% Golden example 1 -- tensor parallel FFN, column-then-row sharding + AllReduce.
% Shows: partition geometry (shards tile the parent exactly), one hue per TP
% rank held across every stage, a collective node as a real operation, and a
% split along the contracted axis drawn as a column sub-flow.
% Layout is entirely by cursor: no absolute coordinate appears below.
%   ../scripts/build.sh tp-ffn-allreduce.tex
\documentclass[border=10pt]{standalone}
\usepackage[cjk]{supertensor}

% --- role ledger: one hue per TP rank, held from W through H to P ----------
\stsetrole{act}{stViolet}   % activations that every rank sees
\stsetrole{r1}{stTeal}      % rank 1
\stsetrole{r2}{stOrange}    % rank 2

% --- geometry ledger: one physical edge per symbolic axis ------------------
\stdim{bt}{6}      % B*T rows
\stdim{d}{4}       % model width
\stdim{dffl}{4}    % d_ff / p  (per-rank hidden width)
\stdim{dff}{8}     % d_ff = p * (d_ff/p); the height of the stacked W_2 column

\begin{document}
\begin{tikzpicture}

% ============================================================ stage A row ===
\ststage{SA}{列切 $\mathbf W_1$：无通信}
\strow{rowA}{bt}
  \stface[role=act, bracket=true]{X}{}{bt}{d}
  \stglyph{mA}{$\times$}
  % Two shards, tiled exactly: gap=0pt makes them adjacent by construction,
  % so neither stretching nor an eyeballed offset can creep in.
  \stface[role=r1]{W1a}{}{d}{dffl}
  \stface[role=r2, gap=0pt]{W1b}{}{d}{dffl}
  \stglyph{eA}{$=$}
  \stface[role=r1]{Ha}{}{bt}{dffl}
  \stface[role=r2, gap=0pt]{Hb}{}{bt}{dffl}
\strowend
\stcaption{X}{$\mathbf X$}{$BT\times d$}
\stcaption{W1a}{$\mathbf W_1^{(1)}$}{$d\times d_{\mathrm{ff}}/p$}
\stcaption{W1b}{$\mathbf W_1^{(2)}$}{$d\times d_{\mathrm{ff}}/p$}
\stcaption{Ha}{$\mathbf H^{(1)}$}{$BT\times d_{\mathrm{ff}}/p$}
\stcaption{Hb}{$\mathbf H^{(2)}$}{$BT\times d_{\mathrm{ff}}/p$}

% ============================================================ stage B row ===
\ststage{SB}{行切 $\mathbf W_2$：一次 All-Reduce}
\strow{rowB}{dff}   % the stacked W_2 column is the tallest object here
  \stface[role=r1]{Ga}{}{bt}{dffl}
  \stface[role=r2, gap=0pt]{Gb}{}{bt}{dffl}
  \stglyph{mB}{$\times$}
  % W_2 is split along the CONTRACTED axis: the shards stack vertically and
  % together have exactly the height of H's width. Splitting reverses concat,
  % which is what gap=0pt inside the column states.
  \stcol{W2}{dff}
    \stface[role=r1]{W2a}{}{dffl}{d}
    \stface[role=r2, gap=0pt]{W2b}{}{dffl}{d}
  \stcolend
  \stglyph{eB}{$=$}
  \stface[role=r1]{Pa}{}{bt}{d}
  \stglyph{plus}{$+$}
  \stface[role=r2]{Pb}{}{bt}{d}
  \stlink{lc}{}
  \stcomm{ar}{All-Reduce}
  \stlink{ly}{}
  \stface[role=act, bracket=true]{Y}{}{bt}{d}
\strowend
\stcaption{Ga}{$\mathbf G^{(1)}$}{$BT\times d_{\mathrm{ff}}/p$}
\stcaption{Gb}{$\mathbf G^{(2)}$}{$BT\times d_{\mathrm{ff}}/p$}
\stcaption{W2}{$\mathbf W_2^{(r)}$}{$d_{\mathrm{ff}}/p\times d$}
\stcaption{Pa}{$\mathbf P^{(1)}$}{$BT\times d$}
\stcaption{Pb}{$\mathbf P^{(2)}$}{$BT\times d$}
\stcaption{Y}{$\mathbf Y$}{$BT\times d$}

% ================================================================= formula ==
% Placed last so it is centered on the figure that was actually drawn.
\sttopformula{F}{$\begin{gathered}
  \mathbf{XW}_1=[\,\mathbf{XW}_1^{(1)}\mid
    \mathbf{XW}_1^{(2)}\,]=[\,\mathbf H^{(1)}\mid\mathbf H^{(2)}\,]\\[1.2mm]
  [\,\mathbf H^{(1)}\mid\mathbf H^{(2)}\,]
  \begin{bmatrix}\mathbf W_2^{(1)}\\[-1pt]\mathbf W_2^{(2)}\end{bmatrix}
  =\sum_{r}\mathbf H^{(r)}\mathbf W_2^{(r)}=\sum_r\mathbf P^{(r)}
\end{gathered}$}

% ============================================================== meaning box ==
\stbbox{all}
\stmeaningbox{mb}{16.4cm}{all}
  {$BT$ 展平后的 token 数，$d$ 模型宽度，$d_{\mathrm{ff}}$ 前馈中间宽度，
   $p$ TP 并行度（图中 $p=2$）}
  {$\mathbf X,\mathbf Y$ 每个 rank 完整持有；$\mathbf W_1^{(r)},\mathbf W_2^{(r)},
   \mathbf H^{(r)},\mathbf P^{(r)}$ 仅本 rank 持有，$\mathbf P^{(r)}$ 是部分和而非最终输出}
  {$\mathbf G^{(r)}=\mathrm{GeLU}(\mathbf H^{(r)})$ 逐元素、无跨 rank 依赖；列切 $\mathbf W_1$ 使 $\mathbf H$ 沿 $d_{\mathrm{ff}}$ 切分；行切 $\mathbf W_2$ 沿收缩维切分，
   故 $\mathbf Y=\sum_r\mathbf P^{(r)}$ 需一次 All-Reduce，前向每层仅此一次通信}
\stsignature{TP-FFN（GeLU + All-Reduce）}{mb}

\end{tikzpicture}
\end{document}