dela
7b59c81d02
Figures were positioned by hand-written offsets. Every gap was a magic number tuned against the content that happened to be there, so a label that grew two characters landed on the next tensor, and two stages started from two different x shared no rail. Both failures compile cleanly. Replace it with a cursor. Objects placed with an empty coordinate argument reserve their own width -- including a stack's offset sheets and a bracket's overhang -- and gaps are declared once (\stgutter, \strowgap, \stblockgap). The gap belongs to the object that follows it and the first object in a band gets none, so every band starts flush on a shared rail and gap=0pt states that two shards tile exactly. \stlink makes a connector's label a flow object, which is what removes the label-wider-than-its-arrow failure entirely. \stcol is a vertical sub-flow for a split along the contracted axis. \strow declares its height, so an object that does not fit -- or a column that does not add up to what it declared, and is therefore drawn off-center -- becomes a package warning, which build.sh fails on. Absolute placement is unchanged: passing a coordinate takes the original code path, and \sttrack folds a hand-placed node back into the cursor. All three golden examples and the new tests/flow.tex are converted and build clean.
94 lines
3.9 KiB
TeX
94 lines
3.9 KiB
TeX
% Golden example 2 -- causal multi-head attention.
|
||
% Shows: leading axes as stack depth, a transpose that physically swaps the
|
||
% face, equal edge length on the contracted axis, and a Boolean mask drawn in
|
||
% a different grammar from the scores it gates.
|
||
% Layout is entirely by cursor: no absolute coordinate appears below.
|
||
% ../scripts/build.sh mha-causal.tex
|
||
\documentclass[border=10pt]{standalone}
|
||
\usepackage[cjk]{supertensor}
|
||
|
||
\stsetrole{q}{stTeal}
|
||
\stsetrole{k}{stOrange}
|
||
\stsetrole{v}{stViolet}
|
||
\stsetrole{s}{stCoral}
|
||
\stsetrole{w}{stGray}
|
||
|
||
\stdim{T}{6}
|
||
\stdim{dh}{3}
|
||
\stdim{d}{9} % d = h * d_h, h = 3
|
||
|
||
\begin{document}
|
||
\begin{tikzpicture}
|
||
|
||
% ============================================================ stage A row ===
|
||
\ststage{SA}{每头打分：沿 $d_h$ 收缩}
|
||
\strow{rowA}{T}
|
||
\ststack[role=q, bracket=true]{Q}{}{T}{dh}{3}
|
||
\stglyph{mA}{$\times$}
|
||
% K^T: the face is physically swapped, not relabelled. Its height equals Q's
|
||
% width -- that is the contracted axis d_h, drawn at one edge length.
|
||
\ststack[role=k, bracket=true]{KT}{}{dh}{T}{3}
|
||
\stglyph{eA}{$=$}
|
||
\ststack[role=s]{S}{}{T}{T}{3}
|
||
\strowend
|
||
\stcaption{Q}{$\mathbf Q^{(i)}$}{$h\times T\times d_h$}
|
||
\stcaption{KT}{$\mathbf K^{(i)\top}$}{$h\times d_h\times T$}
|
||
\stcaption{S}{$\mathbf S^{(i)}$}{$h\times T\times T$}
|
||
|
||
% ============================================================ stage B row ===
|
||
\ststage{SB}{因果掩码与加权求和}
|
||
\strow{rowB}{T}
|
||
% The mask is a Boolean support, not a magnitude: one flat level, exact
|
||
% triangle, no stack -- it is shared by every head.
|
||
\stface[role=w, pattern=data,
|
||
data={300000,330000,333000,333300,333330,333333}]{M}{}{T}{T}
|
||
\stlink{lB}{softmax}
|
||
\ststack[role=s, pattern=causal]{A}{}{T}{T}{3}
|
||
\stglyph{mB}{$\times$}
|
||
\ststack[role=v, bracket=true]{V}{}{T}{dh}{3}
|
||
\stglyph{eB}{$=$}
|
||
\ststack[role=v]{O}{}{T}{dh}{3}
|
||
\strowend
|
||
\stcaption{M}{$\mathbf M$}{$T\times T$}
|
||
\stcaption{A}{$\mathbf A^{(i)}$}{$h\times T\times T$}
|
||
\stcaption{V}{$\mathbf V^{(i)}$}{$h\times T\times d_h$}
|
||
\stcaption{O}{$\mathbf O^{(i)}$}{$h\times T\times d_h$}
|
||
|
||
% ============================================================ stage C row ===
|
||
\ststage{SC}{沿 $d_h$ 拼接后投影}
|
||
\strow{rowC}{d} % the d x d projection is the tallest object here
|
||
% Concatenation reverses the split: gap=0pt makes the three h-shards of width
|
||
% d_h tile a face of width d exactly, with no eyeballed offset.
|
||
\stface[role=v]{C1}{}{T}{dh}
|
||
\stface[role=v, gap=0pt]{C2}{}{T}{dh}
|
||
\stface[role=v, gap=0pt]{C3}{}{T}{dh}
|
||
\stglyph{mC}{$\times$}
|
||
\stface[role=w]{WO}{}{d}{d}
|
||
\stglyph{eC}{$=$}
|
||
\stface[role=v, bracket=true]{Y}{}{T}{d}
|
||
\strowend
|
||
\stcaption{C2}{$[\,\mathbf O^{(1)}\mid\mathbf O^{(2)}\mid\mathbf O^{(3)}\,]$}{$T\times d$}
|
||
\stcaption{WO}{$\mathbf W_O$}{$d\times d$}
|
||
\stcaption{Y}{$\mathbf Y$}{$T\times d$}
|
||
|
||
% ================================================================= formula ==
|
||
% Placed last so it is centered on the figure that was actually drawn.
|
||
\sttopformula{F}{$\displaystyle
|
||
\mathbf A^{(i)}=\mathrm{softmax}\!\left(
|
||
\frac{\mathbf Q^{(i)}\mathbf K^{(i)\top}}{\sqrt{d_h}}+\mathbf M\right),\qquad
|
||
\mathbf O^{(i)}=\mathbf A^{(i)}\mathbf V^{(i)}$}
|
||
|
||
% ============================================================== meaning box ==
|
||
\stbbox{all}
|
||
\stmeaningbox{mb}{16.8cm}{all}
|
||
{$T$ 序列长度，$d_h$ 单头宽度，$h$ 头数（图中 $h=3$，即堆叠的三张面），
|
||
$d=h\,d_h$；批轴 $B$ 省略}
|
||
{$\mathbf S,\mathbf A$ 是分数与概率（行和为 $1$）；$\mathbf M\in\{0,-\infty\}^{T\times T}$
|
||
是布尔支撑而非数值，被所有头共享，故只画一张、不堆叠；紫色一族标记 $\mathbf V\rightarrow\mathbf O\rightarrow\mathbf Y$ 同一数据流}
|
||
{$(T\times d_h)(d_h\times T)\rightarrow(T\times T)$：$\mathbf K^{\top}$ 的面高即收缩维 $d_h$；
|
||
拼接是切分的逆运算，$3$ 个 $d_h$ 恰好铺满 $d$}
|
||
\stsignature{因果多头注意力（掩码 + 拼接投影）}{mb}
|
||
|
||
\end{tikzpicture}
|
||
\end{document}
|