-4-1)
                                                    -- (N-3-1)
                                                    -- (N-2-1)
                                                    -- (N-1-1);


        % Neighborhood gets excited
        \node (N-4-3)[neuron, fill=black!50] at (0.55*4 + 3, 0.75*4) {};
        \node (N-4-2)[neuron, fill=black!10] at (0.55*4 + 2, 0.75*4) {};
        \node (N-4-4)[neuron, fill=black!10] at (0.55*4 + 4, 0.75*4) {};
        \node (N-5-2)[neuron, fill=black!10] at (0.55*5 + 2, 0.75*5) {};
        \node (N-5-3)[neuron, fill=black!10] at (0.55*5 + 3, 0.75*5) {};
        \node (N-5-4)[neuron, fill=black!10] at (0.55*5 + 4, 0.75*5) {};
        \node (N-3-3)[neuron, fill=black!10] at (0.55*3 + 2, 0.75*3) {};
        \node (N-3-3)[neuron, fill=black!10] at (0.55*3 + 3, 0.75*3) {};
        \node (N-3-3)[neuron, fill=black!10] at (0.55*3 + 4, 0.75*3) {};
    \end{tikzpicture}
\end{document}