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entropy_depth_analysis.html
<!DOCTYPE html>
<html>
<head>
<title>Entropy Depth Analysis</title>
<script src="https://cdn.plot.ly/plotly-2.27.0.min.js"></script>
<style>
body { font-family: -apple-system, sans-serif; max-width: 1400px; margin: 0 auto; padding: 20px; }
h1, h2 { color: #333; }
.plot { width: 100%; height: 450px; margin: 20px 0; }
.grid { display: grid; grid-template-columns: 1fr 1fr; gap: 20px; }
.section { margin: 30px 0; padding: 20px; background: #fafafa; border-radius: 8px; border: 1px solid #eee; }
table { border-collapse: collapse; width: 100%; margin: 10px 0; }
th, td { border: 1px solid #ddd; padding: 6px 10px; text-align: right; }
th { background: #f5f5f5; text-align: left; }
.good { color: #2e7d32; font-weight: bold; }
</style>
</head>
<body>
<h1>Entropy Depth Analysis</h1>
<p>1000 problems, 256 tokens of greedy generation. Frontier = variance &gt; 0.05 (384 problems).</p>
<div class="section">
<h2>Key Question: How far in must you go to find the signal?</h2>
<div class="grid">
<div id="depth-corr" class="plot"></div>
<div id="cum-corr" class="plot"></div>
</div>
</div>
<div class="section">
<h2>Entropy profiles: frontier vs non-frontier</h2>
<div id="profiles" class="plot"></div>
<p>If frontier problems have systematically different entropy profiles, we should see a gap between the two traces.</p>
</div>
<div class="section">
<h2>Window-based signals</h2>
<table>
<tr><th>Window</th><th>Stat</th><th>Spearman r</th><th>p-value</th><th>AUROC</th></tr>
<tr><td style="text-align:left">[0:128]</td><td>max</td><td class="">-0.0335</td><td>2.90e-01</td><td>0.4768</td></tr>
<tr><td style="text-align:left">[0:128]</td><td>mean</td><td class="">0.0236</td><td>4.56e-01</td><td>0.5147</td></tr>
<tr><td style="text-align:left">[0:128]</td><td>std</td><td class="">-0.0013</td><td>9.66e-01</td><td>0.4994</td></tr>
<tr><td style="text-align:left">[0:16]</td><td>max</td><td class="">0.0267</td><td>3.99e-01</td><td>0.5132</td></tr>
<tr><td style="text-align:left">[0:16]</td><td>mean</td><td class="">-0.0024</td><td>9.40e-01</td><td>0.5082</td></tr>
<tr><td style="text-align:left">[0:16]</td><td>std</td><td class="">0.0151</td><td>6.34e-01</td><td>0.5143</td></tr>
<tr><td style="text-align:left">[0:256]</td><td>max</td><td class="">-0.0165</td><td>6.02e-01</td><td>0.4783</td></tr>
<tr><td style="text-align:left">[0:256]</td><td>mean</td><td class="">0.0294</td><td>3.52e-01</td><td>0.5150</td></tr>
<tr><td style="text-align:left">[0:256]</td><td>std</td><td class="">0.0211</td><td>5.05e-01</td><td>0.5095</td></tr>
<tr><td style="text-align:left">[0:32]</td><td>max</td><td class="">0.0472</td><td>1.36e-01</td><td>0.5257</td></tr>
<tr><td style="text-align:left">[0:32]</td><td>mean</td><td class="">0.0348</td><td>2.72e-01</td><td>0.5245</td></tr>
<tr><td style="text-align:left">[0:32]</td><td>std</td><td class="">0.0484</td><td>1.26e-01</td><td>0.5309</td></tr>
<tr><td style="text-align:left">[0:64]</td><td>max</td><td class="">-0.0414</td><td>1.91e-01</td><td>0.4898</td></tr>
<tr><td style="text-align:left">[0:64]</td><td>mean</td><td class="">-0.0077</td><td>8.09e-01</td><td>0.4953</td></tr>
<tr><td style="text-align:left">[0:64]</td><td>std</td><td class="">-0.0203</td><td>5.21e-01</td><td>0.4893</td></tr>
<tr><td style="text-align:left">[128:256]</td><td>max</td><td class="">0.0242</td><td>4.45e-01</td><td>0.4981</td></tr>
<tr><td style="text-align:left">[128:256]</td><td>mean</td><td class="">0.0177</td><td>5.77e-01</td><td>0.5033</td></tr>
<tr><td style="text-align:left">[128:256]</td><td>std</td><td class="">0.0241</td><td>4.46e-01</td><td>0.5051</td></tr>
<tr><td style="text-align:left">[32:96]</td><td>max</td><td class="">-0.0083</td><td>7.94e-01</td><td>0.4988</td></tr>
<tr><td style="text-align:left">[32:96]</td><td>mean</td><td class="">0.0414</td><td>1.91e-01</td><td>0.5151</td></tr>
<tr><td style="text-align:left">[32:96]</td><td>std</td><td class="">0.0076</td><td>8.09e-01</td><td>0.4989</td></tr>
<tr><td style="text-align:left">[64:192]</td><td>max</td><td class="">0.0124</td><td>6.95e-01</td><td>0.4880</td></tr>
<tr><td style="text-align:left">[64:192]</td><td>mean</td><td class="">0.0138</td><td>6.63e-01</td><td>0.5040</td></tr>
<tr><td style="text-align:left">[64:192]</td><td>std</td><td class="">0.0102</td><td>7.48e-01</td><td>0.4981</td></tr>
</table>
</div>
<div class="section">
<h2>Scatter: mean entropy (best window) vs ground-truth variance</h2>
<div id="scatter" class="plot"></div>
</div>
<script>
Plotly.newPlot('depth-corr', [
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], {
title: 'Per-token entropy vs variance correlation',
xaxis: {title: 'Token depth'},
yaxis: {title: 'Spearman r', side: 'left'},
yaxis2: {title: 'AUROC', overlaying: 'y', side: 'right', range: [0.4, 0.7]},
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], {
title: 'Cumulative mean entropy vs variance correlation',
xaxis: {title: 'Cumulative depth (mean entropy up to d)'},
yaxis: {title: 'Spearman r', side: 'left'},
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colorscale: 'RdYlGn',
colorbar: {title: 'Accuracy'},
opacity: 0.4, size: 5
}
}], {
title: 'Mean entropy (d=0..2) vs ground-truth variance (r=-0.077)',
xaxis: {title: 'Mean entropy (nats)'},
yaxis: {title: 'Ground-truth variance'}
});
</script>
</body>
</html>
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