\node[anchor=south west, inner sep=0] (image1-3) at (0.456\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/1_448.png}};
\node[anchor=south west, inner sep=0] (image1-4) at (0.608\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/1_512.png}};
\node[anchor=south west, inner sep=0] (image1-5) at (0.76\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/1_768.png}};
\node[anchor=south west, inner sep=0] (image1-6) at (0.912\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/1_1024.png}};

% row 2
\node[anchor=south west, inner sep=0] (image2-0) at (0.0\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/2_224.png}};
\node[anchor=south west, inner sep=0] (image2-1) at (0.152\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/2_320.png}};
\node[anchor=south west, inner sep=0] (image2-2) at (0.304\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/2_384.png}};
\node[anchor=south west, inner sep=0] (image2-3) at (0.456\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/2_448.png}};
\node[anchor=south west, inner sep=0] (image2-4) at (0.608\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/2_512.png}};
\node[anchor=south west, inner sep=0] (image2-5) at (0.76\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/2_768.png}};
\node[anchor=south west, inner sep=0] (image2-6) at (0.912\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/2_1024.png}};

% row 3
\node[anchor=south west, inner sep=0] (image3-0) at (0.0\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/3_224.png}};
\node[anchor=south west, inner sep=0] (image3-1) at (0.152\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/3_320.png}};
\node[anchor=south west, inner sep=0] (image3-2) at (0.304\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/3_384.png}};
\node[anchor=south west, inner sep=0] (image3-3) at (0.456\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/3_448.png}};
\node[anchor=south west, inner sep=0] (image3-4) at (0.608\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/3_512.png}};
\node[anchor=south west, inner sep=0] (image3-5) at (0.76\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/3_768.png}};
\node[anchor=south west, inner sep=0] (image3-6) at (0.912\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/3_1024.png}};

% row 4
\node[anchor=south west, inner sep=0] (image4-0) at (0.0\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/4_224.png}};
\node[anchor=south west, inner sep=0] (image4-1) at (0.152\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/4_320.png}};
\node[anchor=south west, inner sep=0] (image4-2) at (0.304\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/4_384.png}};
\node[anchor=south west, inner sep=0] (image4-3) at (0.456\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/4_448.png}};
\node[anchor=south west, inner sep=0] (image4-4) at (0.608\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/4_512.png}};
\node[anchor=south west, inner sep=0] (image4-5) at (0.76\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/4_768.png}};
\node[anchor=south west, inner sep=0] (image4-6) at (0.912\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/4_1024.png}};

% row 5
\node[anchor=south west, inner sep=0] (image5-0) at (0.0\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/5_224.png}};
\node[anchor=south west, inner sep=0] (image5-1) at (0.152\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/5_320.png}};
\node[anchor=south west, inner sep=0] (image5-2) at (0.304\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/5_384.png}};
\node[anchor=south west, inner sep=0] (image5-3) at (0.456\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/5_448.png}};
\node[anchor=south west, inner sep=0] (image5-4) at (0.608\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/5_512.png}};
\node[anchor=south west, inner sep=0] (image5-5) at (0.76\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/5_768.png}};
\node[anchor=south west, inner sep=0] (image5-6) at (0.912\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/5_1024.png}};

% row 6
\node[anchor=south west, inner sep=0] (image6-0) at (0.0\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/6_224.png}};
\node[anchor=south west, inner sep=0] (image6-1) at (0.152\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/6_320.png}};
\node[anchor=south west, inner sep=0] (image6-2) at (0.304\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/6_384.png}};
\node[anchor=south west, inner sep=0] (image6-3) at (0.456\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/6_448.png}};
\node[anchor=south west, inner sep=0] (image6-4) at (0.608\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/6_512.png}};
\node[anchor=south west, inner sep=0] (image6-5) at (0.76\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/6_768.png}};
\node[anchor=south west, inner sep=0] (image6-6) at (0.912\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/6_1024.png}};

% row 7
\node[anchor=south west, inner sep=0] (image7-0) at (0.0\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/7_224.png}};
\node[anchor=south west, inner sep=0] (image7-1) at (0.152\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/7_320.png}};
\node[anchor=south west, inner sep=0] (image7-2) at (0.304\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/7_384.png}};
\node[anchor=south west, inner sep=0] (image7-3) at (0.456\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/7_448.png}};
\node[anchor=south west, inner sep=0] (image7-4) at (0.608\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/7_512.png}};
\node[anchor=south west, inner sep=0] (image7-5) at (0.76\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/7_768.png}};
\node[anchor=south west, inner sep=0] (image7-6) at (0.912\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/7_1024.png}};

% row 8
\node[anchor=south west, inner sep=0] (image8-0) at (0.0\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/8_224.png}};
\node[anchor=south west, inner sep=0] (image8-1) at (0.152\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/8_320.png}};
\node[anchor=south west, inner sep=0] (image8-2) at (0.304\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/8_384.png}};
\node[anchor=south west, inner sep=0] (image8-3) at (0.456\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/8_448.png}};
\node[anchor=south west, inner sep=0] (image8-4) at (0.608\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/8_512.png}};
\node[anchor=south west, inner sep=0] (image8-5) at (0.76\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/8_768.png}};
\node[anchor=south west, inner sep=0] (image8-6) at (0.912\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/8_1024.png}};

% row 9
\node[anchor=south west, inner sep=0] (image9-0) at (0.0\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/9_224.png}};
\node[anchor=south west, inner sep=0] (image9-1) at (0.152\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/9_320.png}};
\node[anchor=south west, inner sep=0] (image9-2) at (0.304\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/9_384.png}};
\node[anchor=south west, inner sep=0] (image9-3) at (0.456\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/9_448.png}};
\node[anchor=south west, inner sep=0] (image9-4) at (0.608\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/9_512.png}};
\node[anchor=south west, inner sep=0] (image9-5) at (0.76\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/9_768.png}};
\node[anchor=south west, inner sep=0] (image9-6) at (0.912\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/9_1024.png}};

% row 10
\node[anchor=south west, inner sep=0] (image10-0) at (0.0\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/10_224.png}};
\node[anchor=south west, inner sep=0] (image10-1) at (0.152\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/10_320.png}};
\node[anchor=south west, inner sep=0] (image10-2) at (0.304\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/10_384.png}};
\node[anchor=south west, inner sep=0] (image10-3) at (0.456\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/10_448.png}};
\node[anchor=south west, inner sep=0] (image10-4) at (0.608\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/10_512.png}};
\node[anchor=south west, inner sep=0] (image10-5) at (0.76\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/10_768.png}};
\node[anchor=south west, inner sep=0] (image10-6) at (0.912\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/OneD/10_1024.png}};

\node[above=-0.5mm of image1-0] {224\textsuperscript{2}};
\node[above=-0.5mm of image1-1] {320\textsuperscript{2}};
\node[above=-0.5mm of image1-2] {384\textsuperscript{2}};
\node[above=-0.5mm of image1-3] {448\textsuperscript{2}};
\node[above=-0.5mm of image1-4] {512\textsuperscript{2}};
\node[above=-0.5mm of image1-5] {768\textsuperscript{2}};
\node[above=-0.5mm of image1-6] {1024\textsuperscript{2}};

\end{tikzpicture}
\caption{\textbf{1D-learn} attention maps of ten attention heads across seven resolutions, where the query is in the center. We use the colormap:  \includegraphics[width=2cm]{cmrmap.png}. Averaged over $5$k images.}
\label{fig:space_confuse_1d}
\end{figure}

\newpage
\usetikzlibrary{positioning}
\begin{figure}
\vspace{-20pt}
\centering
\begin{tikzpicture}
\hspace{-10pt}

\node[anchor=south west, inner sep=0] (image1-0) at (0.0\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/1_224.png}};
\node[anchor=south west, inner sep=0] (image1-1) at (0.152\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/1_320.png}};
\node[anchor=south west, inner sep=0] (image1-2) at (0.304\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/1_384.png}};
\node[anchor=south west, inner sep=0] (image1-3) at (0.456\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/1_448.png}};
\node[anchor=south west, inner sep=0] (image1-4) at (0.608\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/1_512.png}};
\node[anchor=south west, inner sep=0] (image1-5) at (0.76\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/1_768.png}};
\node[anchor=south west, inner sep=0] (image1-6) at (0.912\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/1_1024.png}};

% row 2
\node[anchor=south west, inner sep=0] (image2-0) at (0.0\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/2_224.png}};
\node[anchor=south west, inner sep=0] (image2-1) at (0.152\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/2_320.png}};
\node[anchor=south west, inner sep=0] (image2-2) at (0.304\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/2_384.png}};
\node[anchor=south west, inner sep=0] (image2-3) at (0.456\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/2_448.png}};
\node[anchor=south west, inner sep=0] (image2-4) at (0.608\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/2_512.png}};
\node[anchor=south west, inner sep=0] (image2-5) at (0.76\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/2_768.png}};
\node[anchor=south west, inner sep=0] (image2-6) at (0.912\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/2_1024.png}};

% row 3
\node[anchor=south west, inner sep=0] (image3-0) at (0.0\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/3_224.png}};
\node[anchor=south west, inner sep=0] (image3-1) at (0.152\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/3_320.png}};
\node[anchor=south west, inner sep=0] (image3-2) at (0.304\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/3_384.png}};
\node[anchor=south west, inner sep=0] (image3-3) at (0.456\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/3_448.png}};
\node[anchor=south west, inner sep=0] (image3-4) at (0.608\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/3_512.png}};
\node[anchor=south west, inner sep=0] (image3-5) at (0.76\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/3_768.png}};
\node[anchor=south west, inner sep=0] (image3-6) at (0.912\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/3_1024.png}};

% row 4
\node[anchor=south west, inner sep=0] (image4-0) at (0.0\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/4_224.png}};
\node[anchor=south west, inner sep=0] (image4-1) at (0.152\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/4_320.png}};
\node[anchor=south west, inner sep=0] (image4-2) at (0.304\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/4_384.png}};
\node[anchor=south west, inner sep=0] (image4-3) at (0.456\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/4_448.png}};
\node[anchor=south west, inner sep=0] (image4-4) at (0.608\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/4_512.png}};
\node[anchor=south west, inner sep=0] (image4-5) at (0.76\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/4_768.png}};
\node[anchor=south west, inner sep=0] (image4-6) at (0.912\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/4_1024.png}};

% row 5
\node[anchor=south west, inner sep=0] (image5-0) at (0.0\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/5_224.png}};
\node[anchor=south west, inner sep=0] (image5-1) at (0.152\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/5_320.png}};
\node[anchor=south west, inner sep=0] (image5-2) at (0.304\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/5_384.png}};
\node[anchor=south west, inner sep=0] (image5-3) at (0.456\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/5_448.png}};
\node[anchor=south west, inner sep=0] (image5-4) at (0.608\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/5_512.png}};
\node[anchor=south west, inner sep=0] (image5-5) at (0.76\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/5_768.png}};
\node[anchor=south west, inner sep=0] (image5-6) at (0.912\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/5_1024.png}};

% row 6
\node[anchor=south west, inner sep=0] (image6-0) at (0.0\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/6_224.png}};
\node[anchor=south west, inner sep=0] (image6-1) at (0.152\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/6_320.png}};
\node[anchor=south west, inner sep=0] (image6-2) at (0.304\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/6_384.png}};
\node[anchor=south west, inner sep=0] (image6-3) at (0.456\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/6_448.png}};
\node[anchor=south west, inner sep=0] (image6-4) at (0.608\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/6_512.png}};
\node[anchor=south west, inner sep=0] (image6-5) at (0.76\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/6_768.png}};
\node[anchor=south west, inner sep=0] (image6-6) at (0.912\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/6_1024.png}};

% row 7
\node[anchor=south west, inner sep=0] (image7-0) at (0.0\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/7_224.png}};
\node[anchor=south west, inner sep=0] (image7-1) at (0.152\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/7_320.png}};
\node[anchor=south west, inner sep=0] (image7-2) at (0.304\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/7_384.png}};
\node[anchor=south west, inner sep=0] (image7-3) at (0.456\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/7_448.png}};
\node[anchor=south west, inner sep=0] (image7-4) at (0.608\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/7_512.png}};
\node[anchor=south west, inner sep=0] (image7-5) at (0.76\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/7_768.png}};
\node[anchor=south west, inner sep=0] (image7-6) at (0.912\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/7_1024.png}};

% row 8
\node[anchor=south west, inner sep=0] (image8-0) at (0.0\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/8_224.png}};
\node[anchor=south west, inner sep=0] (image8-1) at (0.152\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/8_320.png}};
\node[anchor=south west, inner sep=0] (image8-2) at (0.304\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/8_384.png}};
\node[anchor=south west, inner sep=0] (image8-3) at (0.456\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/8_448.png}};
\node[anchor=south west, inner sep=0] (image8-4) at (0.608\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/8_512.png}};
\node[anchor=south west, inner sep=0] (image8-5) at (0.76\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/8_768.png}};
\node[anchor=south west, inner sep=0] (image8-6) at (0.912\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/8_1024.png}};

% row 9
\node[anchor=south west, inner sep=0] (image9-0) at (0.0\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/9_224.png}};
\node[anchor=south west, inner sep=0] (image9-1) at (0.152\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/9_320.png}};
\node[anchor=south west, inner sep=0] (image9-2) at (0.304\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/9_384.png}};
\node[anchor=south west, inner sep=0] (image9-3) at (0.456\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/9_448.png}};
\node[anchor=south west, inner sep=0] (image9-4) at (0.608\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/9_512.png}};
\node[anchor=south west, inner sep=0] (image9-5) at (0.76\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/9_768.png}};
\node[anchor=south west, inner sep=0] (image9-6) at (0.912\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/9_1024.png}};

% row 10
\node[anchor=south west, inner sep=0] (image10-0) at (0.0\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/10_224.png}};
\node[anchor=south west, inner sep=0] (image10-1) at (0.152\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/10_320.png}};
\node[anchor=south west, inner sep=0] (image10-2) at (0.304\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/10_384.png}};
\node[anchor=south west, inner sep=0] (image10-3) at (0.456\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/10_448.png}};
\node[anchor=south west, inner sep=0] (image10-4) at (0.608\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/10_512.png}};
\node[anchor=south west, inner sep=0] (image10-5) at (0.76\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/10_768.png}};
\node[anchor=south west, inner sep=0] (image10-6) at (0.912\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-sincos/10_1024.png}};

\node[above=-0.5mm of image1-0] {224\textsuperscript{2}};
\node[above=-0.5mm of image1-1] {320\textsuperscript{2}};
\node[above=-0.5mm of image1-2] {384\textsuperscript{2}};
\node[above=-0.5mm of image1-3] {448\textsuperscript{2}};
\node[above=-0.5mm of image1-4] {512\textsuperscript{2}};
\node[above=-0.5mm of image1-5] {768\textsuperscript{2}};
\node[above=-0.5mm of image1-6] {1024\textsuperscript{2}};

\end{tikzpicture}
\caption{\textbf{2D-sincos} attention maps of ten attention heads across seven resolutions, where the query is in the center. We use the colormap:  \includegraphics[width=2cm]{cmrmap.png}. Averaged over $5$k images.}
\label{fig:space_confuse_2d_sincos}
\end{figure}

\newpage
\usetikzlibrary{positioning}
\begin{figure}
\vspace{-20pt}
\centering
\begin{tikzpicture}
\hspace{-10pt}

\node[anchor=south west, inner sep=0] (image1-0) at (0.0\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/1_224.png}};
\node[anchor=south west, inner sep=0] (image1-1) at (0.152\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/1_320.png}};
\node[anchor=south west, inner sep=0] (image1-2) at (0.304\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/1_384.png}};
\node[anchor=south west, inner sep=0] (image1-3) at (0.456\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/1_448.png}};
\node[anchor=south west, inner sep=0] (image1-4) at (0.608\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/1_512.png}};
\node[anchor=south west, inner sep=0] (image1-5) at (0.76\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/1_768.png}};
\node[anchor=south west, inner sep=0] (image1-6) at (0.912\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/1_1024.png}};

% row 2
\node[anchor=south west, inner sep=0] (image2-0) at (0.0\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/2_224.png}};
\node[anchor=south west, inner sep=0] (image2-1) at (0.152\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/2_320.png}};
\node[anchor=south west, inner sep=0] (image2-2) at (0.304\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/2_384.png}};
\node[anchor=south west, inner sep=0] (image2-3) at (0.456\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/2_448.png}};
\node[anchor=south west, inner sep=0] (image2-4) at (0.608\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/2_512.png}};
\node[anchor=south west, inner sep=0] (image2-5) at (0.76\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/2_768.png}};
\node[anchor=south west, inner sep=0] (image2-6) at (0.912\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/2_1024.png}};

% row 3
\node[anchor=south west, inner sep=0] (image3-0) at (0.0\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/3_224.png}};
\node[anchor=south west, inner sep=0] (image3-1) at (0.152\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/3_320.png}};
\node[anchor=south west, inner sep=0] (image3-2) at (0.304\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/3_384.png}};
\node[anchor=south west, inner sep=0] (image3-3) at (0.456\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/3_448.png}};
\node[anchor=south west, inner sep=0] (image3-4) at (0.608\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/3_512.png}};
\node[anchor=south west, inner sep=0] (image3-5) at (0.76\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/3_768.png}};
\node[anchor=south west, inner sep=0] (image3-6) at (0.912\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/3_1024.png}};

% row 4
\node[anchor=south west, inner sep=0] (image4-0) at (0.0\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/4_224.png}};
\node[anchor=south west, inner sep=0] (image4-1) at (0.152\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/4_320.png}};
\node[anchor=south west, inner sep=0] (image4-2) at (0.304\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/4_384.png}};
\node[anchor=south west, inner sep=0] (image4-3) at (0.456\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/4_448.png}};
\node[anchor=south west, inner sep=0] (image4-4) at (0.608\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/4_512.png}};
\node[anchor=south west, inner sep=0] (image4-5) at (0.76\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/4_768.png}};
\node[anchor=south west, inner sep=0] (image4-6) at (0.912\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/4_1024.png}};

% row 5
\node[anchor=south west, inner sep=0] (image5-0) at (0.0\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/5_224.png}};
\node[anchor=south west, inner sep=0] (image5-1) at (0.152\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/5_320.png}};
\node[anchor=south west, inner sep=0] (image5-2) at (0.304\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/5_384.png}};
\node[anchor=south west, inner sep=0] (image5-3) at (0.456\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/5_448.png}};
\node[anchor=south west, inner sep=0] (image5-4) at (0.608\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/5_512.png}};
\node[anchor=south west, inner sep=0] (image5-5) at (0.76\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/5_768.png}};
\node[anchor=south west, inner sep=0] (image5-6) at (0.912\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/5_1024.png}};

% row 6
\node[anchor=south west, inner sep=0] (image6-0) at (0.0\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/6_224.png}};
\node[anchor=south west, inner sep=0] (image6-1) at (0.152\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/6_320.png}};
\node[anchor=south west, inner sep=0] (image6-2) at (0.304\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/6_384.png}};
\node[anchor=south west, inner sep=0] (image6-3) at (0.456\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/6_448.png}};
\node[anchor=south west, inner sep=0] (image6-4) at (0.608\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/6_512.png}};
\node[anchor=south west, inner sep=0] (image6-5) at (0.76\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/6_768.png}};
\node[anchor=south west, inner sep=0] (image6-6) at (0.912\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/6_1024.png}};

% row 7
\node[anchor=south west, inner sep=0] (image7-0) at (0.0\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/7_224.png}};
\node[anchor=south west, inner sep=0] (image7-1) at (0.152\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/7_320.png}};
\node[anchor=south west, inner sep=0] (image7-2) at (0.304\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/7_384.png}};
\node[anchor=south west, inner sep=0] (image7-3) at (0.456\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/7_448.png}};
\node[anchor=south west, inner sep=0] (image7-4) at (0.608\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/7_512.png}};
\node[anchor=south west, inner sep=0] (image7-5) at (0.76\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/7_768.png}};
\node[anchor=south west, inner sep=0] (image7-6) at (0.912\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/7_1024.png}};

% row 8
\node[anchor=south west, inner sep=0] (image8-0) at (0.0\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/8_224.png}};
\node[anchor=south west, inner sep=0] (image8-1) at (0.152\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/8_320.png}};
\node[anchor=south west, inner sep=0] (image8-2) at (0.304\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/8_384.png}};
\node[anchor=south west, inner sep=0] (image8-3) at (0.456\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/8_448.png}};
\node[anchor=south west, inner sep=0] (image8-4) at (0.608\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/8_512.png}};
\node[anchor=south west, inner sep=0] (image8-5) at (0.76\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/8_768.png}};
\node[anchor=south west, inner sep=0] (image8-6) at (0.912\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/8_1024.png}};

% row 9
\node[anchor=south west, inner sep=0] (image9-0) at (0.0\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/9_224.png}};
\node[anchor=south west, inner sep=0] (image9-1) at (0.152\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/9_320.png}};
\node[anchor=south west, inner sep=0] (image9-2) at (0.304\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/9_384.png}};
\node[anchor=south west, inner sep=0] (image9-3) at (0.456\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/9_448.png}};
\node[anchor=south west, inner sep=0] (image9-4) at (0.608\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/9_512.png}};
\node[anchor=south west, inner sep=0] (image9-5) at (0.76\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/9_768.png}};
\node[anchor=south west, inner sep=0] (image9-6) at (0.912\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/9_1024.png}};

% row 10
\node[anchor=south west, inner sep=0] (image10-0) at (0.0\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/10_224.png}};
\node[anchor=south west, inner sep=0] (image10-1) at (0.152\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/10_320.png}};
\node[anchor=south west, inner sep=0] (image10-2) at (0.304\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/10_384.png}};
\node[anchor=south west, inner sep=0] (image10-3) at (0.456\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/10_448.png}};
\node[anchor=south west, inner sep=0] (image10-4) at (0.608\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/10_512.png}};
\node[anchor=south west, inner sep=0] (image10-5) at (0.76\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/10_768.png}};
\node[anchor=south west, inner sep=0] (image10-6) at (0.912\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/NaViT/10_1024.png}};

\node[above=-0.5mm of image1-0] {224\textsuperscript{2}};
\node[above=-0.5mm of image1-1] {320\textsuperscript{2}};
\node[above=-0.5mm of image1-2] {384\textsuperscript{2}};
\node[above=-0.5mm of image1-3] {448\textsuperscript{2}};
\node[above=-0.5mm of image1-4] {512\textsuperscript{2}};
\node[above=-0.5mm of image1-5] {768\textsuperscript{2}};
\node[above=-0.5mm of image1-6] {1024\textsuperscript{2}};

\end{tikzpicture}
\caption{\textbf{Factorized} attention maps of ten attention heads across seven resolutions, where the query is in the center. We use the colormap:  \includegraphics[width=2cm]{cmrmap.png}. Averaged over $5$k images.}
\label{fig:space_confuse_factorized}
\end{figure}

\newpage
\usetikzlibrary{positioning}
\begin{figure}
\vspace{-20pt}
\centering
\begin{tikzpicture}
\hspace{-10pt}

\node[anchor=south west, inner sep=0] (image1-0) at (0.0\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/1_224.png}};
\node[anchor=south west, inner sep=0] (image1-1) at (0.152\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/1_320.png}};
\node[anchor=south west, inner sep=0] (image1-2) at (0.304\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/1_384.png}};
\node[anchor=south west, inner sep=0] (image1-3) at (0.456\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/1_448.png}};
\node[anchor=south west, inner sep=0] (image1-4) at (0.608\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/1_512.png}};
\node[anchor=south west, inner sep=0] (image1-5) at (0.76\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/1_768.png}};
\node[anchor=south west, inner sep=0] (image1-6) at (0.912\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/1_1024.png}};

% row 2
\node[anchor=south west, inner sep=0] (image2-0) at (0.0\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/2_224.png}};
\node[anchor=south west, inner sep=0] (image2-1) at (0.152\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/2_320.png}};
\node[anchor=south west, inner sep=0] (image2-2) at (0.304\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/2_384.png}};
\node[anchor=south west, inner sep=0] (image2-3) at (0.456\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/2_448.png}};
\node[anchor=south west, inner sep=0] (image2-4) at (0.608\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/2_512.png}};
\node[anchor=south west, inner sep=0] (image2-5) at (0.76\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/2_768.png}};
\node[anchor=south west, inner sep=0] (image2-6) at (0.912\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/2_1024.png}};

% row 3
\node[anchor=south west, inner sep=0] (image3-0) at (0.0\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/3_224.png}};
\node[anchor=south west, inner sep=0] (image3-1) at (0.152\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/3_320.png}};
\node[anchor=south west, inner sep=0] (image3-2) at (0.304\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/3_384.png}};
\node[anchor=south west, inner sep=0] (image3-3) at (0.456\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/3_448.png}};
\node[anchor=south west, inner sep=0] (image3-4) at (0.608\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/3_512.png}};
\node[anchor=south west, inner sep=0] (image3-5) at (0.76\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/3_768.png}};
\node[anchor=south west, inner sep=0] (image3-6) at (0.912\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/3_1024.png}};

% row 4
\node[anchor=south west, inner sep=0] (image4-0) at (0.0\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/4_224.png}};
\node[anchor=south west, inner sep=0] (image4-1) at (0.152\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/4_320.png}};
\node[anchor=south west, inner sep=0] (image4-2) at (0.304\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/4_384.png}};
\node[anchor=south west, inner sep=0] (image4-3) at (0.456\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/4_448.png}};
\node[anchor=south west, inner sep=0] (image4-4) at (0.608\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/4_512.png}};
\node[anchor=south west, inner sep=0] (image4-5) at (0.76\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/4_768.png}};
\node[anchor=south west, inner sep=0] (image4-6) at (0.912\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/4_1024.png}};

% row 5
\node[anchor=south west, inner sep=0] (image5-0) at (0.0\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/5_224.png}};
\node[anchor=south west, inner sep=0] (image5-1) at (0.152\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/5_320.png}};
\node[anchor=south west, inner sep=0] (image5-2) at (0.304\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/5_384.png}};
\node[anchor=south west, inner sep=0] (image5-3) at (0.456\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/5_448.png}};
\node[anchor=south west, inner sep=0] (image5-4) at (0.608\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/5_512.png}};
\node[anchor=south west, inner sep=0] (image5-5) at (0.76\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/5_768.png}};
\node[anchor=south west, inner sep=0] (image5-6) at (0.912\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/5_1024.png}};

% row 6
\node[anchor=south west, inner sep=0] (image6-0) at (0.0\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/6_224.png}};
\node[anchor=south west, inner sep=0] (image6-1) at (0.152\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/6_320.png}};
\node[anchor=south west, inner sep=0] (image6-2) at (0.304\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/6_384.png}};
\node[anchor=south west, inner sep=0] (image6-3) at (0.456\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/6_448.png}};
\node[anchor=south west, inner sep=0] (image6-4) at (0.608\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/6_512.png}};
\node[anchor=south west, inner sep=0] (image6-5) at (0.76\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/6_768.png}};
\node[anchor=south west, inner sep=0] (image6-6) at (0.912\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/6_1024.png}};

% row 7
\node[anchor=south west, inner sep=0] (image7-0) at (0.0\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/7_224.png}};
\node[anchor=south west, inner sep=0] (image7-1) at (0.152\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/7_320.png}};
\node[anchor=south west, inner sep=0] (image7-2) at (0.304\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/7_384.png}};
\node[anchor=south west, inner sep=0] (image7-3) at (0.456\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/7_448.png}};
\node[anchor=south west, inner sep=0] (image7-4) at (0.608\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/7_512.png}};
\node[anchor=south west, inner sep=0] (image7-5) at (0.76\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/7_768.png}};
\node[anchor=south west, inner sep=0] (image7-6) at (0.912\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/7_1024.png}};

% row 8
\node[anchor=south west, inner sep=0] (image8-0) at (0.0\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/8_224.png}};
\node[anchor=south west, inner sep=0] (image8-1) at (0.152\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/8_320.png}};
\node[anchor=south west, inner sep=0] (image8-2) at (0.304\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/8_384.png}};
\node[anchor=south west, inner sep=0] (image8-3) at (0.456\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/8_448.png}};
\node[anchor=south west, inner sep=0] (image8-4) at (0.608\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/8_512.png}};
\node[anchor=south west, inner sep=0] (image8-5) at (0.76\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/8_768.png}};
\node[anchor=south west, inner sep=0] (image8-6) at (0.912\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/8_1024.png}};

% row 9
\node[anchor=south west, inner sep=0] (image9-0) at (0.0\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/9_224.png}};
\node[anchor=south west, inner sep=0] (image9-1) at (0.152\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/9_320.png}};
\node[anchor=south west, inner sep=0] (image9-2) at (0.304\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/9_384.png}};
\node[anchor=south west, inner sep=0] (image9-3) at (0.456\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/9_448.png}};
\node[anchor=south west, inner sep=0] (image9-4) at (0.608\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/9_512.png}};
\node[anchor=south west, inner sep=0] (image9-5) at (0.76\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/9_768.png}};
\node[anchor=south west, inner sep=0] (image9-6) at (0.912\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/9_1024.png}};

% row 10
\node[anchor=south west, inner sep=0] (image10-0) at (0.0\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/10_224.png}};
\node[anchor=south west, inner sep=0] (image10-1) at (0.152\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/10_320.png}};
\node[anchor=south west, inner sep=0] (image10-2) at (0.304\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/10_384.png}};
\node[anchor=south west, inner sep=0] (image10-3) at (0.456\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/10_448.png}};
\node[anchor=south west, inner sep=0] (image10-4) at (0.608\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/10_512.png}};
\node[anchor=south west, inner sep=0] (image10-5) at (0.76\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/10_768.png}};
\node[anchor=south west, inner sep=0] (image10-6) at (0.912\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/Fourier/10_1024.png}};

\node[above=-0.5mm of image1-0] {224\textsuperscript{2}};
\node[above=-0.5mm of image1-1] {320\textsuperscript{2}};
\node[above=-0.5mm of image1-2] {384\textsuperscript{2}};
\node[above=-0.5mm of image1-3] {448\textsuperscript{2}};
\node[above=-0.5mm of image1-4] {512\textsuperscript{2}};
\node[above=-0.5mm of image1-5] {768\textsuperscript{2}};
\node[above=-0.5mm of image1-6] {1024\textsuperscript{2}};

\end{tikzpicture}
\caption{\textbf{Fourier} attention maps of ten attention heads across seven resolutions, where the query is in the center. We use the colormap:  \includegraphics[width=2cm]{cmrmap.png}. Averaged over $5$k images.}
\label{fig:space_confuse_fourier}
\end{figure}

\newpage
\usetikzlibrary{positioning}
\begin{figure}
\vspace{-20pt}
\centering
\begin{tikzpicture}
\hspace{-10pt}

\node[anchor=south west, inner sep=0] (image1-0) at (0.0\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/1_224.png}};
\node[anchor=south west, inner sep=0] (image1-1) at (0.152\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/1_320.png}};
\node[anchor=south west, inner sep=0] (image1-2) at (0.304\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/1_384.png}};
\node[anchor=south west, inner sep=0] (image1-3) at (0.456\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/1_448.png}};
\node[anchor=south west, inner sep=0] (image1-4) at (0.608\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/1_512.png}};
\node[anchor=south west, inner sep=0] (image1-5) at (0.76\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/1_768.png}};
\node[anchor=south west, inner sep=0] (image1-6) at (0.912\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/1_1024.png}};

% row 2
\node[anchor=south west, inner sep=0] (image2-0) at (0.0\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/2_224.png}};
\node[anchor=south west, inner sep=0] (image2-1) at (0.152\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/2_320.png}};
\node[anchor=south west, inner sep=0] (image2-2) at (0.304\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/2_384.png}};
\node[anchor=south west, inner sep=0] (image2-3) at (0.456\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/2_448.png}};
\node[anchor=south west, inner sep=0] (image2-4) at (0.608\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/2_512.png}};
\node[anchor=south west, inner sep=0] (image2-5) at (0.76\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/2_768.png}};
\node[anchor=south west, inner sep=0] (image2-6) at (0.912\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/2_1024.png}};

% row 3
\node[anchor=south west, inner sep=0] (image3-0) at (0.0\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/3_224.png}};
\node[anchor=south west, inner sep=0] (image3-1) at (0.152\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/3_320.png}};
\node[anchor=south west, inner sep=0] (image3-2) at (0.304\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/3_384.png}};
\node[anchor=south west, inner sep=0] (image3-3) at (0.456\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/3_448.png}};
\node[anchor=south west, inner sep=0] (image3-4) at (0.608\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/3_512.png}};
\node[anchor=south west, inner sep=0] (image3-5) at (0.76\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/3_768.png}};
\node[anchor=south west, inner sep=0] (image3-6) at (0.912\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/3_1024.png}};

% row 4
\node[anchor=south west, inner sep=0] (image4-0) at (0.0\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/4_224.png}};
\node[anchor=south west, inner sep=0] (image4-1) at (0.152\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/4_320.png}};
\node[anchor=south west, inner sep=0] (image4-2) at (0.304\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/4_384.png}};
\node[anchor=south west, inner sep=0] (image4-3) at (0.456\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/4_448.png}};
\node[anchor=south west, inner sep=0] (image4-4) at (0.608\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/4_512.png}};
\node[anchor=south west, inner sep=0] (image4-5) at (0.76\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/4_768.png}};
\node[anchor=south west, inner sep=0] (image4-6) at (0.912\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/4_1024.png}};

% row 5
\node[anchor=south west, inner sep=0] (image5-0) at (0.0\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/5_224.png}};
\node[anchor=south west, inner sep=0] (image5-1) at (0.152\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/5_320.png}};
\node[anchor=south west, inner sep=0] (image5-2) at (0.304\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/5_384.png}};
\node[anchor=south west, inner sep=0] (image5-3) at (0.456\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/5_448.png}};
\node[anchor=south west, inner sep=0] (image5-4) at (0.608\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/5_512.png}};
\node[anchor=south west, inner sep=0] (image5-5) at (0.76\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/5_768.png}};
\node[anchor=south west, inner sep=0] (image5-6) at (0.912\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/5_1024.png}};

% row 6
\node[anchor=south west, inner sep=0] (image6-0) at (0.0\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/6_224.png}};
\node[anchor=south west, inner sep=0] (image6-1) at (0.152\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/6_320.png}};
\node[anchor=south west, inner sep=0] (image6-2) at (0.304\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/6_384.png}};
\node[anchor=south west, inner sep=0] (image6-3) at (0.456\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/6_448.png}};
\node[anchor=south west, inner sep=0] (image6-4) at (0.608\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/6_512.png}};
\node[anchor=south west, inner sep=0] (image6-5) at (0.76\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/6_768.png}};
\node[anchor=south west, inner sep=0] (image6-6) at (0.912\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/6_1024.png}};

% row 7
\node[anchor=south west, inner sep=0] (image7-0) at (0.0\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/7_224.png}};
\node[anchor=south west, inner sep=0] (image7-1) at (0.152\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/7_320.png}};
\node[anchor=south west, inner sep=0] (image7-2) at (0.304\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/7_384.png}};
\node[anchor=south west, inner sep=0] (image7-3) at (0.456\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/7_448.png}};
\node[anchor=south west, inner sep=0] (image7-4) at (0.608\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/7_512.png}};
\node[anchor=south west, inner sep=0] (image7-5) at (0.76\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/7_768.png}};
\node[anchor=south west, inner sep=0] (image7-6) at (0.912\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/7_1024.png}};

% row 8
\node[anchor=south west, inner sep=0] (image8-0) at (0.0\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/8_224.png}};
\node[anchor=south west, inner sep=0] (image8-1) at (0.152\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/8_320.png}};
\node[anchor=south west, inner sep=0] (image8-2) at (0.304\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/8_384.png}};
\node[anchor=south west, inner sep=0] (image8-3) at (0.456\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/8_448.png}};
\node[anchor=south west, inner sep=0] (image8-4) at (0.608\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/8_512.png}};
\node[anchor=south west, inner sep=0] (image8-5) at (0.76\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/8_768.png}};
\node[anchor=south west, inner sep=0] (image8-6) at (0.912\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/8_1024.png}};

% row 9
\node[anchor=south west, inner sep=0] (image9-0) at (0.0\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/9_224.png}};
\node[anchor=south west, inner sep=0] (image9-1) at (0.152\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/9_320.png}};
\node[anchor=south west, inner sep=0] (image9-2) at (0.304\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/9_384.png}};
\node[anchor=south west, inner sep=0] (image9-3) at (0.456\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/9_448.png}};
\node[anchor=south west, inner sep=0] (image9-4) at (0.608\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/9_512.png}};
\node[anchor=south west, inner sep=0] (image9-5) at (0.76\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/9_768.png}};
\node[anchor=south west, inner sep=0] (image9-6) at (0.912\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/9_1024.png}};

% row 10
\node[anchor=south west, inner sep=0] (image10-0) at (0.0\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/10_224.png}};
\node[anchor=south west, inner sep=0] (image10-1) at (0.152\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/10_320.png}};
\node[anchor=south west, inner sep=0] (image10-2) at (0.304\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/10_384.png}};
\node[anchor=south west, inner sep=0] (image10-3) at (0.456\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/10_448.png}};
\node[anchor=south west, inner sep=0] (image10-4) at (0.608\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/10_512.png}};
\node[anchor=south west, inner sep=0] (image10-5) at (0.76\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/10_768.png}};
\node[anchor=south west, inner sep=0] (image10-6) at (0.912\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/BEIT/10_1024.png}};

\node[above=-0.5mm of image1-0] {224\textsuperscript{2}};
\node[above=-0.5mm of image1-1] {320\textsuperscript{2}};
\node[above=-0.5mm of image1-2] {384\textsuperscript{2}};
\node[above=-0.5mm of image1-3] {448\textsuperscript{2}};
\node[above=-0.5mm of image1-4] {512\textsuperscript{2}};
\node[above=-0.5mm of image1-5] {768\textsuperscript{2}};
\node[above=-0.5mm of image1-6] {1024\textsuperscript{2}};

\end{tikzpicture}
\caption{\textbf{RPE-learn} attention maps of ten attention heads across seven resolutions, where the query is in the center. We use the colormap:  \includegraphics[width=2cm]{cmrmap.png}. Averaged over $5$k images.}
\label{fig:space_confuse_rpe_learn}
\end{figure}

\newpage
\usetikzlibrary{positioning}
\begin{figure}
\vspace{-20pt}
\centering
\begin{tikzpicture}
\hspace{-10pt}

\node[anchor=south west, inner sep=0] (image1-0) at (0.0\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/1_224.png}};
\node[anchor=south west, inner sep=0] (image1-1) at (0.152\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/1_320.png}};
\node[anchor=south west, inner sep=0] (image1-2) at (0.304\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/1_384.png}};
\node[anchor=south west, inner sep=0] (image1-3) at (0.456\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/1_448.png}};
\node[anchor=south west, inner sep=0] (image1-4) at (0.608\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/1_512.png}};
\node[anchor=south west, inner sep=0] (image1-5) at (0.76\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/1_768.png}};
\node[anchor=south west, inner sep=0] (image1-6) at (0.912\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/1_1024.png}};

% row 2
\node[anchor=south west, inner sep=0] (image2-0) at (0.0\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/2_224.png}};
\node[anchor=south west, inner sep=0] (image2-1) at (0.152\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/2_320.png}};
\node[anchor=south west, inner sep=0] (image2-2) at (0.304\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/2_384.png}};
\node[anchor=south west, inner sep=0] (image2-3) at (0.456\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/2_448.png}};
\node[anchor=south west, inner sep=0] (image2-4) at (0.608\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/2_512.png}};
\node[anchor=south west, inner sep=0] (image2-5) at (0.76\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/2_768.png}};
\node[anchor=south west, inner sep=0] (image2-6) at (0.912\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/2_1024.png}};

% row 3
\node[anchor=south west, inner sep=0] (image3-0) at (0.0\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/3_224.png}};
\node[anchor=south west, inner sep=0] (image3-1) at (0.152\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/3_320.png}};
\node[anchor=south west, inner sep=0] (image3-2) at (0.304\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/3_384.png}};
\node[anchor=south west, inner sep=0] (image3-3) at (0.456\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/3_448.png}};
\node[anchor=south west, inner sep=0] (image3-4) at (0.608\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/3_512.png}};
\node[anchor=south west, inner sep=0] (image3-5) at (0.76\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/3_768.png}};
\node[anchor=south west, inner sep=0] (image3-6) at (0.912\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/3_1024.png}};

% row 4
\node[anchor=south west, inner sep=0] (image4-0) at (0.0\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/4_224.png}};
\node[anchor=south west, inner sep=0] (image4-1) at (0.152\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/4_320.png}};
\node[anchor=south west, inner sep=0] (image4-2) at (0.304\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/4_384.png}};
\node[anchor=south west, inner sep=0] (image4-3) at (0.456\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/4_448.png}};
\node[anchor=south west, inner sep=0] (image4-4) at (0.608\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/4_512.png}};
\node[anchor=south west, inner sep=0] (image4-5) at (0.76\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/4_768.png}};
\node[anchor=south west, inner sep=0] (image4-6) at (0.912\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/4_1024.png}};

% row 5
\node[anchor=south west, inner sep=0] (image5-0) at (0.0\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/5_224.png}};
\node[anchor=south west, inner sep=0] (image5-1) at (0.152\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/5_320.png}};
\node[anchor=south west, inner sep=0] (image5-2) at (0.304\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/5_384.png}};
\node[anchor=south west, inner sep=0] (image5-3) at (0.456\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/5_448.png}};
\node[anchor=south west, inner sep=0] (image5-4) at (0.608\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/5_512.png}};
\node[anchor=south west, inner sep=0] (image5-5) at (0.76\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/5_768.png}};
\node[anchor=south west, inner sep=0] (image5-6) at (0.912\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/5_1024.png}};

% row 6
\node[anchor=south west, inner sep=0] (image6-0) at (0.0\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/6_224.png}};
\node[anchor=south west, inner sep=0] (image6-1) at (0.152\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/6_320.png}};
\node[anchor=south west, inner sep=0] (image6-2) at (0.304\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/6_384.png}};
\node[anchor=south west, inner sep=0] (image6-3) at (0.456\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/6_448.png}};
\node[anchor=south west, inner sep=0] (image6-4) at (0.608\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/6_512.png}};
\node[anchor=south west, inner sep=0] (image6-5) at (0.76\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/6_768.png}};
\node[anchor=south west, inner sep=0] (image6-6) at (0.912\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/6_1024.png}};

% row 7
\node[anchor=south west, inner sep=0] (image7-0) at (0.0\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/7_224.png}};
\node[anchor=south west, inner sep=0] (image7-1) at (0.152\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/7_320.png}};
\node[anchor=south west, inner sep=0] (image7-2) at (0.304\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/7_384.png}};
\node[anchor=south west, inner sep=0] (image7-3) at (0.456\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/7_448.png}};
\node[anchor=south west, inner sep=0] (image7-4) at (0.608\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/7_512.png}};
\node[anchor=south west, inner sep=0] (image7-5) at (0.76\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/7_768.png}};
\node[anchor=south west, inner sep=0] (image7-6) at (0.912\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/7_1024.png}};

% row 8
\node[anchor=south west, inner sep=0] (image8-0) at (0.0\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/8_224.png}};
\node[anchor=south west, inner sep=0] (image8-1) at (0.152\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/8_320.png}};
\node[anchor=south west, inner sep=0] (image8-2) at (0.304\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/8_384.png}};
\node[anchor=south west, inner sep=0] (image8-3) at (0.456\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/8_448.png}};
\node[anchor=south west, inner sep=0] (image8-4) at (0.608\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/8_512.png}};
\node[anchor=south west, inner sep=0] (image8-5) at (0.76\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/8_768.png}};
\node[anchor=south west, inner sep=0] (image8-6) at (0.912\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/8_1024.png}};

% row 9
\node[anchor=south west, inner sep=0] (image9-0) at (0.0\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/9_224.png}};
\node[anchor=south west, inner sep=0] (image9-1) at (0.152\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/9_320.png}};
\node[anchor=south west, inner sep=0] (image9-2) at (0.304\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/9_384.png}};
\node[anchor=south west, inner sep=0] (image9-3) at (0.456\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/9_448.png}};
\node[anchor=south west, inner sep=0] (image9-4) at (0.608\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/9_512.png}};
\node[anchor=south west, inner sep=0] (image9-5) at (0.76\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/9_768.png}};
\node[anchor=south west, inner sep=0] (image9-6) at (0.912\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/9_1024.png}};

% row 10
\node[anchor=south west, inner sep=0] (image10-0) at (0.0\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/10_224.png}};
\node[anchor=south west, inner sep=0] (image10-1) at (0.152\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/10_320.png}};
\node[anchor=south west, inner sep=0] (image10-2) at (0.304\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/10_384.png}};
\node[anchor=south west, inner sep=0] (image10-3) at (0.456\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/10_448.png}};
\node[anchor=south west, inner sep=0] (image10-4) at (0.608\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/10_512.png}};
\node[anchor=south west, inner sep=0] (image10-5) at (0.76\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/10_768.png}};
\node[anchor=south west, inner sep=0] (image10-6) at (0.912\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-ALiBi/10_1024.png}};

\node[above=-0.5mm of image1-0] {224\textsuperscript{2}};
\node[above=-0.5mm of image1-1] {320\textsuperscript{2}};
\node[above=-0.5mm of image1-2] {384\textsuperscript{2}};
\node[above=-0.5mm of image1-3] {448\textsuperscript{2}};
\node[above=-0.5mm of image1-4] {512\textsuperscript{2}};
\node[above=-0.5mm of image1-5] {768\textsuperscript{2}};
\node[above=-0.5mm of image1-6] {1024\textsuperscript{2}};

\end{tikzpicture}
\caption{\textbf{2D-ALiBi} attention maps of ten attention heads across seven resolutions, where the query is in the center. We use the colormap:  \includegraphics[width=2cm]{cmrmap.png}. Averaged over $5$k images.}
\label{fig:space_confuse_2d_alibi}
\end{figure}

\newpage
\usetikzlibrary{positioning}
\begin{figure}
\vspace{-20pt}
\centering
\begin{tikzpicture}
\hspace{-10pt}

\node[anchor=south west, inner sep=0] (image1-0) at (0.0\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/1_224.png}};
\node[anchor=south west, inner sep=0] (image1-1) at (0.152\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/1_320.png}};
\node[anchor=south west, inner sep=0] (image1-2) at (0.304\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/1_384.png}};
\node[anchor=south west, inner sep=0] (image1-3) at (0.456\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/1_448.png}};
\node[anchor=south west, inner sep=0] (image1-4) at (0.608\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/1_512.png}};
\node[anchor=south west, inner sep=0] (image1-5) at (0.76\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/1_768.png}};
\node[anchor=south west, inner sep=0] (image1-6) at (0.912\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/1_1024.png}};

% row 2
\node[anchor=south west, inner sep=0] (image2-0) at (0.0\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/2_224.png}};
\node[anchor=south west, inner sep=0] (image2-1) at (0.152\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/2_320.png}};
\node[anchor=south west, inner sep=0] (image2-2) at (0.304\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/2_384.png}};
\node[anchor=south west, inner sep=0] (image2-3) at (0.456\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/2_448.png}};
\node[anchor=south west, inner sep=0] (image2-4) at (0.608\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/2_512.png}};
\node[anchor=south west, inner sep=0] (image2-5) at (0.76\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/2_768.png}};
\node[anchor=south west, inner sep=0] (image2-6) at (0.912\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/2_1024.png}};

% row 3
\node[anchor=south west, inner sep=0] (image3-0) at (0.0\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/3_224.png}};
\node[anchor=south west, inner sep=0] (image3-1) at (0.152\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/3_320.png}};
\node[anchor=south west, inner sep=0] (image3-2) at (0.304\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/3_384.png}};
\node[anchor=south west, inner sep=0] (image3-3) at (0.456\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/3_448.png}};
\node[anchor=south west, inner sep=0] (image3-4) at (0.608\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/3_512.png}};
\node[anchor=south west, inner sep=0] (image3-5) at (0.76\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/3_768.png}};
\node[anchor=south west, inner sep=0] (image3-6) at (0.912\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/3_1024.png}};

% row 4
\node[anchor=south west, inner sep=0] (image4-0) at (0.0\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/4_224.png}};
\node[anchor=south west, inner sep=0] (image4-1) at (0.152\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/4_320.png}};
\node[anchor=south west, inner sep=0] (image4-2) at (0.304\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/4_384.png}};
\node[anchor=south west, inner sep=0] (image4-3) at (0.456\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/4_448.png}};
\node[anchor=south west, inner sep=0] (image4-4) at (0.608\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/4_512.png}};
\node[anchor=south west, inner sep=0] (image4-5) at (0.76\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/4_768.png}};
\node[anchor=south west, inner sep=0] (image4-6) at (0.912\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/4_1024.png}};

% row 5
\node[anchor=south west, inner sep=0] (image5-0) at (0.0\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/5_224.png}};
\node[anchor=south west, inner sep=0] (image5-1) at (0.152\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/5_320.png}};
\node[anchor=south west, inner sep=0] (image5-2) at (0.304\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/5_384.png}};
\node[anchor=south west, inner sep=0] (image5-3) at (0.456\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/5_448.png}};
\node[anchor=south west, inner sep=0] (image5-4) at (0.608\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/5_512.png}};
\node[anchor=south west, inner sep=0] (image5-5) at (0.76\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/5_768.png}};
\node[anchor=south west, inner sep=0] (image5-6) at (0.912\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/5_1024.png}};

% row 6
\node[anchor=south west, inner sep=0] (image6-0) at (0.0\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/6_224.png}};
\node[anchor=south west, inner sep=0] (image6-1) at (0.152\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/6_320.png}};
\node[anchor=south west, inner sep=0] (image6-2) at (0.304\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/6_384.png}};
\node[anchor=south west, inner sep=0] (image6-3) at (0.456\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/6_448.png}};
\node[anchor=south west, inner sep=0] (image6-4) at (0.608\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/6_512.png}};
\node[anchor=south west, inner sep=0] (image6-5) at (0.76\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/6_768.png}};
\node[anchor=south west, inner sep=0] (image6-6) at (0.912\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/6_1024.png}};

% row 7
\node[anchor=south west, inner sep=0] (image7-0) at (0.0\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/7_224.png}};
\node[anchor=south west, inner sep=0] (image7-1) at (0.152\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/7_320.png}};
\node[anchor=south west, inner sep=0] (image7-2) at (0.304\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/7_384.png}};
\node[anchor=south west, inner sep=0] (image7-3) at (0.456\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/7_448.png}};
\node[anchor=south west, inner sep=0] (image7-4) at (0.608\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/7_512.png}};
\node[anchor=south west, inner sep=0] (image7-5) at (0.76\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/7_768.png}};
\node[anchor=south west, inner sep=0] (image7-6) at (0.912\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/7_1024.png}};

% row 8
\node[anchor=south west, inner sep=0] (image8-0) at (0.0\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/8_224.png}};
\node[anchor=south west, inner sep=0] (image8-1) at (0.152\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/8_320.png}};
\node[anchor=south west, inner sep=0] (image8-2) at (0.304\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/8_384.png}};
\node[anchor=south west, inner sep=0] (image8-3) at (0.456\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/8_448.png}};
\node[anchor=south west, inner sep=0] (image8-4) at (0.608\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/8_512.png}};
\node[anchor=south west, inner sep=0] (image8-5) at (0.76\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/8_768.png}};
\node[anchor=south west, inner sep=0] (image8-6) at (0.912\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/8_1024.png}};

% row 9
\node[anchor=south west, inner sep=0] (image9-0) at (0.0\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/9_224.png}};
\node[anchor=south west, inner sep=0] (image9-1) at (0.152\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/9_320.png}};
\node[anchor=south west, inner sep=0] (image9-2) at (0.304\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/9_384.png}};
\node[anchor=south west, inner sep=0] (image9-3) at (0.456\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/9_448.png}};
\node[anchor=south west, inner sep=0] (image9-4) at (0.608\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/9_512.png}};
\node[anchor=south west, inner sep=0] (image9-5) at (0.76\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/9_768.png}};
\node[anchor=south west, inner sep=0] (image9-6) at (0.912\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/9_1024.png}};

% row 10
\node[anchor=south west, inner sep=0] (image10-0) at (0.0\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/10_224.png}};
\node[anchor=south west, inner sep=0] (image10-1) at (0.152\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/10_320.png}};
\node[anchor=south west, inner sep=0] (image10-2) at (0.304\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/10_384.png}};
\node[anchor=south west, inner sep=0] (image10-3) at (0.456\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/10_448.png}};
\node[anchor=south west, inner sep=0] (image10-4) at (0.608\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/10_512.png}};
\node[anchor=south west, inner sep=0] (image10-5) at (0.76\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/10_768.png}};
\node[anchor=south west, inner sep=0] (image10-6) at (0.912\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/2D-RoPE/10_1024.png}};

\node[above=-0.5mm of image1-0] {224\textsuperscript{2}};
\node[above=-0.5mm of image1-1] {320\textsuperscript{2}};
\node[above=-0.5mm of image1-2] {384\textsuperscript{2}};
\node[above=-0.5mm of image1-3] {448\textsuperscript{2}};
\node[above=-0.5mm of image1-4] {512\textsuperscript{2}};
\node[above=-0.5mm of image1-5] {768\textsuperscript{2}};
\node[above=-0.5mm of image1-6] {1024\textsuperscript{2}};

\end{tikzpicture}
\caption{\textbf{2D-RoPE} attention maps of ten attention heads across seven resolutions, where the query is in the center. We use the colormap:  \includegraphics[width=2cm]{cmrmap.png}. Averaged over $5$k images.}
\label{fig:space_confuse_2d_rope}
\end{figure}

\newpage
\usetikzlibrary{positioning}
\begin{figure}
\vspace{-20pt}
\centering
\begin{tikzpicture}
\hspace{-10pt}

\node[anchor=south west, inner sep=0] (image1-0) at (0.0\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/1_224.png}};
\node[anchor=south west, inner sep=0] (image1-1) at (0.152\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/1_320.png}};
\node[anchor=south west, inner sep=0] (image1-2) at (0.304\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/1_384.png}};
\node[anchor=south west, inner sep=0] (image1-3) at (0.456\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/1_448.png}};
\node[anchor=south west, inner sep=0] (image1-4) at (0.608\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/1_512.png}};
\node[anchor=south west, inner sep=0] (image1-5) at (0.76\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/1_768.png}};
\node[anchor=south west, inner sep=0] (image1-6) at (0.912\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/1_1024.png}};

% row 2
\node[anchor=south west, inner sep=0] (image2-0) at (0.0\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/2_224.png}};
\node[anchor=south west, inner sep=0] (image2-1) at (0.152\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/2_320.png}};
\node[anchor=south west, inner sep=0] (image2-2) at (0.304\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/2_384.png}};
\node[anchor=south west, inner sep=0] (image2-3) at (0.456\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/2_448.png}};
\node[anchor=south west, inner sep=0] (image2-4) at (0.608\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/2_512.png}};
\node[anchor=south west, inner sep=0] (image2-5) at (0.76\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/2_768.png}};
\node[anchor=south west, inner sep=0] (image2-6) at (0.912\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/2_1024.png}};

% row 3
\node[anchor=south west, inner sep=0] (image3-0) at (0.0\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/3_224.png}};
\node[anchor=south west, inner sep=0] (image3-1) at (0.152\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/3_320.png}};
\node[anchor=south west, inner sep=0] (image3-2) at (0.304\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/3_384.png}};
\node[anchor=south west, inner sep=0] (image3-3) at (0.456\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/3_448.png}};
\node[anchor=south west, inner sep=0] (image3-4) at (0.608\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/3_512.png}};
\node[anchor=south west, inner sep=0] (image3-5) at (0.76\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/3_768.png}};
\node[anchor=south west, inner sep=0] (image3-6) at (0.912\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/3_1024.png}};

% row 4
\node[anchor=south west, inner sep=0] (image4-0) at (0.0\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/4_224.png}};
\node[anchor=south west, inner sep=0] (image4-1) at (0.152\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/4_320.png}};
\node[anchor=south west, inner sep=0] (image4-2) at (0.304\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/4_384.png}};
\node[anchor=south west, inner sep=0] (image4-3) at (0.456\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/4_448.png}};
\node[anchor=south west, inner sep=0] (image4-4) at (0.608\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/4_512.png}};
\node[anchor=south west, inner sep=0] (image4-5) at (0.76\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/4_768.png}};
\node[anchor=south west, inner sep=0] (image4-6) at (0.912\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/4_1024.png}};

% row 5
\node[anchor=south west, inner sep=0] (image5-0) at (0.0\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/5_224.png}};
\node[anchor=south west, inner sep=0] (image5-1) at (0.152\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/5_320.png}};
\node[anchor=south west, inner sep=0] (image5-2) at (0.304\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/5_384.png}};
\node[anchor=south west, inner sep=0] (image5-3) at (0.456\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/5_448.png}};
\node[anchor=south west, inner sep=0] (image5-4) at (0.608\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/5_512.png}};
\node[anchor=south west, inner sep=0] (image5-5) at (0.76\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/5_768.png}};
\node[anchor=south west, inner sep=0] (image5-6) at (0.912\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/5_1024.png}};

% row 6
\node[anchor=south west, inner sep=0] (image6-0) at (0.0\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/6_224.png}};
\node[anchor=south west, inner sep=0] (image6-1) at (0.152\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/6_320.png}};
\node[anchor=south west, inner sep=0] (image6-2) at (0.304\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/6_384.png}};
\node[anchor=south west, inner sep=0] (image6-3) at (0.456\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/6_448.png}};
\node[anchor=south west, inner sep=0] (image6-4) at (0.608\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/6_512.png}};
\node[anchor=south west, inner sep=0] (image6-5) at (0.76\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/6_768.png}};
\node[anchor=south west, inner sep=0] (image6-6) at (0.912\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/6_1024.png}};

% row 7
\node[anchor=south west, inner sep=0] (image7-0) at (0.0\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/7_224.png}};
\node[anchor=south west, inner sep=0] (image7-1) at (0.152\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/7_320.png}};
\node[anchor=south west, inner sep=0] (image7-2) at (0.304\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/7_384.png}};
\node[anchor=south west, inner sep=0] (image7-3) at (0.456\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/7_448.png}};
\node[anchor=south west, inner sep=0] (image7-4) at (0.608\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/7_512.png}};
\node[anchor=south west, inner sep=0] (image7-5) at (0.76\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/7_768.png}};
\node[anchor=south west, inner sep=0] (image7-6) at (0.912\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/7_1024.png}};

% row 8
\node[anchor=south west, inner sep=0] (image8-0) at (0.0\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/8_224.png}};
\node[anchor=south west, inner sep=0] (image8-1) at (0.152\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/8_320.png}};
\node[anchor=south west, inner sep=0] (image8-2) at (0.304\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/8_384.png}};
\node[anchor=south west, inner sep=0] (image8-3) at (0.456\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/8_448.png}};
\node[anchor=south west, inner sep=0] (image8-4) at (0.608\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/8_512.png}};
\node[anchor=south west, inner sep=0] (image8-5) at (0.76\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/8_768.png}};
\node[anchor=south west, inner sep=0] (image8-6) at (0.912\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/8_1024.png}};

% row 9
\node[anchor=south west, inner sep=0] (image9-0) at (0.0\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/9_224.png}};
\node[anchor=south west, inner sep=0] (image9-1) at (0.152\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/9_320.png}};
\node[anchor=south west, inner sep=0] (image9-2) at (0.304\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/9_384.png}};
\node[anchor=south west, inner sep=0] (image9-3) at (0.456\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/9_448.png}};
\node[anchor=south west, inner sep=0] (image9-4) at (0.608\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/9_512.png}};
\node[anchor=south west, inner sep=0] (image9-5) at (0.76\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/9_768.png}};
\node[anchor=south west, inner sep=0] (image9-6) at (0.912\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/9_1024.png}};

% row 10
\node[anchor=south west, inner sep=0] (image10-0) at (0.0\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/10_224.png}};
\node[anchor=south west, inner sep=0] (image10-1) at (0.152\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/10_320.png}};
\node[anchor=south west, inner sep=0] (image10-2) at (0.304\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/10_384.png}};
\node[anchor=south west, inner sep=0] (image10-3) at (0.456\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/10_448.png}};
\node[anchor=south west, inner sep=0] (image10-4) at (0.608\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/10_512.png}};
\node[anchor=south west, inner sep=0] (image10-5) at (0.76\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/10_768.png}};
\node[anchor=south west, inner sep=0] (image10-6) at (0.912\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-2/10_1024.png}};

\node[above=-0.5mm of image1-0] {224\textsuperscript{2}};
\node[above=-0.5mm of image1-1] {320\textsuperscript{2}};
\node[above=-0.5mm of image1-2] {384\textsuperscript{2}};
\node[above=-0.5mm of image1-3] {448\textsuperscript{2}};
\node[above=-0.5mm of image1-4] {512\textsuperscript{2}};
\node[above=-0.5mm of image1-5] {768\textsuperscript{2}};
\node[above=-0.5mm of image1-6] {1024\textsuperscript{2}};

\end{tikzpicture}
\caption{\textcolor{LHcolor_dark}{\textbf{LH-}\boldmath{$180$}} attention maps of ten attention heads across seven resolutions, where the query is in the center. We use the colormap:  \includegraphics[width=2cm]{cmrmap.png}. Averaged over $5$k images.}
\label{fig:space_confuse_lh_180}
\end{figure}

\newpage
\usetikzlibrary{positioning}
\begin{figure}
\vspace{-20pt}
\centering
\begin{tikzpicture}
\hspace{-10pt}

\node[anchor=south west, inner sep=0] (image1-0) at (0.0\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/1_224.png}};
\node[anchor=south west, inner sep=0] (image1-1) at (0.152\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/1_320.png}};
\node[anchor=south west, inner sep=0] (image1-2) at (0.304\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/1_384.png}};
\node[anchor=south west, inner sep=0] (image1-3) at (0.456\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/1_448.png}};
\node[anchor=south west, inner sep=0] (image1-4) at (0.608\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/1_512.png}};
\node[anchor=south west, inner sep=0] (image1-5) at (0.76\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/1_768.png}};
\node[anchor=south west, inner sep=0] (image1-6) at (0.912\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/1_1024.png}};

% row 2
\node[anchor=south west, inner sep=0] (image2-0) at (0.0\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/2_224.png}};
\node[anchor=south west, inner sep=0] (image2-1) at (0.152\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/2_320.png}};
\node[anchor=south west, inner sep=0] (image2-2) at (0.304\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/2_384.png}};
\node[anchor=south west, inner sep=0] (image2-3) at (0.456\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/2_448.png}};
\node[anchor=south west, inner sep=0] (image2-4) at (0.608\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/2_512.png}};
\node[anchor=south west, inner sep=0] (image2-5) at (0.76\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/2_768.png}};
\node[anchor=south west, inner sep=0] (image2-6) at (0.912\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/2_1024.png}};

% row 3
\node[anchor=south west, inner sep=0] (image3-0) at (0.0\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/3_224.png}};
\node[anchor=south west, inner sep=0] (image3-1) at (0.152\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/3_320.png}};
\node[anchor=south west, inner sep=0] (image3-2) at (0.304\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/3_384.png}};
\node[anchor=south west, inner sep=0] (image3-3) at (0.456\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/3_448.png}};
\node[anchor=south west, inner sep=0] (image3-4) at (0.608\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/3_512.png}};
\node[anchor=south west, inner sep=0] (image3-5) at (0.76\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/3_768.png}};
\node[anchor=south west, inner sep=0] (image3-6) at (0.912\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/3_1024.png}};

% row 4
\node[anchor=south west, inner sep=0] (image4-0) at (0.0\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/4_224.png}};
\node[anchor=south west, inner sep=0] (image4-1) at (0.152\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/4_320.png}};
\node[anchor=south west, inner sep=0] (image4-2) at (0.304\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/4_384.png}};
\node[anchor=south west, inner sep=0] (image4-3) at (0.456\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/4_448.png}};
\node[anchor=south west, inner sep=0] (image4-4) at (0.608\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/4_512.png}};
\node[anchor=south west, inner sep=0] (image4-5) at (0.76\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/4_768.png}};
\node[anchor=south west, inner sep=0] (image4-6) at (0.912\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/4_1024.png}};

% row 5
\node[anchor=south west, inner sep=0] (image5-0) at (0.0\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/5_224.png}};
\node[anchor=south west, inner sep=0] (image5-1) at (0.152\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/5_320.png}};
\node[anchor=south west, inner sep=0] (image5-2) at (0.304\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/5_384.png}};
\node[anchor=south west, inner sep=0] (image5-3) at (0.456\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/5_448.png}};
\node[anchor=south west, inner sep=0] (image5-4) at (0.608\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/5_512.png}};
\node[anchor=south west, inner sep=0] (image5-5) at (0.76\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/5_768.png}};
\node[anchor=south west, inner sep=0] (image5-6) at (0.912\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/5_1024.png}};

% row 6
\node[anchor=south west, inner sep=0] (image6-0) at (0.0\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/6_224.png}};
\node[anchor=south west, inner sep=0] (image6-1) at (0.152\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/6_320.png}};
\node[anchor=south west, inner sep=0] (image6-2) at (0.304\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/6_384.png}};
\node[anchor=south west, inner sep=0] (image6-3) at (0.456\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/6_448.png}};
\node[anchor=south west, inner sep=0] (image6-4) at (0.608\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/6_512.png}};
\node[anchor=south west, inner sep=0] (image6-5) at (0.76\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/6_768.png}};
\node[anchor=south west, inner sep=0] (image6-6) at (0.912\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/6_1024.png}};

% row 7
\node[anchor=south west, inner sep=0] (image7-0) at (0.0\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/7_224.png}};
\node[anchor=south west, inner sep=0] (image7-1) at (0.152\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/7_320.png}};
\node[anchor=south west, inner sep=0] (image7-2) at (0.304\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/7_384.png}};
\node[anchor=south west, inner sep=0] (image7-3) at (0.456\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/7_448.png}};
\node[anchor=south west, inner sep=0] (image7-4) at (0.608\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/7_512.png}};
\node[anchor=south west, inner sep=0] (image7-5) at (0.76\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/7_768.png}};
\node[anchor=south west, inner sep=0] (image7-6) at (0.912\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/7_1024.png}};

% row 8
\node[anchor=south west, inner sep=0] (image8-0) at (0.0\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/8_224.png}};
\node[anchor=south west, inner sep=0] (image8-1) at (0.152\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/8_320.png}};
\node[anchor=south west, inner sep=0] (image8-2) at (0.304\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/8_384.png}};
\node[anchor=south west, inner sep=0] (image8-3) at (0.456\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/8_448.png}};
\node[anchor=south west, inner sep=0] (image8-4) at (0.608\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/8_512.png}};
\node[anchor=south west, inner sep=0] (image8-5) at (0.76\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/8_768.png}};
\node[anchor=south west, inner sep=0] (image8-6) at (0.912\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/8_1024.png}};

% row 9
\node[anchor=south west, inner sep=0] (image9-0) at (0.0\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/9_224.png}};
\node[anchor=south west, inner sep=0] (image9-1) at (0.152\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/9_320.png}};
\node[anchor=south west, inner sep=0] (image9-2) at (0.304\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/9_384.png}};
\node[anchor=south west, inner sep=0] (image9-3) at (0.456\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/9_448.png}};
\node[anchor=south west, inner sep=0] (image9-4) at (0.608\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/9_512.png}};
\node[anchor=south west, inner sep=0] (image9-5) at (0.76\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/9_768.png}};
\node[anchor=south west, inner sep=0] (image9-6) at (0.912\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/9_1024.png}};

% row 10
\node[anchor=south west, inner sep=0] (image10-0) at (0.0\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/10_224.png}};
\node[anchor=south west, inner sep=0] (image10-1) at (0.152\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/10_320.png}};
\node[anchor=south west, inner sep=0] (image10-2) at (0.304\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/10_384.png}};
\node[anchor=south west, inner sep=0] (image10-3) at (0.456\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/10_448.png}};
\node[anchor=south west, inner sep=0] (image10-4) at (0.608\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/10_512.png}};
\node[anchor=south west, inner sep=0] (image10-5) at (0.76\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/10_768.png}};
\node[anchor=south west, inner sep=0] (image10-6) at (0.912\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-4/10_1024.png}};

\node[above=-0.5mm of image1-0] {224\textsuperscript{2}};
\node[above=-0.5mm of image1-1] {320\textsuperscript{2}};
\node[above=-0.5mm of image1-2] {384\textsuperscript{2}};
\node[above=-0.5mm of image1-3] {448\textsuperscript{2}};
\node[above=-0.5mm of image1-4] {512\textsuperscript{2}};
\node[above=-0.5mm of image1-5] {768\textsuperscript{2}};
\node[above=-0.5mm of image1-6] {1024\textsuperscript{2}};

\end{tikzpicture}
\caption{\textcolor{LHcolor_dark}{\textbf{LH-}\boldmath{$90$}} attention maps of ten attention heads across seven resolutions, where the query is in the center. We use the colormap:  \includegraphics[width=2cm]{cmrmap.png}. Averaged over $5$k images.}
\label{fig:space_confuse_lh_90}
\end{figure}

\newpage
\usetikzlibrary{positioning}
\begin{figure}
\vspace{-20pt}
\centering
\begin{tikzpicture}
\hspace{-10pt}

\node[anchor=south west, inner sep=0] (image1-0) at (0.0\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/1_224.png}};
\node[anchor=south west, inner sep=0] (image1-1) at (0.152\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/1_320.png}};
\node[anchor=south west, inner sep=0] (image1-2) at (0.304\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/1_384.png}};
\node[anchor=south west, inner sep=0] (image1-3) at (0.456\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/1_448.png}};
\node[anchor=south west, inner sep=0] (image1-4) at (0.608\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/1_512.png}};
\node[anchor=south west, inner sep=0] (image1-5) at (0.76\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/1_768.png}};
\node[anchor=south west, inner sep=0] (image1-6) at (0.912\textwidth, -0.152\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/1_1024.png}};

% row 2
\node[anchor=south west, inner sep=0] (image2-0) at (0.0\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/2_224.png}};
\node[anchor=south west, inner sep=0] (image2-1) at (0.152\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/2_320.png}};
\node[anchor=south west, inner sep=0] (image2-2) at (0.304\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/2_384.png}};
\node[anchor=south west, inner sep=0] (image2-3) at (0.456\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/2_448.png}};
\node[anchor=south west, inner sep=0] (image2-4) at (0.608\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/2_512.png}};
\node[anchor=south west, inner sep=0] (image2-5) at (0.76\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/2_768.png}};
\node[anchor=south west, inner sep=0] (image2-6) at (0.912\textwidth, -0.304\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/2_1024.png}};

% row 3
\node[anchor=south west, inner sep=0] (image3-0) at (0.0\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/3_224.png}};
\node[anchor=south west, inner sep=0] (image3-1) at (0.152\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/3_320.png}};
\node[anchor=south west, inner sep=0] (image3-2) at (0.304\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/3_384.png}};
\node[anchor=south west, inner sep=0] (image3-3) at (0.456\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/3_448.png}};
\node[anchor=south west, inner sep=0] (image3-4) at (0.608\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/3_512.png}};
\node[anchor=south west, inner sep=0] (image3-5) at (0.76\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/3_768.png}};
\node[anchor=south west, inner sep=0] (image3-6) at (0.912\textwidth, -0.456\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/3_1024.png}};

% row 4
\node[anchor=south west, inner sep=0] (image4-0) at (0.0\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/4_224.png}};
\node[anchor=south west, inner sep=0] (image4-1) at (0.152\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/4_320.png}};
\node[anchor=south west, inner sep=0] (image4-2) at (0.304\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/4_384.png}};
\node[anchor=south west, inner sep=0] (image4-3) at (0.456\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/4_448.png}};
\node[anchor=south west, inner sep=0] (image4-4) at (0.608\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/4_512.png}};
\node[anchor=south west, inner sep=0] (image4-5) at (0.76\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/4_768.png}};
\node[anchor=south west, inner sep=0] (image4-6) at (0.912\textwidth, -0.608\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/4_1024.png}};

% row 5
\node[anchor=south west, inner sep=0] (image5-0) at (0.0\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/5_224.png}};
\node[anchor=south west, inner sep=0] (image5-1) at (0.152\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/5_320.png}};
\node[anchor=south west, inner sep=0] (image5-2) at (0.304\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/5_384.png}};
\node[anchor=south west, inner sep=0] (image5-3) at (0.456\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/5_448.png}};
\node[anchor=south west, inner sep=0] (image5-4) at (0.608\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/5_512.png}};
\node[anchor=south west, inner sep=0] (image5-5) at (0.76\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/5_768.png}};
\node[anchor=south west, inner sep=0] (image5-6) at (0.912\textwidth, -0.76\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/5_1024.png}};

% row 6
\node[anchor=south west, inner sep=0] (image6-0) at (0.0\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/6_224.png}};
\node[anchor=south west, inner sep=0] (image6-1) at (0.152\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/6_320.png}};
\node[anchor=south west, inner sep=0] (image6-2) at (0.304\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/6_384.png}};
\node[anchor=south west, inner sep=0] (image6-3) at (0.456\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/6_448.png}};
\node[anchor=south west, inner sep=0] (image6-4) at (0.608\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/6_512.png}};
\node[anchor=south west, inner sep=0] (image6-5) at (0.76\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/6_768.png}};
\node[anchor=south west, inner sep=0] (image6-6) at (0.912\textwidth, -0.912\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/6_1024.png}};

% row 7
\node[anchor=south west, inner sep=0] (image7-0) at (0.0\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/7_224.png}};
\node[anchor=south west, inner sep=0] (image7-1) at (0.152\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/7_320.png}};
\node[anchor=south west, inner sep=0] (image7-2) at (0.304\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/7_384.png}};
\node[anchor=south west, inner sep=0] (image7-3) at (0.456\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/7_448.png}};
\node[anchor=south west, inner sep=0] (image7-4) at (0.608\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/7_512.png}};
\node[anchor=south west, inner sep=0] (image7-5) at (0.76\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/7_768.png}};
\node[anchor=south west, inner sep=0] (image7-6) at (0.912\textwidth, -1.064\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/7_1024.png}};

% row 8
\node[anchor=south west, inner sep=0] (image8-0) at (0.0\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/8_224.png}};
\node[anchor=south west, inner sep=0] (image8-1) at (0.152\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/8_320.png}};
\node[anchor=south west, inner sep=0] (image8-2) at (0.304\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/8_384.png}};
\node[anchor=south west, inner sep=0] (image8-3) at (0.456\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/8_448.png}};
\node[anchor=south west, inner sep=0] (image8-4) at (0.608\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/8_512.png}};
\node[anchor=south west, inner sep=0] (image8-5) at (0.76\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/8_768.png}};
\node[anchor=south west, inner sep=0] (image8-6) at (0.912\textwidth, -1.216\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/8_1024.png}};

% row 9
\node[anchor=south west, inner sep=0] (image9-0) at (0.0\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/9_224.png}};
\node[anchor=south west, inner sep=0] (image9-1) at (0.152\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/9_320.png}};
\node[anchor=south west, inner sep=0] (image9-2) at (0.304\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/9_384.png}};
\node[anchor=south west, inner sep=0] (image9-3) at (0.456\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/9_448.png}};
\node[anchor=south west, inner sep=0] (image9-4) at (0.608\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/9_512.png}};
\node[anchor=south west, inner sep=0] (image9-5) at (0.76\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/9_768.png}};
\node[anchor=south west, inner sep=0] (image9-6) at (0.912\textwidth, -1.368\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/9_1024.png}};

% row 10
\node[anchor=south west, inner sep=0] (image10-0) at (0.0\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/10_224.png}};
\node[anchor=south west, inner sep=0] (image10-1) at (0.152\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/10_320.png}};
\node[anchor=south west, inner sep=0] (image10-2) at (0.304\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/10_384.png}};
\node[anchor=south west, inner sep=0] (image10-3) at (0.456\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/10_448.png}};
\node[anchor=south west, inner sep=0] (image10-4) at (0.608\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/10_512.png}};
\node[anchor=south west, inner sep=0] (image10-5) at (0.76\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/10_768.png}};
\node[anchor=south west, inner sep=0] (image10-6) at (0.912\textwidth, -1.52\textwidth) {\includegraphics[width=.15\textwidth]{attn_maps/LH-8/10_1024.png}};

\node[above=-0.5mm of image1-0] {224\textsuperscript{2}};
\node[above=-0.5mm of image1-1] {320\textsuperscript{2}};
\node[above=-0.5mm of image1-2] {384\textsuperscript{2}};
\node[above=-0.5mm of image1-3] {448\textsuperscript{2}};
\node[above=-0.5mm of image1-4] {512\textsuperscript{2}};
\node[above=-0.5mm of image1-5] {768\textsuperscript{2}};
\node[above=-0.5mm of image1-6] {1024\textsuperscript{2}};

\end{tikzpicture}
\caption{\textcolor{LHcolor_dark}{\textbf{LH-}\boldmath{$45$}} attention maps of ten attention heads across seven resolutions, where the query is in the center. We use the colormap:  \includegraphics[width=2cm]{cmrmap.png}. Averaged over $5$k images.}
\label{fig:space_confuse_lh_45}
\end{figure}

\newpage
\clearpage
\subsection{Accuracy Gaps and Class-level Effects}\label{appn:classlevel}
\begin{figure}[ht]
\centering
\input{model_legend}
\begin{tikzpicture}
% Row 1
\node[anchor=south west, inner sep=0] (image1) at (0,0) {\includegraphics[width=.34\textwidth]{yousef_pngs/hist/1D-learn.png}};

\node[anchor=south west, inner sep=0] (image2) at (image1.south east) {\includegraphics[width=.34\textwidth]{yousef_pngs/hist/2D-sincos.png}};
\node[anchor=south west, inner sep=0] (image3) at (image2.south east) {\includegraphics[width=.34\textwidth]{yousef_pngs/hist/Factorized.png}};

% Row 2
\node[anchor=north west, inner sep=0] (image4) at (image1.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/hist/2D-RoPE.png}};

\node[anchor=north west, inner sep=0] (image5) at (image4.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/hist/LH-180.png}};
\node[anchor=north west, inner sep=0] (image6) at (image5.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/hist/LH-90.png}};

% Row 3
\node[anchor=north west, inner sep=0] (image7) at (image4.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/hist/LH-45.png}};

\end{tikzpicture}
\SmallCaption{We calculate the difference in accuracy for the first $5$k ImageNet \cite{imagenet} examples when extrapolating from $224^2$ px for models trained at $224^2$ px}
\end{figure}
\newpage
\begin{figure}[ht]
\input{model_legend}
\begin{tikzpicture}
% Row 1
\node[anchor=south west, inner sep=0] (image1) at (0,0) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_dec/74.png}};
\node[align=center] at ([xshift=-0.5cm]image1.west) {\small{1}};

\node[anchor=south west, inner sep=0] (image2) at (image1.south east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_dec/415.png}};
\node[anchor=south west, inner sep=0] (image3) at (image2.south east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_dec/497.png}};

% Row 2
\node[anchor=north west, inner sep=0] (image4) at (image1.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_dec/638.png}};
\node[align=center] at ([xshift=-0.5cm]image4.west) {\small{2}};

\node[anchor=north west, inner sep=0] (image5) at (image4.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_dec/652.png}};
\node[anchor=north west, inner sep=0] (image6) at (image5.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_dec/664.png}};

% Row 3
\node[anchor=north west, inner sep=0] (image7) at (image4.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_dec/681.png}};
\node[align=center] at ([xshift=-0.5cm]image7.west) {\small{3}};

\node[anchor=north west, inner sep=0] (image8) at (image7.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_dec/754.png}};
\node[anchor=north west, inner sep=0] (image9) at (image8.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_dec/809.png}};

% Row 4
\node[anchor=north west, inner sep=0] (image10) at (image7.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_dec/837.png}};
\node[align=center] at ([xshift=-0.5cm]image10.west) {\small{4}};

\node[anchor=north west, inner sep=0] (image11) at (image10.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_inc/73.png}};
\node[anchor=north west, inner sep=0] (image12) at (image11.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_inc/252.png}};

% Row 5
\node[anchor=north west, inner sep=0] (image13) at (image10.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_inc/335.png}};
\node[align=center] at ([xshift=-0.5cm]image13.west) {\small{5}};

\node[anchor=north west, inner sep=0] (image14) at (image13.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_inc/584.png}};
\node[anchor=north west, inner sep=0] (image15) at (image14.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_inc/660.png}};

% Row 5
\node[anchor=north west, inner sep=0] (image16) at (image13.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_inc/723.png}};
\node[align=center] at ([xshift=-0.5cm]image16.west) {\small{6}};

\node[anchor=north west, inner sep=0] (image17) at (image16.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_inc/817.png}};
\node[anchor=north west, inner sep=0] (image18) at (image17.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_inc/856.png}};

\end{tikzpicture}
\SmallCaption{We calculate the prediction frequency for each class for the first $5$k ImageNet \cite{imagenet}, and plot those frequencies for the classes with the largest decrease [$(1, 1) \to (4, 2)$], increase [$(4, 3) \to (7, 2)]$, and spread [$(7, 3) \to (10, 3)$] at $1024^2$ px.}
\end{figure}
\newpage
\begin{figure}[ht]
\centering
\input{model_legend}
\begin{tikzpicture}
% Row 1
\node[anchor=south west, inner sep=0] (image1) at (0,0) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_inc/902.png}};
\node[align=center] at ([xshift=-0.5cm]image1.west) {\small{7}};

\node[anchor=south west, inner sep=0] (image2) at (image1.south east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_inc/925.png}};
\node[anchor=south west, inner sep=0] (image3) at (image2.south east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_spread/252.png}};

% Row 2
\node[anchor=north west, inner sep=0] (image4) at (image1.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_spread/335.png}};
\node[align=center] at ([xshift=-0.5cm]image4.west) {\small{8}};

\node[anchor=north west, inner sep=0] (image5) at (image4.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_spread/473.png}};
\node[anchor=north west, inner sep=0] (image6) at (image5.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_spread/584.png}};

% Row 3
\node[anchor=north west, inner sep=0] (image7) at (image4.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_spread/611.png}};
\node[align=center] at ([xshift=-0.5cm]image7.west) {\small{9}};

\node[anchor=north west, inner sep=0] (image8) at (image7.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_spread/678.png}};
\node[anchor=north west, inner sep=0] (image9) at (image8.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_spread/335.png}};

% Row 4
\node[anchor=north west, inner sep=0] (image10) at (image7.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_spread/723.png}};
\node[align=center] at ([xshift=-0.5cm]image10.west) {\small{10}};

\node[anchor=north west, inner sep=0] (image11) at (image10.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_spread/836.png}};

\node[anchor=north west, inner sep=0] (image12) at (image11.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/freq_spread/902.png}};

\end{tikzpicture}
\SmallCaption{A continuation of increase, and spread plots.}
\end{figure}
\newpage
\begin{figure}[ht]
\input{model_legend}
\begin{tikzpicture}
% Row 1
\node[anchor=south west, inner sep=0] (image1) at (0,0) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_dec/67.png}};
\node[align=center] at ([xshift=-0.5cm]image1.west) {\small{2}};

\node[anchor=south west, inner sep=0] (image2) at (image1.south east) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_dec/74.png}};
\node[anchor=south west, inner sep=0] (image3) at (image2.south east) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_dec/124.png}};

% Row 2
\node[anchor=north west, inner sep=0] (image4) at (image1.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_dec/197.png}};
\node[align=center] at ([xshift=-0.5cm]image4.west) {\small{2}};

\node[anchor=north west, inner sep=0] (image5) at (image4.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_dec/246.png}};
\node[anchor=north west, inner sep=0] (image6) at (image5.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_dec/avg.png}};

% Row 3
\node[anchor=north west, inner sep=0] (image7) at (image4.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_inc/73.png}};
\node[align=center] at ([xshift=-0.5cm]image7.west) {\small{3}};

\node[anchor=north west, inner sep=0] (image8) at (image7.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_inc/167.png}};
\node[anchor=north west, inner sep=0] (image9) at (image8.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_inc/349.png}};

% Row 4
\node[anchor=north west, inner sep=0] (image10) at (image7.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_inc/413.png}};
\node[align=center] at ([xshift=-0.5cm]image10.west) {\small{4}};

\node[anchor=north west, inner sep=0] (image11) at (image10.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_inc/482.png}};
\node[anchor=north west, inner sep=0] (image12) at (image11.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_inc/avg.png}};

% Row 5
\node[anchor=north west, inner sep=0] (image13) at (image10.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_spread/57.png}};
\node[align=center] at ([xshift=-0.5cm]image13.west) {\small{5}};

\node[anchor=north west, inner sep=0] (image14) at (image13.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_spread/104.png}};
\node[anchor=north west, inner sep=0] (image15) at (image14.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_spread/174.png}};

% Row 5
\node[anchor=north west, inner sep=0] (image16) at (image13.south west) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_spread/254.png}};
\node[align=center] at ([xshift=-0.5cm]image16.west) {\small{6}};

\node[anchor=north west, inner sep=0] (image17) at (image16.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_spread/258.png}};
\node[anchor=north west, inner sep=0] (image18) at (image17.north east) {\includegraphics[width=.34\textwidth]{yousef_pngs/trends_spread/avg.png}};

\end{tikzpicture}