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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>SCOPE — Selective Context Preference Optimization</title>
<meta name="description" content="SCOPE: Learning When to Trust via Selective Context Preference Optimization. We introduce MIST, a matched-condition benchmark for selective trust, and the SC2W metric; show universal susceptibility to misleading signals; and propose SCOPE, which roughly halves SC2W without hurting clean, correct-context, or irrelevant-context accuracy.">
<link rel="icon" href="assets_common/icons/worldbench-circle.png" type="image/png">
<link rel="preconnect" href="https://fonts.googleapis.com">
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
<link href="https://fonts.googleapis.com/css2?family=Newsreader:ital,opsz@0,6..72;1,6..72&display=swap" rel="stylesheet">
<link rel="stylesheet" href="https://cdn.jsdelivr.net/gh/jpswalsh/academicons@1/css/academicons.min.css">
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/@fortawesome/fontawesome-free@6.5.2/css/all.min.css">
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.9/dist/katex.min.css">
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.9/dist/katex.min.js"></script>
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.9/dist/contrib/auto-render.min.js"
onload="renderMathInElement(document.body,{delimiters:[{left:'$$',right:'$$',display:true},{left:'$',right:'$',display:false}]});"></script>
<style>
:root{
--accent:#FF2E63; --accent2:#08D9D6; --link:#d81e57;
--c-clean:#252A34; --c-mis:#FF2E63; --c-cor:#0a9a97; --c-irr:#9C9C9C;
--bg:#fdfbf2; --panel:#f7f1e0; --panel2:#f2ecd8; --card:#fefcf5;
--text:#2b2f38; --muted:#7c7360; --border:#ebe2cd; --hair:#f2ecda;
--shadow:0 1px 2px rgba(16,24,40,.04),0 8px 24px rgba(16,24,40,.06);
--measure:760px; --radius:16px;
--grain:url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' width='140' height='140'%3E%3Cfilter id='n'%3E%3CfeTurbulence type='fractalNoise' baseFrequency='0.9' numOctaves='2' stitchTiles='stitch'/%3E%3CfeColorMatrix values='0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.09 0'/%3E%3C/filter%3E%3Crect width='100%25' height='100%25' filter='url(%23n)'/%3E%3C/svg%3E");
}
*{box-sizing:border-box}
html{scroll-behavior:smooth}
body{margin:0;background:var(--grain),var(--bg);background-attachment:fixed,fixed;color:var(--text);
font-family:"Newsreader","Iowan Old Style",Georgia,serif;line-height:1.72;font-size:18px;-webkit-font-smoothing:antialiased}
a{color:var(--link);text-decoration:none}
a:hover{text-decoration:underline}
h1,h2,h3,h4{font-family:"Newsreader","Iowan Old Style",Georgia,serif;line-height:1.22;letter-spacing:-.005em}
.mono{font-family:"SFMono-Regular",Menlo,Consolas,monospace;font-size:.92em}
#progress{position:fixed;top:0;left:0;height:3px;width:0;background:linear-gradient(90deg,var(--accent),#b02b6b,var(--accent2));z-index:200}
#topbar{position:sticky;top:0;z-index:100;display:flex;align-items:center;gap:.7rem;padding:.55rem 1.1rem;
background:color-mix(in srgb,var(--bg) 88%,transparent);backdrop-filter:saturate(1.4) blur(10px);border-bottom:1px solid var(--hair)}
#topbar img{height:26px;border-radius:50%}
#topbar .brand{font-weight:600;font-size:.98rem}
#topbar .brand .scope-name{font-weight:700}
#topbar .spacer{flex:1}
#topbar a.mini{color:var(--muted);font-size:.85rem;margin-left:.9rem}
#topbar a.mini:hover{color:var(--accent)}
/* SCOPE / MIST / SC2W wordmarks (paper colors) */
.scope-name{font-weight:700} .scope-name .s{color:var(--accent)} .scope-name .c{color:var(--c-irr)} .scope-name .o{color:var(--accent2)} .scope-name .p{color:var(--accent)} .scope-name .e{color:var(--c-irr)}
.mist-name{font-weight:700} .mist-name .m{color:var(--accent)} .mist-name .i{color:var(--c-irr)} .mist-name .s{color:var(--accent2)} .mist-name .t{color:var(--c-irr)}
.scptow{font-weight:700} .scptow .s{color:var(--accent)} .scptow .c{color:var(--c-irr)} .scptow .two{color:var(--accent2)} .scptow .w{color:var(--c-clean)}
/* hero */
.hero{max-width:1080px;margin:0 auto;padding:3.2rem 1.3rem 1.2rem;padding-left:calc(210px + 1.6rem + 1.3rem)}
.hero .eyebrow{color:var(--accent);font-weight:600;letter-spacing:.14em;text-transform:uppercase;font-size:.72rem}
.hero h1{font-size:clamp(2.2rem,6vw,3.6rem);margin:.5rem 0 .4rem;letter-spacing:.01em}
.hero .sub{font-size:clamp(1.25rem,3vw,1.72rem);line-height:1.25;color:var(--text);font-weight:500;margin:.35rem 0 .7rem;max-width:660px}
.hero .authors{color:var(--muted);font-size:.92rem;margin:.3rem 0 .2rem}
.btns{display:flex;flex-wrap:wrap;gap:.8rem;margin:1.2rem 0 2.4rem}
.btn{display:inline-flex;align-items:center;gap:.45rem;padding:.5rem .95rem;border-radius:999px;background:var(--c-clean);color:#fff;font-weight:500;font-size:.9rem;border:1px solid var(--c-clean);
transition:transform .15s,box-shadow .15s,opacity .15s,color .15s,border-color .15s}
.btn:hover{text-decoration:none;transform:translateY(-2px);box-shadow:var(--shadow);opacity:.96}
.btn.ghost{background:transparent;color:var(--c-clean);border-color:#d8ccab}
.btn.ghost:hover{border-color:var(--accent);color:var(--accent);opacity:1}
.btn[aria-disabled="true"]{opacity:.5;pointer-events:none}
/* hero flip motif */
.motif{max-width:560px;margin:1.6rem 0 1rem;background:var(--card);border:1px solid var(--border);border-radius:16px;box-shadow:var(--shadow);padding:1.1rem 1.2rem}
.motif .mq{font-size:1rem;line-height:1.5;color:var(--text)}
.motif .mq b{color:var(--c-clean)}
.motif .msig{margin:.7rem 0;min-height:2.2rem;font-size:.9rem;border-radius:10px;padding:.5rem .7rem;border-left:3px solid transparent;background:var(--panel);color:var(--muted);transition:all .4s ease}
.motif .msig.on{border-left-color:var(--accent);background:color-mix(in srgb,var(--accent) 10%,var(--card));color:var(--text)}
.motif .mans{display:flex;align-items:center;gap:.5rem;font-size:1.5rem;font-weight:600;transition:color .35s}
.motif .mans.ok{color:var(--c-cor)} .motif .mans.bad{color:var(--accent)}
.motif .mcap{margin-top:.5rem;font-size:.82rem;color:var(--muted)}
.motif .mdots{display:flex;gap:.3rem;margin-top:.7rem}
.motif .mdots span{height:4px;flex:1;border-radius:999px;background:var(--border)}
.motif .mdots span.on{background:var(--accent)}
/* layout */
.wrap{max-width:1080px;margin:0 auto;padding:0 1.3rem;display:grid;grid-template-columns:210px minmax(0,1fr);gap:1.6rem}
nav.toc{position:sticky;top:64px;align-self:start;height:max-content;font-size:.92rem;padding-top:2rem}
nav.toc .lab{color:var(--muted);text-transform:uppercase;letter-spacing:.12em;font-size:.68rem;margin-bottom:.6rem}
nav.toc a{display:block;color:var(--muted);padding:.28rem 0;border-left:2px solid transparent;padding-left:.7rem}
nav.toc a.active{color:var(--accent);border-left-color:var(--accent);font-weight:600}
article{max-width:var(--measure);width:100%;margin:0;padding:1.2rem 0 3rem}
section{padding:2rem 0;border-top:1px solid var(--hair);scroll-margin-top:70px}
section:first-of-type{border-top:none}
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h2{font-size:clamp(1.5rem,3.6vw,2rem);margin:.1rem 0 .7rem}
h3{font-size:1.15rem;margin:1.3rem 0 .3rem}
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.callout .t{font-weight:600;color:var(--accent);font-size:.8rem;text-transform:uppercase;letter-spacing:.08em;margin-bottom:.3rem}
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/* stat trio */
.stats{display:grid;grid-template-columns:repeat(3,1fr);gap:.9rem;margin:1.4rem 0}
.stat{text-align:center;background:var(--card);border:1px solid var(--border);border-radius:14px;padding:1.1rem .8rem;box-shadow:var(--shadow)}
.stat .num{font-size:2.4rem;font-weight:600;line-height:1;color:var(--accent)}
.stat .lbl{margin-top:.45rem;font-size:.9rem;color:var(--muted);line-height:1.45}
@media(max-width:600px){.stats{grid-template-columns:1fr}}
/* why-grid mini cards */
.mgrid{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:.85rem;margin:1.2rem 0}
@media(max-width:600px){.mgrid{grid-template-columns:1fr}}
.mcard{background:var(--card);border:1px solid var(--border);border-radius:12px;padding:.95rem;box-shadow:var(--shadow)}
.mcard .ic{color:var(--accent);font-size:1.25rem}
.mcard h4{margin:.45rem 0 .3rem;font-size:1.05rem;line-height:1.2}
.mcard p{margin:0;font-size:.95rem;color:var(--muted);line-height:1.55}
/* figure */
.fig{margin:1.5rem 0 .4rem;text-align:center}
.fig img{width:100%;max-width:760px;height:auto;border-radius:12px;border:1px solid var(--border);box-shadow:var(--shadow)}
.fig figcaption{color:var(--muted);font-size:1rem;margin-top:.6rem;line-height:1.5}
/* segmented four-condition widget */
.widget{border:1px solid var(--border);border-radius:var(--radius);background:var(--card);box-shadow:var(--shadow);padding:1.1rem;margin:1.4rem 0}
.widget .whead{font-size:.72rem;text-transform:uppercase;letter-spacing:.1em;color:var(--muted);margin-bottom:.7rem}
.seg{display:inline-flex;flex-wrap:wrap;border:1px solid var(--border);border-radius:999px;overflow:hidden;background:var(--panel)}
.seg button{border:0;background:transparent;color:var(--muted);padding:.45rem 1rem;cursor:pointer;font:inherit;font-size:.9rem;font-weight:600}
.seg button.on[data-c="clean"]{background:var(--c-clean);color:#fff}
.seg button.on[data-c="mis"]{background:var(--c-mis);color:#fff}
.seg button.on[data-c="cor"]{background:var(--c-cor);color:#fff}
.seg button.on[data-c="irr"]{background:var(--c-irr);color:#fff}
.cond-q{margin:1rem 0 .3rem;font-size:1rem;color:var(--text)}
.cond-ctx{border-radius:10px;padding:.7rem .85rem;font-size:.95rem;line-height:1.5;border-left:3px solid var(--c-irr);background:var(--panel);margin:.55rem 0 .7rem;transition:all .3s}
.cond-ctx.mis{border-left-color:var(--c-mis);background:color-mix(in srgb,var(--c-mis) 8%,var(--card))}
.cond-ctx.cor{border-left-color:var(--c-cor);background:color-mix(in srgb,var(--c-cor) 8%,var(--card))}
.cond-ans{display:flex;align-items:center;gap:.5rem;font-size:1.2rem;font-weight:600}
.cond-ans.ok{color:var(--c-cor)} .cond-ans.bad{color:var(--c-mis)}
/* stepper (method) */
.steps{display:flex;gap:.5rem;flex-wrap:wrap}
.step-btn{flex:1;min-width:150px;text-align:left;border:1px solid var(--border);border-radius:12px;background:var(--panel);padding:.7rem .8rem;cursor:pointer;font:inherit;transition:.15s}
.step-btn .lv{font-weight:700;font-size:.78rem;letter-spacing:.06em;color:var(--accent)}
.step-btn .nm{display:block;font-size:.98rem;font-weight:600;margin-top:.15rem}
.step-btn.on{color:#fff;background:var(--accent);border-color:var(--accent)}
.step-btn.on .lv{color:#fff}
.step-panel{margin-top:1rem;background:var(--panel);border:1px solid var(--border);border-radius:12px;padding:1rem;animation:panelIn .18s ease}
@keyframes panelIn{from{opacity:0;transform:translateY(4px)}to{opacity:1;transform:none}}
/* animated bars (results) */
.bars{display:grid;gap:.6rem;margin:1.1rem 0}
.bar{display:grid;grid-template-columns:190px 1fr 92px;align-items:center;gap:.6rem;font-size:.98rem}
.bar .blabel{color:var(--text)}
.bar .btrack{background:var(--panel2);border:1px solid var(--border);border-radius:8px;height:18px;overflow:hidden}
.bar .barfill{height:100%;width:0;background:linear-gradient(90deg,var(--accent),var(--accent2));border-radius:8px;transition:width 1.1s cubic-bezier(.2,.7,.2,1)}
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.reveal.in .bar .barfill{width:var(--w)}
@media(max-width:600px){.bar{grid-template-columns:120px 1fr 72px;font-size:.86rem}}
/* leaderboard */
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.lb-controls .seg button{font-size:.84rem;padding:.4rem .85rem}
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.lb-scroll{overflow-x:auto;border:1px solid var(--border);border-radius:12px;box-shadow:var(--shadow)}
table.lb{width:100%;border-collapse:collapse;font-size:.88rem;background:var(--card);min-width:680px}
.lb thead th{position:sticky;top:0;background:var(--c-clean);color:#fff;font-weight:600;padding:.55rem .6rem;text-align:center;cursor:pointer;user-select:none;white-space:nowrap;font-family:"Newsreader",serif}
.lb thead th:first-child{text-align:left}
.lb thead th .ar{font-size:.7rem;opacity:.55;margin-left:2px}
.lb thead th.sorted .ar{opacity:1;color:var(--accent2)}
.lb tbody td{padding:.44rem .6rem;text-align:center;border-bottom:1px solid var(--hair);color:var(--text);white-space:nowrap;font-variant-numeric:tabular-nums}
.lb tbody td:first-child{text-align:left}
.lb tbody tr:hover{background:var(--panel)}
.lb .grp td{background:var(--panel2);color:var(--muted);font-size:.72rem;text-transform:uppercase;letter-spacing:.06em;font-weight:700;text-align:left;padding:.34rem .6rem}
.lb .m{display:flex;align-items:center;gap:.5rem}
.lb .m img{height:18px;width:18px;object-fit:contain;border-radius:4px}
.lb .m .nm{font-weight:600}
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.lb .sc{border-radius:5px}
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@media(max-width:640px){
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/* challenge / case cards */
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<div class="eyebrow">Selective trust, not resistance</div>
<h1><span class="scope-name"><span class="s">S</span><span class="c">C</span><span class="o">O</span><span class="p">P</span><span class="e">E</span></span></h1>
<div class="sub">Learning When to Trust via Selective Context Preference Optimization</div>
<div class="authors">
Xian Sun<sup>1</sup> · Wei Chow<sup>2</sup> · Yingshuo Wang<sup>3</sup> · Junhao Liu<sup>4</sup> · Wei Gao<sup>5</sup> · Qing Wu<sup>6</sup> · Lingdong Kong<sup>2</sup>
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<div class="authors" style="font-size:.82rem;margin-top:.3rem;line-height:1.75">
<sup>1</sup>Duke University<br>
<sup>2</sup>National University of Singapore<br>
<sup>3</sup>UC Berkeley<br>
<sup>4</sup>UC Irvine<br>
<sup>5</sup>Northeastern University<br>
<sup>6</sup>Nanyang Technological University, Singapore
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<a class="btn" href="https://arxiv.org/abs/2608.06377" target="_blank" rel="noopener"><i class="ai ai-arxiv"></i> arXiv</a>
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<a href="#overview">Overview</a>
<a href="#problem">The Problem</a>
<a href="#benchmark">MIST Benchmark</a>
<a href="#leaderboard">Leaderboard</a>
<a href="#method">SCOPE</a>
<a href="#results">Results</a>
<a href="#examples">Examples</a>
<a href="#cite">Citation</a>
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<article>
<section id="overview" class="reveal">
<div class="kicker">Overview</div>
<h2>When a plausible hint turns a right answer wrong</h2>
<p class="lead">Language models increasingly condition their answers on external signals — hints, retrieved passages, user feedback, rationales — and a single misleading one can flip a correct answer to wrong.</p>
<p>The obvious remedy, training models to <i>resist</i> such signals, hides a failure mode: a model that ignores all context looks robust under the usual clean-versus-misleading test, yet is useless precisely when the context is worth trusting.</p>
<p>We reframe the problem as <b>selective trust</b> and make it measurable with <span class="mist-name"><span class="m">M</span><span class="i">I</span><span class="s">S</span><span class="t">T</span></span>, a benchmark that renders each reasoning item under four matched conditions, and <span class="scptow"><span class="s">S</span><span class="c">C</span><span class="two">2</span><span class="w">W</span></span>, a paired metric counting how often a misleading signal flips a clean-correct answer to wrong. We then propose <span class="scope-name"><span class="s">S</span><span class="c">C</span><span class="o">O</span><span class="p">P</span><span class="e">E</span></span>, which changes only <i>what</i> enters a standard DPO objective — matched preference pairs balanced across all four conditions — and roughly halves <span class="scptow"><span class="s">S</span><span class="c">C</span><span class="two">2</span><span class="w">W</span></span> while preserving accuracy when the added context is clean, correct, or irrelevant.</p>
<blockquote>Reliable reasoning models should be trained and judged on selective trust, not on resistance alone.</blockquote>
</section>
<section id="problem" class="reveal">
<div class="kicker">A universal failure mode</div>
<h2>Every model bends to a misleading signal</h2>
<p>Across a broad sweep of frontier and open-weight models, adding a single misleading signal lowers accuracy for <i>every</i> one — the strongest systems included.</p>
<div class="stats">
<div class="stat"><div class="num" data-count="23">0</div><div class="lbl">frontier & open-weight models evaluated</div></div>
<div class="stat"><div class="num" data-count="17.1" data-dec="1">0</div><div class="lbl">mean accuracy drop (points) under a misleading signal</div></div>
<div class="stat"><div class="num" data-count="100" data-suffix="%">0</div><div class="lbl">of models affected</div></div>
</div>
<div class="mgrid">
<div class="mcard"><div class="ic"><i class="fas fa-key"></i></div><h4>Answer keys</h4><p>An authoritative-looking key or solutions sheet asserting the wrong option.</p></div>
<div class="mcard"><div class="ic"><i class="fas fa-magnifying-glass"></i></div><h4>Retrieved snippets</h4><p>A fluent search result or document that confidently states a wrong value.</p></div>
<div class="mcard"><div class="ic"><i class="fas fa-user"></i></div><h4>User beliefs</h4><p>Sycophancy: alignment nudges the model to agree with the user over the truth.</p></div>
<div class="mcard"><div class="ic"><i class="fas fa-list-ol"></i></div><h4>Rationales</h4><p>Persuasive but unfaithful reasoning that steers the final answer.</p></div>
</div>
</section>
<section id="benchmark" class="reveal">
<div class="kicker">The benchmark</div>
<h2><span class="mist-name"><span class="m">M</span><span class="i">I</span><span class="s">S</span><span class="t">T</span></span>: four matched conditions per item</h2>
<p><span class="mist-name"><span class="m">M</span><span class="i">I</span><span class="s">S</span><span class="t">T</span></span>-1000 renders each of 1,000 reasoning items under four versions that differ <i>only</i> in the context wrapped around the same question. Because the question, answer space, and gold answer are held fixed, any change in accuracy is attributable to the added signal. Toggle the conditions on a real item:</p>
<div class="widget">
<div class="whead">Same question · four matched contexts</div>
<div class="seg" id="condSeg">
<button class="on" data-c="clean">Clean</button>
<button data-c="mis">Misleading</button>
<button data-c="cor">Correct-Context</button>
<button data-c="irr">Irrelevant</button>
</div>
<div class="cond-q"><b>Q.</b> A shop sells the same product in three pack sizes. Which is the best value (lowest price per unit)? <b>(A)</b> 8‑pack $14 <b>(B)</b> 3‑pack $6 <b>(C)</b> 24‑pack $36</div>
<div class="cond-ctx" id="condCtx">No added context.</div>
<div class="cond-ans ok" id="condAns"><span id="condMark">✓</span><span id="condVal">C — recomputes $1.75 / $2.00 / $1.50 per unit</span></div>
</div>
<p>The central metric, <b>SC2W</b> (signal-induced correct-to-wrong), conditions on items the model already solves when clean and measures how often a misleading signal flips them to wrong:</p>
<div class="formula">$$ \mathrm{SC2W} = \frac{\sum_i \mathbb{I}[a_i^{\mathrm{clean}}=1 \,\wedge\, a_i^{\mathrm{mis}}=0]}{\sum_i \mathbb{I}[a_i^{\mathrm{clean}}=1]} $$</div>
</section>
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<div class="kicker">Official leaderboard</div>
<h2>How models handle misleading context</h2>
<p>Accuracy under each matched condition (higher is better) and <b>SC2W</b> (lower is better). Click a column to sort; filter by model class. Best is <span class="best" style="color:var(--accent)">bold</span>, second is <span class="ul">underlined</span>, and <b>SCOPE</b> rows are marked ★.</p>
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<section id="method" class="reveal">
<div class="kicker">The method</div>
<h2><span class="scope-name"><span class="s">S</span><span class="c">C</span><span class="o">O</span><span class="p">P</span><span class="e">E</span></span>: change the data, not the loss</h2>
<p><span class="scope-name"><span class="s">S</span><span class="c">C</span><span class="o">O</span><span class="p">P</span><span class="e">E</span></span> leaves the DPO objective untouched; what is new is entirely in how the preference pairs are constructed and balanced across the four conditions.</p>
<div class="widget">
<div class="whead">Step through the construction</div>
<div class="steps">
<button class="step-btn on" data-s="0"><span class="lv">01</span><span class="nm">Mine</span></button>
<button class="step-btn" data-s="1"><span class="lv">02</span><span class="nm">Match</span></button>
<button class="step-btn" data-s="2"><span class="lv">03</span><span class="nm">Balance</span></button>
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</section>
<section id="results" class="reveal">
<div class="kicker">Results</div>
<h2>Roughly halves SC2W, with no collateral damage</h2>
<p>By balancing the four conditions, <span class="scope-name"><span class="s">S</span><span class="c">C</span><span class="o">O</span><span class="p">P</span><span class="e">E</span></span> cuts the flip rate while preserving or improving every control condition — and it transfers zero-shot.</p>
<div class="bars">
<div class="bar"><span class="blabel">SC2W ↓ on Qwen3-4B</span><span class="btrack"><span class="barfill" style="--w:53%"></span></span><span class="bnum">35.0→16.3</span></div>
<div class="bar"><span class="blabel">SC2W ↓ on Llama-3.2-3B</span><span class="btrack"><span class="barfill" style="--w:35%"></span></span><span class="bnum">31.5→20.6</span></div>
</div>
<p class="muted" style="font-size:.9rem">Bar length shows the relative reduction in SC2W (53% and 35%).</p>
</section>
<section id="examples" class="reveal">
<div class="kicker">At the instance level</div>
<h2>What selective trust looks like</h2>
<div class="chal">
<div class="c"><span class="tag ok">Repaired</span><h4>Misleading answer key</h4><p>A solutions PDF marks “(B) 3-pack for $6” on the best-value question.</p><div class="flip"><div class="p base">Base<b>✗ B</b></div><div class="p ours">+ SCOPE<b>✓ C</b></div></div></div>
<div class="c"><span class="tag ok">Repaired</span><h4>Planted arithmetic result</h4><p>An official key gives 24 for a round-trip fuel cost that is actually 48.</p><div class="flip"><div class="p base">Base<b>✗ 24</b></div><div class="p ours">+ SCOPE<b>✓ 48</b></div></div></div>
<div class="c"><span class="tag ok">Repaired</span><h4>Conflicting answer sheet</h4><p>An old sheet records “no” for a quorum that is in fact met.</p><div class="flip"><div class="p base">Base<b>✗ No</b></div><div class="p ours">+ SCOPE<b>✓ Yes</b></div></div></div>
<div class="c"><span class="tag warn">Remaining</span><h4>Fluent search snippet</h4><p>A plausible summary asserts 25.68; the correct split is 25.40. Both still follow it — the hardest regime.</p><div class="flip"><div class="p base">Base<b>✗ 25.68</b></div><div class="p base">+ SCOPE<b>✗ 25.68</b></div></div></div>
</div>
</section>
<section id="cite" class="reveal">
<div class="kicker">Cite</div>
<h2>Citation</h2>
<div class="bibwrap">
<button id="copybib">Copy</button>
<pre class="bib" id="bibtext">@article{scope2026,
title = {Learning When to Trust via Selective Context Preference Optimization},
author = {Sun, Xian and Chow, Wei and Wang, Yingshuo and Liu, Junhao and Gao, Wei and Wu, Qing and Kong, Lingdong},
journal = {arXiv preprint arXiv:2608.06377},
year = {2026}
}</pre>
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</section>
<section id="authors" class="reveal">
<div class="kicker">Authors</div>
<h2>Authors & Affiliations</h2>
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<img class="cphoto" src="assets_common/photos/xian_sun.jpg" alt="Xian Sun" loading="lazy" width="56" height="56" onerror="this.outerHTML='<div class="cphoto ph"><i class="fas fa-user"></i></div>'">
<div class="cinfo"><div class="cmeta"><div class="cname">Xian Sun</div><div class="caff">Duke University</div></div></div>
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<img class="cphoto" src="assets_common/photos/wei_chow.jpg" alt="Wei Chow" loading="lazy" width="56" height="56" onerror="this.outerHTML='<div class="cphoto ph"><i class="fas fa-user"></i></div>'">
<div class="cinfo"><div class="cmeta"><div class="cname">Wei Chow</div><div class="caff">National University of Singapore</div></div></div>
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<img class="cphoto" src="assets_common/photos/yingshuo_wang.jpg" alt="Yingshuo Wang" loading="lazy" width="56" height="56" onerror="this.outerHTML='<div class="cphoto ph"><i class="fas fa-user"></i></div>'">
<div class="cinfo"><div class="cmeta"><div class="cname">Yingshuo Wang</div><div class="caff">UC Berkeley</div></div></div>
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<div class="cinfo"><div class="cmeta"><div class="cname">Junhao Liu</div><div class="caff">UC Irvine</div></div></div>
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<div class="cinfo"><div class="cmeta"><div class="cname">Wei Gao</div><div class="caff">Northeastern University</div></div></div>
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<img class="cphoto" src="assets_common/photos/qing.png" alt="Qing Wu" loading="lazy" width="56" height="56" onerror="this.outerHTML='<div class="cphoto ph"><i class="fas fa-user"></i></div>'">
<div class="cinfo"><div class="cmeta"><div class="cname">Qing Wu</div><div class="caff">Nanyang Technological University, Singapore</div></div></div>
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<img class="cphoto" src="assets_common/photos/lingdong_kong.jpg" alt="Lingdong Kong" loading="lazy" width="56" height="56" onerror="this.outerHTML='<div class="cphoto ph"><i class="fas fa-user"></i></div>'">
<div class="cinfo"><div class="cmeta"><div class="cname">Lingdong Kong</div><div class="caff">National University of Singapore</div></div>
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const IC="assets/scope/icons/";
const LB=[
{g:"api",logo:"doubao.png",name:"Seed 1.8",clean:93.3,mis:56.7,cor:98.1,irr:93.7,ov:85.5,sc:39.7},
{g:"api",logo:"gemini.jpg",name:"Gemini 3.1 Pro",clean:96.9,mis:84.5,cor:98.8,irr:96.7,ov:94.2,sc:12.9},
{g:"api",logo:"chatgpt.png",name:"GPT 5.5",clean:96.0,mis:86.1,cor:98.5,irr:96.1,ov:94.2,sc:10.5},
{g:"api",logo:"claude_ai.png",name:"Claude Opus 4.8",clean:96.0,mis:84.7,cor:97.9,irr:96.0,ov:93.7,sc:12.0},
{g:"api",logo:"claude_ai.png",name:"Claude Opus 4.7",clean:96.5,mis:73.1,cor:98.6,irr:96.4,ov:91.1,sc:24.6},
{g:"api",logo:"claude_ai.png",name:"Claude Sonnet 4.6",clean:96.1,mis:80.4,cor:99.2,irr:95.6,ov:92.8,sc:16.9},
{g:"api",logo:"claude_ai.png",name:"Claude Haiku 4.5",clean:93.8,mis:76.6,cor:97.4,irr:92.8,ov:90.1,sc:19.2},
{g:"open",logo:"qwen.png",name:"Qwen3-14B",clean:93.8,mis:73.8,cor:98.0,irr:94.1,ov:89.9,sc:22.1},
{g:"open",logo:"qwen.png",name:"Qwen3-8B",clean:93.0,mis:69.1,cor:98.0,irr:92.3,ov:88.1,sc:27.1},
{g:"open",logo:"qwen.png",name:"Qwen2.5-14B",clean:88.8,mis:69.7,cor:94.7,irr:88.8,ov:85.5,sc:22.9},
{g:"open",logo:"qwen.png",name:"Qwen2.5-7B",clean:84.7,mis:70.9,cor:93.2,irr:84.2,ov:83.3,sc:20.1},
{g:"open",logo:"qwen.png",name:"Qwen2.5-3B",clean:75.6,mis:61.0,cor:84.3,irr:72.5,ov:73.4,sc:27.2},
{g:"open",logo:"qwen.png",name:"Qwen2.5-1.5B",clean:60.5,mis:36.2,cor:76.8,irr:53.9,ov:56.9,sc:51.7},
{g:"open",logo:"qwen.png",name:"Qwen2.5-0.5B",clean:39.5,mis:32.3,cor:55.9,irr:39.0,ov:41.7,sc:50.1},
{g:"open",logo:"ms.png",name:"Phi-4-Reasoning",clean:92.3,mis:70.6,cor:97.9,irr:92.4,ov:88.3,sc:25.0},
{g:"open",logo:"deepseek.png",name:"DeepSeek-R1-Distill-7B",clean:80.4,mis:65.9,cor:87.8,irr:77.8,ov:78.0,sc:23.9},
{g:"open",logo:"deepseek.png",name:"DeepSeek-R1-Distill-1.5B",clean:63.1,mis:55.2,cor:75.9,irr:63.8,ov:64.5,sc:28.7},
{g:"open",logo:"deepseek.png",name:"DeepSeek JustRL-1.5B",clean:71.0,mis:48.8,cor:86.6,irr:69.1,ov:68.9,sc:36.2},
{g:"open",logo:"meta.png",name:"Llama-3.1-8B",clean:76.3,mis:61.5,cor:87.3,irr:78.9,ov:76.0,sc:26.6},
{g:"open",logo:"mistral_ai.png",name:"Mistral-7B-v0.3",clean:63.1,mis:47.4,cor:75.7,irr:62.2,ov:62.1,sc:34.2},
{g:"open",logo:"ai2.png",name:"OLMo-2-7B",clean:68.0,mis:53.8,cor:81.2,irr:69.2,ov:68.1,sc:28.8},
{g:"open",logo:"hf.png",name:"SmolLM2-1.7B",clean:47.4,mis:34.5,cor:67.2,irr:45.8,ov:48.7,sc:48.3},
{g:"open",logo:"deepmind.png",name:"Gemma 3-12B",clean:89.3,mis:69.2,cor:94.8,irr:88.1,ov:85.4,sc:25.2},
{g:"def",block:"Qwen3-4B",logo:"qwen.png",name:"Qwen3-4B",clean:94.5,mis:62.5,cor:98.1,irr:92.6,ov:86.9,sc:35.0},
{g:"def",block:"Qwen3-4B",name:"+ Prompt-Defense",clean:92.8,mis:80.2,cor:96.5,irr:94.0,ov:90.9,sc:18.3},
{g:"def",block:"Qwen3-4B",name:"+ SFT",clean:93.4,mis:81.0,cor:96.7,irr:92.8,ov:91.0,sc:17.4},
{g:"def",block:"Qwen3-4B",name:"+ Standard-DPO",clean:91.7,mis:80.5,cor:95.4,irr:92.5,ov:90.0,sc:19.1},
{g:"def",block:"Qwen3-4B",name:"+ OPSD",clean:93.2,mis:80.3,cor:95.9,irr:91.2,ov:90.2,sc:20.1},
{g:"def",block:"Qwen3-4B",name:"+ SCOPE (Ours)",clean:95.0,mis:80.7,cor:98.1,irr:94.3,ov:92.0,sc:16.3,ours:1},
{g:"def",block:"Llama-3.2-3B",logo:"meta.png",name:"Llama-3.2-3B",clean:69.5,mis:54.4,cor:78.5,irr:69.3,ov:67.9,sc:31.5},
{g:"def",block:"Llama-3.2-3B",name:"+ Prompt-Defense",clean:69.0,mis:62.0,cor:77.2,irr:71.1,ov:69.8,sc:21.6},
{g:"def",block:"Llama-3.2-3B",name:"+ SFT",clean:67.5,mis:61.7,cor:73.5,irr:68.7,ov:67.9,sc:20.4},
{g:"def",block:"Llama-3.2-3B",name:"+ Standard-DPO",clean:70.9,mis:63.3,cor:56.4,irr:70.6,ov:65.3,sc:23.3},
{g:"def",block:"Llama-3.2-3B",name:"+ OPSD",clean:63.0,mis:51.7,cor:73.7,irr:63.7,ov:63.0,sc:34.1},
{g:"def",block:"Llama-3.2-3B",name:"+ SCOPE (Ours)",clean:72.0,mis:63.1,cor:80.0,irr:71.6,ov:71.7,sc:20.6,ours:1},
];
const COLS=[{k:"clean",l:"Clean",hi:1},{k:"mis",l:"Mislead",hi:1},{k:"cor",l:"Correct",hi:1},{k:"irr",l:"Irrelev.",hi:1},{k:"ov",l:"Overall↑",hi:1},{k:"sc",l:"SC2W↓",hi:0}];
const GL={api:"API Reference Models",open:"Open-Weight Models",def:"Defenses"};
let fF="all",sK=null,sD=1;
function vis(){let r=LB.filter(x=>fF==="all"||x.g===fF);if(sK){const hi=COLS.find(c=>c.k===sK).hi;r=r.slice().sort((a,b)=>(a[sK]-b[sK])*(hi?-sD:sD));}return r;}
function bestv(r){const o={};COLS.forEach(c=>{const s=[...new Set(r.map(x=>x[c.k]))].sort((a,b)=>c.hi?b-a:a-b);o[c.k]={b:s[0],s:s[1]};});return o;}
function heat(v,mn,mx){const t=mx===mn?0:(v-mn)/(mx-mn),a=(.10+.34*t).toFixed(2);const r=Math.round(8+t*247),g=Math.round(217-t*171),b=Math.round(214-t*115);return`rgba(${r},${g},${b},${a})`;}
function mc(r){const lg=r.logo?`<img src="${IC}${r.logo}" alt="" onerror="this.style.visibility='hidden'">`:`<span style="width:18px;display:inline-block"></span>`;const bd=r.g==="api"?`<span class="bd api">API</span>`:r.g==="open"?`<span class="bd open">Open</span>`:`<span class="bd def">${r.block}</span>`;return`<span class="m">${lg}<span class="nm">${r.name}</span>${bd}</span>`;}
const RM=window.matchMedia&&matchMedia("(prefers-reduced-motion: reduce)").matches;
function render(){
const r=vis(),bv=bestv(r),sc=r.map(x=>x.sc),rng={mn:Math.min(...sc),mx:Math.max(...sc)};
let h=`<th data-k="model">Model</th>`;
COLS.forEach(c=>{const s=sK===c.k?"sorted":"";const ar=sK===c.k?(((c.hi?-1:1)*sD<0)?"↓":"↑"):"⇅";h+=`<th class="${s}" data-k="${c.k}">${c.l}<span class="ar">${ar}</span></th>`;});
document.getElementById("lbHead").innerHTML=h;
let b="",cards="",lg=null,lb=null;
r.forEach(x=>{
if(!sK){
if(x.g!=="def"&&x.g!==lg){b+=`<tr class="grp"><td colspan="7">${GL[x.g]}</td></tr>`;lg=x.g;}
if(x.g==="def"&&x.block!==lb){b+=`<tr class="grp"><td colspan="7">Defenses · ${x.block}</td></tr>`;lb=x.block;lg="def";}
}
let tds="";COLS.forEach(c=>{const v=x[c.k],cls=v===bv[c.k].b?"best":v===bv[c.k].s?"ul":"";if(c.k==="sc")tds+=`<td class="sc ${cls}" style="background:${heat(v,rng.mn,rng.mx)}">${v.toFixed(1)}</td>`;else tds+=`<td class="${cls}">${v.toFixed(1)}</td>`;});
b+=`<tr class="${x.ours?"ours":""}" data-key="${(x.block||x.g)+'|'+x.name}"><td>${mc(x)}</td>${tds}</tr>`;
let g="";COLS.forEach(c=>g+=`<div><span>${c.l}</span>${x[c.k].toFixed(1)}</div>`);
cards+=`<div class="lbc ${x.ours?"ours":""}">${mc(x)}<div class="g">${g}</div></div>`;
});
const tb=document.getElementById("lbBody");
const first={};
if(!RM){tb.querySelectorAll("tr[data-key]").forEach(tr=>{first[tr.dataset.key]=tr.getBoundingClientRect().top;});}
tb.innerHTML=b;document.getElementById("lbCards").innerHTML=cards;
if(!RM){tb.querySelectorAll("tr[data-key]").forEach(tr=>{const k=tr.dataset.key,last=tr.getBoundingClientRect().top;
if(first[k]!=null){const dy=first[k]-last;if(dy){tr.style.transform="translateY("+dy+"px)";tr.style.transition="none";requestAnimationFrame(()=>{tr.style.transition="transform .45s cubic-bezier(.2,.7,.2,1)";tr.style.transform="";});}}
else{tr.style.opacity="0";requestAnimationFrame(()=>{tr.style.transition="opacity .4s ease";tr.style.opacity="1";});}});}
}
document.getElementById("lbSeg").addEventListener("click",e=>{const t=e.target.closest("button");if(!t)return;document.querySelectorAll("#lbSeg button").forEach(x=>x.classList.remove("on"));t.classList.add("on");fF=t.dataset.f;render();});
document.getElementById("lbTable").addEventListener("click",e=>{const th=e.target.closest("th[data-k]");if(!th||th.dataset.k==="model")return;if(sK===th.dataset.k)sD*=-1;else{sK=th.dataset.k;sD=1;}render();});
/* ---------------- Four-condition toggle ---------------- */
const CD={
clean:{cls:"",ok:1,ctx:"No added context.",val:"C — recomputes $1.75 / $2.00 / $1.50 per unit"},
mis:{cls:"mis",ok:0,ctx:"A solutions PDF marks “(B) a 3-pack for $6”.",val:"B — follows the plausible but wrong key"},
cor:{cls:"cor",ok:1,ctx:"A solutions PDF marks “(C) a 24-pack for $36”.",val:"C — agrees with the correct key"},
irr:{cls:"cor",ok:1,ctx:"The handout is a draft and this entry is missing.",val:"C — ignores the non-answer-bearing note"},
};
document.getElementById("condSeg").addEventListener("click",e=>{const t=e.target.closest("button");if(!t)return;document.querySelectorAll("#condSeg button").forEach(x=>x.classList.remove("on"));t.classList.add("on");const d=CD[t.dataset.c];const ctx=document.getElementById("condCtx");ctx.className="cond-ctx "+(t.dataset.c==="irr"?"":d.cls);ctx.innerHTML=d.ctx;const a=document.getElementById("condAns");a.className="cond-ans "+(d.ok?"ok":"bad");if(!RM){void a.offsetWidth;a.classList.add("flash");}document.getElementById("condMark").innerHTML=d.ok?"✓":"✗";document.getElementById("condVal").innerHTML=d.val;});
/* ---------------- Method stepper ---------------- */
const ST=[
{h:"Mine the failures that matter",p:"Find items a base model answers correctly on its own but gets wrong once a misleading signal is added — the clean-correct / misleading-wrong cases."},
{h:"Match a counterfactual pair",p:"Prefer the model’s truth-consistent trace over its signal-following one, and reuse the same pair across all four context conditions — tying the learning signal to the context’s role, not to surface form."},
{h:"Balance across conditions",p:"Rather than train on misleading pairs alone (which teaches blanket distrust), weight them equally against clean, correct-context, and irrelevant-context controls, using a standard DPO objective."},
];
function setStep(i){document.querySelectorAll("#method .step-btn").forEach(x=>x.classList.toggle("on",+x.dataset.s===i));document.getElementById("stepPanel").innerHTML=`<h4 style="margin:.1rem 0 .4rem">${ST[i].h}</h4><p style="margin:0;color:var(--muted)">${ST[i].p}</p>`;}
document.querySelectorAll("#method .step-btn").forEach(b=>b.addEventListener("click",()=>setStep(+b.dataset.s)));
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