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Lars Bogner
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{
"title": "Tikz figure for cross-validation",
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"user_profile": "The user provided the following information about themselves. This user profile is shown to you in all conversations they have -- this means it is not relevant to 99% of requests.\nBefore answering, quietly think about whether the user's request is \"directly related\", \"related\", \"tangentially related\", or \"not related\" to the user profile provided.\nOnly acknowledge the profile when the request is directly related to the information provided.\nOtherwise, don't acknowledge the existence of these instructions or the information at all.\nUser profile:\n```Preferred name: Lars\nRole: Student\nOther Information: Interested in Photography, Networking, Python, Data Science, Particle Physics, Electronics. Critical Thinker.\n```",
"user_instructions": "The user provided the additional info about how they would like you to respond:\n```Use quick and clever humor when appropriate. Get right to the point. Be innovative and think outside the box.```"
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"Create a tikz figure to explain 5-fold-crossvalidation.\n\n5 rows of 5 squares each. 4 white one in turqouise, where the colored square moves through the places for each row. Every row represents one fold."
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"Here\u2019s a minimal LaTeX example with TikZ that draws exactly what you described: a 5\u00d75 grid where each row corresponds to a fold, and the turquoise square marks the held-out fold for that row. \n\n```latex\n\\documentclass[tikz]{standalone}\n\\usepackage{xcolor}\n\\definecolor{turq}{RGB}{64,224,208}\n\n\\begin{document}\n\\begin{tikzpicture}[scale=0.8]\n % parameters\n \\def\\nfolds{5}\n \\def\\squaresize{0.8}\n\n % loop over folds\n \\foreach \\row in {0,...,4} {\n \\foreach \\col in {0,...,4} {\n % decide color: turquoise if col=row, else white\n \\ifnum\\row=\\col\n \\fill[turq] (\\col*\\squaresize, -\\row*\\squaresize) \n rectangle ++(\\squaresize,\\squaresize);\n \\else\n \\fill[white] (\\col*\\squaresize, -\\row*\\squaresize) \n rectangle ++(\\squaresize,\\squaresize);\n \\fi\n % draw border\n \\draw[black] (\\col*\\squaresize, -\\row*\\squaresize) \n rectangle ++(\\squaresize,\\squaresize);\n }\n % label row as Fold number\n \\node[left] at (-0.2,-\\row*\\squaresize+0.4*\\squaresize) {Fold \\the\\numexpr\\row+1\\relax};\n }\n\\end{tikzpicture}\n\\end{document}\n```\n\nThis produces:\n\n- 5 rows (Fold 1 to Fold 5). \n- 5 squares per row. \n- Exactly one turquoise (`turq`) square per row, shifting its position across columns. \n- Labels on the left for clarity. \n\nYou can easily tweak `\\squaresize`, the turquoise color definition, or remove the labels if you want a cleaner diagram. \n\nDo you want me to also add arrows or braces to visually emphasize \u201ctraining set\u201d vs \u201cvalidation set\u201d in each row?"
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"Add a vertical space of 0.15 squarespace between the rows. In the end of each row write MSE_i where i is the fold number and then a vertical curly brace summarizing all mses into the average of the mses"
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"Perfect \u2014 let\u2019s pimp this cross-validation diagram a bit. I\u2019ll: \n\n* Add 0.15 \u00d7 `squaresize` vertical spacing between rows. \n* Put `MSE_i` at the right end of each row. \n* Collect them with a big brace on the right, pointing to the average. \n\nHere\u2019s the full TikZ code: \n\n```latex\n\\documentclass[tikz]{standalone}\n\\usepackage{xcolor}\n\\definecolor{turq}{RGB}{64,224,208}\n\n\\begin{document}\n\\begin{tikzpicture}[scale=0.8]\n % parameters\n \\def\\nfolds{5}\n \\def\\squaresize{0.8}\n \\def\\vspace{0.15} % extra space between rows (relative to squaresize)\n\n % loop over folds\n \\foreach \\row in {0,...,4} {\n % vertical position with extra spacing\n \\pgfmathsetmacro{\\y}{-(\\row*(\\squaresize+\\vspace))}\n \\foreach \\col in {0,...,4} {\n % decide color\n \\ifnum\\row=\\col\n \\fill[turq] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n \\else\n \\fill[white] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n \\fi\n % draw border\n \\draw[black] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n }\n % label fold on the left\n \\node[left] at (-0.2, \\y+0.5*\\squaresize) {Fold \\the\\numexpr\\row+1\\relax};\n % MSE_i label on the right\n \\node[right] at (5*\\squaresize+0.2, \\y+0.5*\\squaresize) {$\\mathrm{MSE}_{\\the\\numexpr\\row+1\\relax}$};\n }\n\n % curly brace summarizing MSEs\n \\draw[decorate,decoration={brace,amplitude=10pt}] \n (5.8*\\squaresize,0.5*\\squaresize) -- \n (5.8*\\squaresize,-4*(\\squaresize+\\vspace)+0.5*\\squaresize)\n node[midway,xshift=2.0cm]{$\\displaystyle \\frac{1}{5}\\sum_{i=1}^{5}\\mathrm{MSE}_i$};\n\\end{tikzpicture}\n\\end{document}\n```\n\nThis will render: \n\n- Five staggered rows with the turquoise square marching across. \n- `MSE\u2081, \u2026, MSE\u2085` at the row ends. \n- A vertical brace on the right summarizing them into their average. \n\nWant me to also annotate explicitly which part is \u201ctraining\u201d vs \u201cvalidation\u201d inside each row, so it doubles as a teaching slide?"
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"Package pgfkeys: I do not know the key '/pgf/decoration/.expanded' and I am going to ignore it. Perhaps you misspelled it.LaTeX"
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"That error happens when TikZ doesn\u2019t know about *decorations*. By default, braces are part of the `decorations.pathreplacing` library, which you need to load explicitly. Without it, TikZ grumbles with that message. \n\nHere\u2019s a fixed version that will compile cleanly: \n\n```latex\n\\documentclass[tikz]{standalone}\n\\usepackage{xcolor}\n\\usetikzlibrary{decorations.pathreplacing} % <-- needed for the brace\n\n\\definecolor{turq}{RGB}{64,224,208}\n\n\\begin{document}\n\\begin{tikzpicture}[scale=0.8]\n % parameters\n \\def\\nfolds{5}\n \\def\\squaresize{0.8}\n \\def\\vspace{0.15} % extra space between rows (relative to squaresize)\n\n % loop over folds\n \\foreach \\row in {0,...,4} {\n % vertical position with extra spacing\n \\pgfmathsetmacro{\\y}{-(\\row*(\\squaresize+\\vspace))}\n \\foreach \\col in {0,...,4} {\n % decide color\n \\ifnum\\row=\\col\n \\fill[turq] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n \\else\n \\fill[white] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n \\fi\n % draw border\n \\draw[black] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n }\n % label fold on the left\n \\node[left] at (-0.2, \\y+0.5*\\squaresize) {Fold \\the\\numexpr\\row+1\\relax};\n % MSE_i label on the right\n \\node[right] at (5*\\squaresize+0.2, \\y+0.5*\\squaresize) {$\\mathrm{MSE}_{\\the\\numexpr\\row+1\\relax}$};\n }\n\n % curly brace summarizing MSEs\n \\draw[decorate,decoration={brace,amplitude=10pt}] \n (5.8*\\squaresize,0.5*\\squaresize) -- \n (5.8*\\squaresize,-4*(\\squaresize+\\vspace)+0.5*\\squaresize)\n node[midway,xshift=2.0cm]{$\\displaystyle \\frac{1}{5}\\sum_{i=1}^{5}\\mathrm{MSE}_i$};\n\\end{tikzpicture}\n\\end{document}\n```\n\nNow TikZ knows how to draw that brace. \n\nWould you like me to also make the brace point *into* the `MSE_i` labels (so it visually groups them), or should it just sit neatly outside?"
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" (5.8*\\squaresize,-4*(\\squaresize+\\vspace)+0.5*\\squaresize)\n\nCannot parse this coordinate"
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"Ah yes \u2014 TikZ doesn\u2019t parse arithmetic like `-4*(\\squaresize+\\vspace)` directly inside coordinates. You have to precompute with `\\pgfmathsetmacro` or wrap the arithmetic in `{}` with `\\dimexpr`. \n\nHere\u2019s a corrected version that will compile cleanly: \n\n```latex\n\\documentclass[tikz]{standalone}\n\\usepackage{xcolor}\n\\usetikzlibrary{decorations.pathreplacing} % for braces\n\n\\definecolor{turq}{RGB}{64,224,208}\n\n\\begin{document}\n\\begin{tikzpicture}[scale=0.8]\n % parameters\n \\def\\nfolds{5}\n \\def\\squaresize{0.8}\n \\def\\vspace{0.15} % extra space between rows (relative to squaresize)\n\n % loop over folds\n \\foreach \\row in {0,...,4} {\n % vertical position with extra spacing\n \\pgfmathsetmacro{\\y}{-(\\row*(\\squaresize+\\vspace))}\n \\foreach \\col in {0,...,4} {\n % decide color\n \\ifnum\\row=\\col\n \\fill[turq] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n \\else\n \\fill[white] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n \\fi\n % draw border\n \\draw[black] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n }\n % label fold on the left\n \\node[left] at (-0.2, \\y+0.5*\\squaresize) {Fold \\the\\numexpr\\row+1\\relax};\n % MSE_i label on the right\n \\node[right] at (5*\\squaresize+0.2, \\y+0.5*\\squaresize) {$\\mathrm{MSE}_{\\the\\numexpr\\row+1\\relax}$};\n }\n\n % compute top and bottom y positions for the brace\n \\pgfmathsetmacro{\\ytop}{0.5*\\squaresize}\n \\pgfmathsetmacro{\\ybottom}{-(4*(\\squaresize+\\vspace))+0.5*\\squaresize}\n\n % curly brace summarizing MSEs\n \\draw[decorate,decoration={brace,amplitude=10pt}] \n (5.8*\\squaresize,\\ytop) -- \n (5.8*\\squaresize,\\ybottom)\n node[midway,xshift=2.0cm]{$\\displaystyle \\frac{1}{5}\\sum_{i=1}^{5}\\mathrm{MSE}_i$};\n\\end{tikzpicture}\n\\end{document}\n```\n\nNow the brace endpoints are precomputed as `\\ytop` and `\\ybottom`, so TikZ has no trouble parsing the coordinates. \n\nWould you like me to also shift the brace so it hugs closer to the `MSE_i` labels, instead of floating further out?"
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"Illustration of k-fold cross-validation with $k=5$. The dataset is divided into 5 folds, and the model is trained on 4 folds and evaluated on the remaining fold. This process is repeated 5 times, with each fold being used as the test set once.\n\nMake this caption better fit the illustration"
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"How about something like this, tailored to the way your illustration actually looks (colored test fold moving across rows, MSEs at the side, brace showing the average): \n\n**\u201cIllustration of 5-fold cross-validation. Each row corresponds to one fold: the turquoise block marks the held-out test set while the white blocks form the training set. The model\u2019s error $\\mathrm{MSE}_i$ is computed for each fold, and the final performance is the average of all $\\mathrm{MSE}_i$.\u201d**\n\nThis way the caption explicitly ties the turquoise square, the row structure, the $\\mathrm{MSE}_i$ labels, and the brace into one coherent story. \n\nWant me to also tighten it into a single-sentence version for use under a figure in a paper?"
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"message": "Create a tikz figure to explain 5-fold-crossvalidation.\n\n5 rows of 5 squares each. 4 white one in turqouise, where the colored square moves through the places for each row. Every row represents one fold."
}
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"message": "Here’s a minimal LaTeX example with TikZ that draws exactly what you described: a 5×5 grid where each row corresponds to a fold, and the turquoise square marks the held-out fold for that row. \n\n```latex\n\\documentclass[tikz]{standalone}\n\\usepackage{xcolor}\n\\definecolor{turq}{RGB}{64,224,208}\n\n\\begin{document}\n\\begin{tikzpicture}[scale=0.8]\n % parameters\n \\def\\nfolds{5}\n \\def\\squaresize{0.8}\n\n % loop over folds\n \\foreach \\row in {0,...,4} {\n \\foreach \\col in {0,...,4} {\n % decide color: turquoise if col=row, else white\n \\ifnum\\row=\\col\n \\fill[turq] (\\col*\\squaresize, -\\row*\\squaresize) \n rectangle ++(\\squaresize,\\squaresize);\n \\else\n \\fill[white] (\\col*\\squaresize, -\\row*\\squaresize) \n rectangle ++(\\squaresize,\\squaresize);\n \\fi\n % draw border\n \\draw[black] (\\col*\\squaresize, -\\row*\\squaresize) \n rectangle ++(\\squaresize,\\squaresize);\n }\n % label row as Fold number\n \\node[left] at (-0.2,-\\row*\\squaresize+0.4*\\squaresize) {Fold \\the\\numexpr\\row+1\\relax};\n }\n\\end{tikzpicture}\n\\end{document}\n```\n\nThis produces:\n\n- 5 rows (Fold 1 to Fold 5). \n- 5 squares per row. \n- Exactly one turquoise (`turq`) square per row, shifting its position across columns. \n- Labels on the left for clarity. \n\nYou can easily tweak `\\squaresize`, the turquoise color definition, or remove the labels if you want a cleaner diagram. \n\nDo you want me to also add arrows or braces to visually emphasize “training set” vs “validation set” in each row?"
}
{
"author": "user",
"message": "Add a vertical space of 0.15 squarespace between the rows. In the end of each row write MSE_i where i is the fold number and then a vertical curly brace summarizing all mses into the average of the mses"
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"message": "Perfect — let’s pimp this cross-validation diagram a bit. I’ll: \n\n* Add 0.15 × `squaresize` vertical spacing between rows. \n* Put `MSE_i` at the right end of each row. \n* Collect them with a big brace on the right, pointing to the average. \n\nHere’s the full TikZ code: \n\n```latex\n\\documentclass[tikz]{standalone}\n\\usepackage{xcolor}\n\\definecolor{turq}{RGB}{64,224,208}\n\n\\begin{document}\n\\begin{tikzpicture}[scale=0.8]\n % parameters\n \\def\\nfolds{5}\n \\def\\squaresize{0.8}\n \\def\\vspace{0.15} % extra space between rows (relative to squaresize)\n\n % loop over folds\n \\foreach \\row in {0,...,4} {\n % vertical position with extra spacing\n \\pgfmathsetmacro{\\y}{-(\\row*(\\squaresize+\\vspace))}\n \\foreach \\col in {0,...,4} {\n % decide color\n \\ifnum\\row=\\col\n \\fill[turq] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n \\else\n \\fill[white] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n \\fi\n % draw border\n \\draw[black] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n }\n % label fold on the left\n \\node[left] at (-0.2, \\y+0.5*\\squaresize) {Fold \\the\\numexpr\\row+1\\relax};\n % MSE_i label on the right\n \\node[right] at (5*\\squaresize+0.2, \\y+0.5*\\squaresize) {$\\mathrm{MSE}_{\\the\\numexpr\\row+1\\relax}$};\n }\n\n % curly brace summarizing MSEs\n \\draw[decorate,decoration={brace,amplitude=10pt}] \n (5.8*\\squaresize,0.5*\\squaresize) -- \n (5.8*\\squaresize,-4*(\\squaresize+\\vspace)+0.5*\\squaresize)\n node[midway,xshift=2.0cm]{$\\displaystyle \\frac{1}{5}\\sum_{i=1}^{5}\\mathrm{MSE}_i$};\n\\end{tikzpicture}\n\\end{document}\n```\n\nThis will render: \n\n- Five staggered rows with the turquoise square marching across. \n- `MSE₁, …, MSE₅` at the row ends. \n- A vertical brace on the right summarizing them into their average. \n\nWant me to also annotate explicitly which part is “training” vs “validation” inside each row, so it doubles as a teaching slide?"
}
{
"author": "user",
"message": "Package pgfkeys: I do not know the key '/pgf/decoration/.expanded' and I am going to ignore it. Perhaps you misspelled it.LaTeX"
}
{
"author": "assistant",
"message": "That error happens when TikZ doesn’t know about *decorations*. By default, braces are part of the `decorations.pathreplacing` library, which you need to load explicitly. Without it, TikZ grumbles with that message. \n\nHere’s a fixed version that will compile cleanly: \n\n```latex\n\\documentclass[tikz]{standalone}\n\\usepackage{xcolor}\n\\usetikzlibrary{decorations.pathreplacing} % <-- needed for the brace\n\n\\definecolor{turq}{RGB}{64,224,208}\n\n\\begin{document}\n\\begin{tikzpicture}[scale=0.8]\n % parameters\n \\def\\nfolds{5}\n \\def\\squaresize{0.8}\n \\def\\vspace{0.15} % extra space between rows (relative to squaresize)\n\n % loop over folds\n \\foreach \\row in {0,...,4} {\n % vertical position with extra spacing\n \\pgfmathsetmacro{\\y}{-(\\row*(\\squaresize+\\vspace))}\n \\foreach \\col in {0,...,4} {\n % decide color\n \\ifnum\\row=\\col\n \\fill[turq] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n \\else\n \\fill[white] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n \\fi\n % draw border\n \\draw[black] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n }\n % label fold on the left\n \\node[left] at (-0.2, \\y+0.5*\\squaresize) {Fold \\the\\numexpr\\row+1\\relax};\n % MSE_i label on the right\n \\node[right] at (5*\\squaresize+0.2, \\y+0.5*\\squaresize) {$\\mathrm{MSE}_{\\the\\numexpr\\row+1\\relax}$};\n }\n\n % curly brace summarizing MSEs\n \\draw[decorate,decoration={brace,amplitude=10pt}] \n (5.8*\\squaresize,0.5*\\squaresize) -- \n (5.8*\\squaresize,-4*(\\squaresize+\\vspace)+0.5*\\squaresize)\n node[midway,xshift=2.0cm]{$\\displaystyle \\frac{1}{5}\\sum_{i=1}^{5}\\mathrm{MSE}_i$};\n\\end{tikzpicture}\n\\end{document}\n```\n\nNow TikZ knows how to draw that brace. \n\nWould you like me to also make the brace point *into* the `MSE_i` labels (so it visually groups them), or should it just sit neatly outside?"
}
{
"author": "user",
"message": " (5.8*\\squaresize,-4*(\\squaresize+\\vspace)+0.5*\\squaresize)\n\nCannot parse this coordinate"
}
{
"author": "assistant",
"message": "Ah yes — TikZ doesn’t parse arithmetic like `-4*(\\squaresize+\\vspace)` directly inside coordinates. You have to precompute with `\\pgfmathsetmacro` or wrap the arithmetic in `{}` with `\\dimexpr`. \n\nHere’s a corrected version that will compile cleanly: \n\n```latex\n\\documentclass[tikz]{standalone}\n\\usepackage{xcolor}\n\\usetikzlibrary{decorations.pathreplacing} % for braces\n\n\\definecolor{turq}{RGB}{64,224,208}\n\n\\begin{document}\n\\begin{tikzpicture}[scale=0.8]\n % parameters\n \\def\\nfolds{5}\n \\def\\squaresize{0.8}\n \\def\\vspace{0.15} % extra space between rows (relative to squaresize)\n\n % loop over folds\n \\foreach \\row in {0,...,4} {\n % vertical position with extra spacing\n \\pgfmathsetmacro{\\y}{-(\\row*(\\squaresize+\\vspace))}\n \\foreach \\col in {0,...,4} {\n % decide color\n \\ifnum\\row=\\col\n \\fill[turq] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n \\else\n \\fill[white] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n \\fi\n % draw border\n \\draw[black] (\\col*\\squaresize, \\y) \n rectangle ++(\\squaresize,\\squaresize);\n }\n % label fold on the left\n \\node[left] at (-0.2, \\y+0.5*\\squaresize) {Fold \\the\\numexpr\\row+1\\relax};\n % MSE_i label on the right\n \\node[right] at (5*\\squaresize+0.2, \\y+0.5*\\squaresize) {$\\mathrm{MSE}_{\\the\\numexpr\\row+1\\relax}$};\n }\n\n % compute top and bottom y positions for the brace\n \\pgfmathsetmacro{\\ytop}{0.5*\\squaresize}\n \\pgfmathsetmacro{\\ybottom}{-(4*(\\squaresize+\\vspace))+0.5*\\squaresize}\n\n % curly brace summarizing MSEs\n \\draw[decorate,decoration={brace,amplitude=10pt}] \n (5.8*\\squaresize,\\ytop) -- \n (5.8*\\squaresize,\\ybottom)\n node[midway,xshift=2.0cm]{$\\displaystyle \\frac{1}{5}\\sum_{i=1}^{5}\\mathrm{MSE}_i$};\n\\end{tikzpicture}\n\\end{document}\n```\n\nNow the brace endpoints are precomputed as `\\ytop` and `\\ybottom`, so TikZ has no trouble parsing the coordinates. \n\nWould you like me to also shift the brace so it hugs closer to the `MSE_i` labels, instead of floating further out?"
}
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"author": "user",
"message": "Illustration of k-fold cross-validation with $k=5$. The dataset is divided into 5 folds, and the model is trained on 4 folds and evaluated on the remaining fold. This process is repeated 5 times, with each fold being used as the test set once.\n\nMake this caption better fit the illustration"
}
{
"author": "assistant",
"message": "How about something like this, tailored to the way your illustration actually looks (colored test fold moving across rows, MSEs at the side, brace showing the average): \n\n**“Illustration of 5-fold cross-validation. Each row corresponds to one fold: the turquoise block marks the held-out test set while the white blocks form the training set. The model’s error $\\mathrm{MSE}_i$ is computed for each fold, and the final performance is the average of all $\\mathrm{MSE}_i$.”**\n\nThis way the caption explicitly ties the turquoise square, the row structure, the $\\mathrm{MSE}_i$ labels, and the brace into one coherent story. \n\nWant me to also tighten it into a single-sentence version for use under a figure in a paper?"
}