Datasets:

ziyan98
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E2K-loop-v0.2

<title>E2K-40 Internalization</title>
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<div class="wrap">
<header>
  <h1><span class="zh">E2K-40:把验真的可泛化知识内化进权重</span><span class="en">E2K-40: Internalizing verified, generalizable knowledge into weights</span></h1>
  <div class="sub"><span><span class="zh">进展 2026-09-11</span><span class="en">Progress 2026-09-11</span></span>
    <span class="lang" role="group" aria-label="Language"><button type="button" id="lang-zh" aria-pressed="true">中文</button> · <button type="button" id="lang-en" aria-pressed="false">EN</button></span></div>
</header>

<!-- ===== 0. Setup ===== -->
<section id="setup">
  <h2><span class="zh">设置</span><span class="en">Setup</span></h2>
  <div class="setup">
    <div><div class="k"><span class="zh">模型</span><span class="en">Model</span></div><div class="v">Qwen3.8-27B<br><span class="zh">(Qwen3.5 架构:Gated-DeltaNet + 注意力混合)</span><span class="en">(Qwen3.5 architecture: hybrid Gated-DeltaNet + attention)</span></div></div>
    <div><div class="k">Benchmark</div><div class="v">ARC-AGI-3<br><span class="zh">交互式网格游戏;本文一道题 <code>cd82-fb555c5d</code>(ARC3_004),6 个 level,64×64 棋盘,16 色</span><span class="en">interactive grid games; one game here, <code>cd82-fb555c5d</code> (ARC3_004): 6 levels, 64×64 board, 16 colours</span></div></div>
    <div><div class="k">Harness</div><div class="v"><span class="zh">Qwen Code 代理循环:模型按其后训练的方式用工具玩游戏(MCP 工具 <code>look / act / status</code>);知识以工作区 <code>QWEN.md</code> 进入上下文;每个条件 100 局</span><span class="en">Qwen Code agent loop: the model plays through tools the way it was post-trained (MCP tools <code>look / act / status</code>); knowledge enters as the workspace's <code>QWEN.md</code>; 100 episodes per condition</span></div></div>
    <div><div class="k"><span class="zh">RL 策略</span><span class="en">RL policy</span></div><div class="v"><span class="zh">同一模型,裸 prompt:每步收到棋盘,输出一个 JSON 动作;slime(Megatron 训练 + SGLang 采样),16×GH200</span><span class="en">Same model, bare prompt: receives the board each step, emits one JSON action; slime (Megatron training + SGLang sampling), 16×GH200</span></div></div>
  </div>

  <div class="hidden">
    <div class="h"><span class="zh">游戏机制 —— 对模型隐藏</span><span class="en">Game mechanics — hidden from the model</span></div>
    <div class="tablewrap"><table class="booktabs" style="margin-top:6px">
      <thead><tr><th><span class="zh">动作</span><span class="en">Action</span></th><th><span class="zh">真实效果(来自源码与引擎逐条核过)</span><span class="en">True effect (checked against the source and the live engine)</span></th></tr></thead>
      <tbody>
        <tr><td class="mono">ACTION1–4</td><td><span class="zh">把"涂色器"沿 3×3 环移动一格(上 / 下 / 左 / 右);移出环或移到中心 = 无效果,但仍计一步</span><span class="en">Move the applicator one place around a 3×3 ring (up / down / left / right); off the ring or onto the centre = no effect, still costs a step</span></td></tr>
        <tr><td class="mono">ACTION5</td><td><span class="zh">用当前颜色涂画布中面向涂色器的区域:在边上 = 一半,在角上 = 一个三角;覆盖写</span><span class="en">Paint the canvas region facing the applicator with the selected colour: a half from an edge, a triangle from a corner; overwrites</span></td></tr>
        <tr><td class="mono">ACTION6 x y</td><td><span class="zh">点击:点在色板框上 = 选色;点在涂色器旁的小方块上 = 涂该边中段(仅 level 3–6);其它位置 = 无效果</span><span class="en">Click: on a colour box = select that colour; on the small sprite beside the applicator = paint that edge's middle third (levels 3–6 only); elsewhere = nothing</span></td></tr>
        <tr><td class="mono">RESET</td><td><span class="zh">恢复本 level 起始状态,不计步</span><span class="en">Restore the level's starting state; free</span></td></tr>
        <tr><td><span class="zh">目标 / 预算</span><span class="en">Goal / budget</span></td><td><span class="zh">画布 = 参考图案(忽略两条对角线);每 level 99 步,第 100 步 = 输</span><span class="en">Canvas = reference pattern (two diagonals ignored); 99 actions per level, the 100th loses</span></td></tr>
      </tbody>
    </table></div>
    <p class="caption" style="margin-top:8px"><span class="zh">模型看到的只有 64×64 的整数网格和动作<i>名字</i>(下方灰框),没有任何说明;上表全部要靠它自己在游戏里发现。</span><span class="en">The model sees only the 64×64 integer grid and the action <i>names</i> (grey box below) — no description; everything in the table it has to discover by playing.</span></p>
  </div>

  <h3><span class="zh">一局的前八步(真实引擎)</span><span class="en">Eight steps of one episode (real engine)</span></h3>
  <div class="demo">
    <div>
      <img id="demo-board" class="board" alt="Board of cd82 level 1 after the current step" src="">
      <div class="ctl"><button type="button" id="demo-prev" aria-label="Previous step">‹</button><button type="button" id="demo-play" aria-pressed="true">❚❚</button><button type="button" id="demo-next" aria-label="Next step">›</button><span id="demo-label"></span></div>
    </div>
    <ol class="steps" id="demo-steps">
      <li data-i="0"><span class="n">0</span><span class="a">start</span><span class="m"><span class="zh">level 1 起始</span><span class="en">level 1 start</span></span><span class="d"></span></li>
      <li data-i="1"><span class="n">1</span><span class="a">ACTION6 37 4</span><span class="m"><span class="zh">点左侧色板框 → 选白色</span><span class="en">click the left colour box → select white</span></span><span class="d">Δ95</span></li>
      <li data-i="2"><span class="n">2</span><span class="a">ACTION5</span><span class="m"><span class="zh">画布已是白色 → 什么都没变</span><span class="en">canvas already white → nothing changes</span></span><span class="d">Δ0</span></li>
      <li data-i="3"><span class="n">3</span><span class="a">ACTION6 43 4</span><span class="m"><span class="zh">点右侧色板框 → 选紫色</span><span class="en">click the right colour box → select purple</span></span><span class="d">Δ95</span></li>
      <li data-i="4"><span class="n">4</span><span class="a">ACTION5</span><span class="m"><span class="zh">上半画布涂成紫色</span><span class="en">paint the top half of the canvas purple</span></span><span class="d">Δ51</span></li>
      <li data-i="5"><span class="n">5</span><span class="a">ACTION3</span><span class="m"><span class="zh">涂色器移到左上角</span><span class="en">applicator moves to the top-left corner</span></span><span class="d">Δ200</span></li>
      <li data-i="6"><span class="n">6</span><span class="a">ACTION5</span><span class="m"><span class="zh">左上三角涂成紫色</span><span class="en">paint the top-left triangle purple</span></span><span class="d">Δ16</span></li>
      <li data-i="7"><span class="n">7</span><span class="a">ACTION1</span><span class="m"><span class="zh">角上再"上" → 无效果</span><span class="en">"up" from a corner → no effect</span></span><span class="d">Δ0</span></li>
      <li data-i="8"><span class="n">8</span><span class="a">RESET</span><span class="m"><span class="zh">恢复起始</span><span class="en">back to the start</span></span><span class="d">Δ269</span></li>
    </ol>
  </div>
  <p class="caption"><b><span class="zh">图 1.</span><span class="en">Figure 1.</span></b> <span class="zh">Δ = 该步改变的格子数,是模型能观察到的全部反馈。</span><span class="en">Δ = cells changed by the step — the only feedback the model can observe.</span></p>

  <pre class="obs">{{OBS_HEAD}}
  …  (64 rows × 64 integers; {{OBS_LEN}} characters ≈ 8.6k tokens per observation)
{{OBS_TAIL}}</pre>
  <p class="caption"><span class="zh">模型每步收到的观测:状态、完成的 level 数、整数网格、可用动作名 —— 仅此而已。</span><span class="en">The observation the model receives each step: state, levels completed, the integer grid, the available action names — and nothing else.</span></p>
</section>

<!-- ===== 1. Motivation ===== -->
<section id="motivation">
  <h2><span class="zh">动机:从自蒸馏到显式、可验证、可组合的知识</span><span class="en">Motivation: from self-distillation to explicit, verifiable, composable knowledge</span></h2>
  <p><span class="zh"><b>SDPO(自蒸馏策略优化)怎么做。</b>同一个模型跑两遍:教师的 prompt 里放进 oracle 答案(或其它特权信息),学生只看原 prompt;在学生自己采出的 token 上最小化 KL(π<sub>学生</sub> ∥ π<sub>教师</sub>),可再加 RL reward。学生学会"像看到了答案那样"作答。</span><span class="en"><b>How SDPO (self-distillation policy optimization) works.</b> The same model is run twice: the teacher's prompt contains the oracle answer (or other privileged information), the student sees only the original prompt; on the student's own samples the KL(π<sub>student</sub> ∥ π<sub>teacher</sub>) is minimized, optionally with an RL reward. The student learns to answer "as if it had seen the answer".</span></p>
  <p><span class="zh"><b>问题。</b>信号全部来自模型对<i>那个答案</i>的自我反思:学到的东西隐含在答案里、绑定于具体题目,没有外部检验,也不会超出 oracle 给的范围 —— 它复制答案,不产生新知识。</span><span class="en"><b>The problem.</b> All signal comes from the model reflecting on <i>that answer</i>: what is learned stays implicit and answer-bound, nothing checks it externally, and it never grows beyond what the oracle handed over — it copies answers rather than producing knowledge.</span></p>
  <p><span class="zh"><b>我们的想法。</b>LLM 擅长组合创新,缺的是对"什么算知识"的约束。所以把知识做成显式的声明式规则,用两个 reward 引导模型自己去获得:<b>正确性</b>(在游戏里复现)和<b>泛化性</b>(在别的 level 上仍成立)。多轮迭代:第一轮拿到最底层的原子(ARC 里的动作映射),后面各轮把原子放在一起,组合出新的、更高层的知识;每轮的知识再通过 SFT ⊕ RL 内化。整个过程只需在现有 multi-step RL(harness)循环里加一个 SFT 项。</span><span class="en"><b>Our idea.</b> LLMs are good at combinatorial innovation; what is missing is a constraint on what counts as knowledge. So knowledge becomes explicit declarative rules that the model acquires itself under two rewards: <b>correctness</b> (reproduced in the game) and <b>generalization</b> (still holds on other levels). Iterated over rounds: round 1 yields the lowest-level atoms (ARC action mappings), later rounds put atoms together and compose new, higher-level knowledge; each round's set is internalized by SFT ⊕ RL. Only one SFT term is added to the existing multi-step RL (harness) loop.</span></p>

  <figure>
    <svg viewBox="0 0 960 250" role="img" aria-label="Left: SDPO runs the same model with and without the oracle answer in context and minimizes a KL between the two distributions. Right: our loop extracts claims from play, rewards them for correctness and generalization, keeps the verified set K, internalizes K by SFT and RL, and feeds K back so the next round composes atoms into higher-level knowledge.">
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        <text x="8" y="18" font-weight="600">(a) SDPO</text>
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        <text x="83" y="77" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="zh">教师(同一模型)</text><text x="83" y="77" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="en">teacher (same model)</text>
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        <text x="312" y="122" fill="var(--bad)" font-weight="600">min KL</text>
        <text x="8" y="232" font-size="12" fill="var(--muted)" class="zh">信号 = 对答案 a* 的自我反思;隐式、绑定题目、无外部检验</text>
        <text x="8" y="232" font-size="12" fill="var(--muted)" class="en">signal = self-reflection on the answer a*; implicit, answer-bound, unchecked</text>
        <line x1="420" y1="10" x2="420" y2="240" stroke="currentColor" stroke-opacity=".3" stroke-dasharray="3 4"/>
        <text x="440" y="18" font-weight="600" class="zh">(b) 本文:迭代获取显式知识</text><text x="440" y="18" font-weight="600" class="en">(b) Ours: iterated explicit knowledge</text>
        <rect x="440" y="40" width="118" height="46" rx="4" fill="var(--exp-soft)" stroke="var(--exp)" stroke-width="1.3"/>
        <text x="499" y="59" text-anchor="middle" class="zh">游玩 | 𝒦<tspan baseline-shift="sub" font-size="9">r−1</tspan></text><text x="499" y="59" text-anchor="middle" class="en">play | 𝒦<tspan baseline-shift="sub" font-size="9">r−1</tspan></text>
        <text x="499" y="77" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="zh">经验 𝒟<tspan baseline-shift="sub" font-size="9">r</tspan></text><text x="499" y="77" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="en">experience 𝒟<tspan baseline-shift="sub" font-size="9">r</tspan></text>
        <rect x="586" y="40" width="118" height="46" rx="4" fill="none" stroke="currentColor" stroke-width="1.3"/>
        <text x="645" y="59" text-anchor="middle" class="zh">提取 · 组合</text><text x="645" y="59" text-anchor="middle" class="en">extract · compose</text>
        <text x="645" y="77" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="zh">候选 claims</text><text x="645" y="77" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="en">candidate claims</text>
        <rect x="732" y="40" width="118" height="46" rx="4" fill="none" stroke="currentColor" stroke-width="1.3"/>
        <text x="791" y="59" text-anchor="middle" class="zh">验真(游戏)</text><text x="791" y="59" text-anchor="middle" class="en">verify (in game)</text>
        <text x="791" y="77" text-anchor="middle" font-size="11.5" fill="var(--ok)">R<tspan baseline-shift="sub" font-size="9">corr</tspan> · R<tspan baseline-shift="sub" font-size="9">gen</tspan></text>
        <rect x="878" y="40" width="76" height="46" rx="4" fill="var(--know-soft)" stroke="var(--know)" stroke-width="1.3"/>
        <text x="916" y="67" text-anchor="middle" font-weight="600">𝒦<tspan baseline-shift="sub" font-size="9">r</tspan></text>
        <line x1="558" y1="63" x2="584" y2="63" stroke="currentColor" stroke-width="1.3" marker-end="url(#arr)"/>
        <line x1="704" y1="63" x2="730" y2="63" stroke="currentColor" stroke-width="1.3" marker-end="url(#arr)"/>
        <line x1="850" y1="63" x2="876" y2="63" stroke="currentColor" stroke-width="1.3" marker-end="url(#arr)"/>
        <rect x="586" y="150" width="264" height="46" rx="4" fill="none" stroke="var(--know)" stroke-width="1.8"/>
        <text x="718" y="169" text-anchor="middle" font-weight="600" class="zh">内化:SFT(𝒦<tspan baseline-shift="sub" font-size="9">r</tspan>)⊕ RL,同一个 multi-step 循环</text>
        <text x="718" y="169" text-anchor="middle" font-weight="600" class="en">internalize: SFT(𝒦<tspan baseline-shift="sub" font-size="9">r</tspan>) ⊕ RL, one multi-step loop</text>
        <text x="718" y="187" text-anchor="middle" font-size="11.5" fill="var(--muted)">θ ← θ − η∇[ℒ<tspan baseline-shift="sub" font-size="9">PG</tspan> + w·NLL(𝒦<tspan baseline-shift="sub" font-size="9">r</tspan>)]</text>
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        <line x1="916" y1="140" x2="852" y2="140" stroke="var(--know)" stroke-width="1.3"/>
        <line x1="852" y1="140" x2="852" y2="148" stroke="var(--know)" stroke-width="1.3" marker-end="url(#arr)"/>
        <path d="M916 86 L916 120 L470 120 L470 88" fill="none" stroke="var(--exp)" stroke-width="1.3" stroke-dasharray="4 3" marker-end="url(#arr)"/>
        <text x="600" y="115" font-size="11.5" fill="var(--exp)" class="zh">下一轮:𝒦<tspan baseline-shift="sub" font-size="9">r</tspan> 入上下文,原子被组合成更高层知识</text>
        <text x="600" y="115" font-size="11.5" fill="var(--exp)" class="en">next round: 𝒦<tspan baseline-shift="sub" font-size="9">r</tspan> in context, atoms compose into higher-level knowledge</text>
        <text x="440" y="232" font-size="12" fill="var(--muted)" class="zh">信号 = 游戏给的正确性 + 跨 level 泛化;显式、可组合、可迁移</text>
        <text x="440" y="232" font-size="12" fill="var(--muted)" class="en">signal = correctness from the game + cross-level generalization; explicit, composable, transferable</text>
      </g>
    </svg>
    <figcaption><b><span class="zh">图 2.</span><span class="en">Figure 2.</span></b> <span class="zh">(a) SDPO 让模型对着 oracle 答案反思自己;(b) 本文让模型在正确性与泛化性两个 reward 下多轮获取显式知识,并在同一 RL 循环里内化。</span><span class="en">(a) SDPO has the model reflect on itself against an oracle answer; (b) ours has the model acquire explicit knowledge over rounds under correctness and generalization rewards, internalized inside the same RL loop.</span></figcaption>
  </figure>
</section>

<!-- ===== 2. Framework ===== -->
<section id="framework">
  <h2><span class="zh">框架</span><span class="en">Framework</span></h2>
  <div class="algo">
    <div class="title"><span class="zh">算法 1  迭代式知识获取与内化</span><span class="en">Algorithm 1  Iterated knowledge acquisition and internalization</span></div>
    <ol>
      <li>𝒦<sub>0</sub> ← ∅;  <span class="kw">for</span> r = 1 … R <span class="kw">do</span></li>
      <li>&nbsp;&nbsp;𝒟<sub>r</sub> ← Play(π<sub>θ</sub>, levels 1–4 | 𝒦<sub>r−1</sub> in context) <span class="cm">▷ <span class="zh">带当前知识的经验</span><span class="en">experience with current knowledge</span></span></li>
      <li>&nbsp;&nbsp;𝒞 ← Extract(𝒟<sub>r</sub>, 𝒦<sub>r−1</sub>) <span class="cm">▷ <span class="zh">原子 → 组合</span><span class="en">atoms → compositions</span></span></li>
      <li>&nbsp;&nbsp;𝒦<sub>r</sub> ← 𝒦<sub>r−1</sub> ∪ { c ∈ 𝒞 : R<sub>corr</sub>(c) = 1, R<sub>gen</sub>(c) ≥ γ } <span class="cm">▷ <span class="zh">在游戏里验真;答案型拒绝</span><span class="en">verified by play; answers rejected</span></span></li>
      <li>&nbsp;&nbsp;θ ← θ − η ∇<sub>θ</sub> [ ℒ<sub>PG</sub>(τ ∼ π<sub>θ</sub>) + w · NLL<sub>θ</sub>(𝒦<sub>r</sub>) ] <span class="cm">▷ <span class="zh">同一 multi-step RL 循环</span><span class="en">same multi-step RL loop</span></span></li>
      <li><span class="kw">return</span> Eval(π<sub>θ</sub>, levels 5–6 | 𝒦 ∉ context)</li>
    </ol>
  </div>
  <p class="tabcap"><span class="zh">当前实现的是 r = 1;NLL 项只作用于声明式陈述,从不作用于轨迹。</span><span class="en">Currently r = 1; the NLL term applies to declarative statements only, never to trajectories.</span></p>
  <div class="tablewrap"><table class="booktabs">
    <thead><tr><th><span class="zh">实验组</span><span class="en">Arm</span></th><th><span class="zh">SFT 何时进入</span><span class="en">When SFT enters</span></th><th><span class="zh">每步目标</span><span class="en">Per-step objective</span></th></tr></thead>
    <tbody>
      <tr><td>baseline</td><td>—</td><td>ℒ<sub>PG</sub></td></tr>
      <tr><td>sft_first</td><td><span class="zh">RL 前 4 轮纯 SFT</span><span class="en">4 SFT-only rollouts before RL</span></td><td>NLL → ℒ<sub>PG</sub></td></tr>
      <tr><td>sft_interleaved</td><td><span class="zh">每轮 RL 后 2 轮 SFT</span><span class="en">2 SFT rollouts after every RL rollout</span></td><td>ℒ<sub>PG</sub> ⇄ NLL</td></tr>
      <tr><td>sft_joint</td><td><span class="zh">每一步</span><span class="en">every step</span></td><td>ℒ<sub>PG</sub> + w·NLL</td></tr>
      <tr><td>oracle</td><td><span class="zh">同 sft_first,𝒦 = 手写规则(14 条)</span><span class="en">as sft_first, 𝒦 = hand-written rules (14)</span></td><td>NLL → ℒ<sub>PG</sub></td></tr>
    </tbody>
  </table></div>
  <p class="tabcap"><b><span class="zh">表 1.</span><span class="en">Table 1.</span></b> <span class="zh">消融:同一 𝒦、同一 RL(Dr.GRPO,每轮 32 局 × ≤80 步)、同一评测(level 5–6,prompt 中无 𝒦);只改 SFT 的调度。</span><span class="en">Ablation: same 𝒦, same RL (Dr.GRPO, 32 episodes × ≤80 decisions per rollout), same evaluation (levels 5–6, no 𝒦 in the prompt); only the SFT schedule changes.</span></p>
</section>

<!-- ===== 3. Verification ===== -->
<section id="verify">
  <h2><span class="zh">怎么验真:让代码替模型检验</span><span class="en">How a claim is verified: code checks the model</span></h2>
  <p><span class="zh">验真者是同一个模型的另一个会话,拿到一条 claim 和过去的对局记录。它<b>不判断</b> claim 对不对,而是<b>写代码</b>去复现:把 claim 拆成子句,对每个子句设计检查 —— 在对局记录里数、或开一局新游戏用 <code>act</code> 去试;计数 <code>reproduced / total</code>,声明极性(数成功还是数违例:"从不发生"的子句 0/N 才算通过);再用 <code>set_level(k)</code> 在至少两个别的 level 上重跑同样的检查。产出一份结构化 ledger。过滤器只读 ledger:任一子句被驳回 → 删掉该子句;本 level 检查成立 → 正确;别的 level 的结果 → 泛化分 0–3;点击配方 / 解法型 → 拒绝。</span><span class="en">The verifier is another session of the same model, given one claim and the past episode journals. It does <b>not judge</b> the claim; it <b>writes code</b> that reproduces it: the claim is split into clauses, each gets a check — counted in the journals, or tried in a fresh episode through <code>act</code>; it records <code>reproduced / total</code> with a declared polarity (successes or violations: a "never happens" clause passes at 0/N); then the same checks are re-run on at least two other levels via <code>set_level(k)</code>. The output is a structured ledger. The filter reads only the ledger: any refuted clause is cut; home-level checks hold → correct; the other-level results → a generalization score 0–3; click recipes / solutions → rejected.</span></p>
  <figure>
    <svg viewBox="0 0 960 200" role="img" aria-label="Verification loop: a claim goes to the verifier model, which writes code; the code drives fresh episodes through the game tools look, act, status and set_level and reads the journals; it produces per-clause counts reproduced over total with a polarity and per-level results; a ledger is written; the filter gates correctness, scores generalization 0 to 3 and rejects answers; surviving clauses enter the knowledge set.">
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      <g font-family="Source Serif 4, Georgia, serif" font-size="13" fill="currentColor">
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        <text x="62" y="67" text-anchor="middle" font-weight="600">claim c</text>
        <text x="62" y="85" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="zh">子句 c1 … cN</text><text x="62" y="85" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="en">clauses c1 … cN</text>

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        <text x="226" y="67" text-anchor="middle" font-weight="600" class="zh">验真者写代码</text><text x="226" y="67" text-anchor="middle" font-weight="600" class="en">verifier writes code</text>
        <text x="226" y="85" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="zh">同一模型,另一会话</text><text x="226" y="85" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="en">same model, own session</text>

        <rect x="334" y="30" width="176" height="82" rx="4" fill="var(--exp-soft)" stroke="var(--exp)" stroke-width="1.3"/>
        <text x="422" y="52" text-anchor="middle" font-weight="600" class="zh">代码跑游戏</text><text x="422" y="52" text-anchor="middle" font-weight="600" class="en">code runs the game</text>
        <text x="422" y="70" text-anchor="middle" font-size="11.5">look · act · status</text>
        <text x="422" y="86" text-anchor="middle" font-size="11.5">set_level(k)</text>
        <text x="422" y="103" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="zh">+ 读对局记录</text><text x="422" y="103" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="en">+ reads journals</text>

        <rect x="552" y="30" width="176" height="82" rx="4" fill="none" stroke="currentColor" stroke-width="1.3"/>
        <text x="640" y="52" text-anchor="middle" font-weight="600">ledger</text>
        <text x="640" y="70" text-anchor="middle" font-size="11.5" class="zh">每子句 reproduced/total,极性</text><text x="640" y="70" text-anchor="middle" font-size="11.5" class="en">per clause reproduced/total, polarity</text>
        <text x="640" y="86" text-anchor="middle" font-size="11.5" class="zh">每个别的 level:held / failed</text><text x="640" y="86" text-anchor="middle" font-size="11.5" class="en">per other level: held / failed</text>
        <text x="640" y="103" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="zh">被驳回的子句 + 观察证据</text><text x="640" y="103" text-anchor="middle" font-size="11.5" fill="var(--muted)" class="en">refuted clauses + the observation</text>

        <rect x="770" y="30" width="184" height="82" rx="4" fill="var(--know-soft)" stroke="var(--know)" stroke-width="1.3"/>
        <text x="862" y="52" text-anchor="middle" font-weight="600" class="zh">过滤 → 𝒦</text><text x="862" y="52" text-anchor="middle" font-weight="600" class="en">filter → 𝒦</text>
        <text x="862" y="70" text-anchor="middle" font-size="11.5" class="zh">正确:硬门槛</text><text x="862" y="70" text-anchor="middle" font-size="11.5" class="en">correctness: gate</text>
        <text x="862" y="86" text-anchor="middle" font-size="11.5" class="zh">泛化:打分 0–3</text><text x="862" y="86" text-anchor="middle" font-size="11.5" class="en">generalization: score 0–3</text>
        <text x="862" y="103" text-anchor="middle" font-size="11.5" fill="var(--bad)" class="zh">答案型:拒绝</text><text x="862" y="103" text-anchor="middle" font-size="11.5" fill="var(--bad)" class="en">answer-like: rejected</text>

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        <!-- the verifier never sees the source -->
        <text x="6" y="150" font-size="12" fill="var(--muted)" class="zh">验真者拿不到游戏源码,只能通过 look / act / status / set_level 操作;源码只用于人工审计。</text>
        <text x="6" y="150" font-size="12" fill="var(--muted)" class="en">The verifier never sees the game source; it can only drive the game via look / act / status / set_level. The source is used for human audit only.</text>
        <text x="6" y="172" font-size="12" fill="var(--muted)" class="zh">检查种类是固定词表(home_level_fresh, other_level:k, negative_expectation, …),写的是"测了什么条件",不是"希望说明什么"。</text>
        <text x="6" y="172" font-size="12" fill="var(--muted)" class="en">Check kinds are a fixed vocabulary (home_level_fresh, other_level:k, negative_expectation, …) naming the condition tested, not the hoped-for conclusion.</text>
      </g>
    </svg>
    <figcaption><b><span class="zh">图 3.</span><span class="en">Figure 3.</span></b> <span class="zh">验真回路。正确性和泛化性都由游戏本身给出,不由模型的自我评价给出。</span><span class="en">The verification loop. Correctness and generalization come from the game itself, never from the model's self-assessment.</span></figcaption>
  </figure>

  <div class="ledger">
    <div class="box"><span class="tag"><span class="zh">子句 c1 · holds · home_level_fresh 4 次检查</span><span class="en">clause c1 · holds · home_level_fresh, 4 checks</span></span>Clicking any cell of a framed legend box, frame included, sets the applicator's fill colour to that box's colour.<span class="obs2"><span class="zh">别的 level:level 2 held(7 个色框、坐标不同,机制相同)· level 3 held → 泛化 3</span><span class="en">other levels: level 2 held (7 boxes at other coordinates, same mechanism) · level 3 held → generalization 3</span></span></div>
    <div class="box no"><span class="tag"><span class="zh">子句 c2 · refuted · 被删</span><span class="en">clause c2 · refuted · cut</span></span>Rows 3 and 6 of the frame are inert targets: clicking them changes nothing.<span class="obs2"><span class="zh">观察:在 (39,3)、(37,6)、(43,6) 点击各改变 94–95 格;记录里 18 次中 13 次"无变化"都是涂色器已持有该色的情形。</span><span class="en">observation: clicks at (39,3), (37,6), (43,6) changed 94–95 cells; the 13 of 18 journal instances that changed nothing were all cases where the applicator already held that colour.</span></span></div>
  </div>
  <p class="caption"><span class="zh">一份真实 ledger 的两条子句(verifier v2 示例):一条 claim 里对的部分进入 𝒦,错的子句连同证据被去掉 —— 不是整条接受或整条拒绝。</span><span class="en">Two clauses of a real ledger (verifier v2 example): the correct part of a claim enters 𝒦, the wrong clause is removed with its evidence — not accept-or-reject the whole claim.</span></p>
</section>

<!-- ===== 4. Evidence ===== -->
<section id="results">
  <h2><span class="zh">上下文中的知识有效;RL 起点无信号</span><span class="en">Knowledge in context works; the RL start has no signal</span></h2>
  <figure>
    <div class="fig-panel"><img src="data:image/png;base64,{{FIG_B64}}" alt="Bar chart of level-1 clear rate: agent harness with no knowledge 9/100, mechanism rules in context 33/91, full knowledge set in context 100/100; RL starting policy with no knowledge 0/320. Error bars are 95% Wilson intervals."></div>
    <figcaption><b><span class="zh">图 4.</span><span class="en">Figure 4.</span></b> <span class="zh">同一策略,只改上下文:level 1 通关率 9/100 → 33/91 → 100/100(agent harness)。RL 起点 π₀(裸 prompt,无知识)为 0/320,纯 RL 基线梯度恒为 0 —— 内化只能从 SFT 组开始。误差棒:95% Wilson 区间。</span><span class="en">Same policy, only the context changes: level-1 clear rate 9/100 → 33/91 → 100/100 (agent harness). The RL start π₀ (bare prompt, no knowledge) is 0/320, so the pure-RL baseline's gradient is identically zero — internalization has to start from the SFT arms. Error bars: 95% Wilson intervals.</span></figcaption>
  </figure>
</section>

<!-- ===== 5. Knowledge demo ===== -->
<section id="knowledge">
  <h2><span class="zh">知识长什么样</span><span class="en">What the knowledge looks like</span></h2>
  <div class="boards">
    <figure class="train"><img src="data:image/png;base64,{{BOARD1}}" alt="Level 1 starting board"><figcaption>L1 · train</figcaption></figure>
    <figure class="train"><img src="data:image/png;base64,{{BOARD2}}" alt="Level 2 starting board"><figcaption>L2 · train</figcaption></figure>
    <figure class="train"><img src="data:image/png;base64,{{BOARD3}}" alt="Level 3 starting board"><figcaption>L3 · train</figcaption></figure>
    <figure class="train"><img src="data:image/png;base64,{{BOARD4}}" alt="Level 4 starting board"><figcaption>L4 · train</figcaption></figure>
    <figure class="test"><img src="data:image/png;base64,{{BOARD5}}" alt="Level 5 starting board"><figcaption>L5 · test</figcaption></figure>
    <figure class="test"><img src="data:image/png;base64,{{BOARD6}}" alt="Level 6 starting board"><figcaption>L6 · test</figcaption></figure>
  </div>
  <p class="caption"><b><span class="zh">图 5.</span><span class="en">Figure 5.</span></b> <span class="zh">六个 level 的起始棋盘。同一套机制、不同布局:知识若可泛化,应在 L5–L6 上仍成立。</span><span class="en">Starting boards of the six levels. Same mechanics, different layouts: knowledge that generalizes should still hold on L5–L6.</span></p>
  <div class="atoms">
    <div class="atom"><span class="tag"><span class="zh">已验真 · level 1 · 泛化 3/3</span><span class="en">verified · level 1 · generalization 3/3</span></span>Clicking the colour box whose colour the applicator already holds changes no board cell.</div>
    <div class="atom"><span class="tag"><span class="zh">已验真 · level 1 · 泛化 3/3</span><span class="en">verified · level 1 · generalization 3/3</span></span>An ACTION5 that changes no cell means that region already holds that colour.</div>
    <div class="atom"><span class="tag"><span class="zh">已验真 · level 1 · 泛化 3/3</span><span class="en">verified · level 1 · generalization 3/3</span></span>The canvas is written only by a painting action or by a level (re)load.</div>
    <div class="atom"><span class="tag"><span class="zh">已验真 · level 1 · 泛化 3/3</span><span class="en">verified · level 1 · generalization 3/3</span></span>ACTION6 aimed at a cell that belongs to no interactive sprite changes no board cell.</div>
    <div class="atom new"><span class="tag"><span class="zh">新 · level 1 · 动作映射(验真中)</span><span class="en">new · level 1 · action mapping (being verified)</span></span>ACTION6's x is the column and y the row: the legend fires for calls with x 35–43 and y 2–6, while the transposed calls hit background and fire nothing.</div>
    <div class="atom new"><span class="tag"><span class="zh">新 · level 2(验真中)</span><span class="en">new · level 2 (being verified)</span></span>RESET restores the board to its initial state, changing exactly the drifted cells and refilling the 64-cell bottom row; it consumes one action.<span class="cond"><span class="zh">条件:任何漂移后的状态</span><span class="en">condition: any state after drift</span></span></div>
    <div class="atom new"><span class="tag"><span class="zh">新 · level 3(验真中)</span><span class="en">new · level 3 (being verified)</span></span>ACTION3 merges the mid-board container from the split configuration and is a no-op from the merged one; ACTION4 inverts ACTION3 back to split.<span class="cond"><span class="zh">条件:容器处于初始拆分或合并布局</span><span class="en">condition: the container is in its split or merged layout</span></span></div>
    <div class="atom new"><span class="tag"><span class="zh">新 · level 4 · 组合两条原子(验真中)</span><span class="en">new · level 4 · composes two atoms (being verified)</span></span>ACTION1 and ACTION2 also fire 228/229-cell container transforms, reaching shapes where ACTION3 and ACTION4 change no container cells.<span class="cond"><span class="zh">条件:容器最近一次由 ACTION1/2 变换</span><span class="en">condition: the container was last transformed by ACTION1/2</span></span></div>
  </div>
  <p class="caption"><span class="zh">蓝色:人工深审后保留的 level-1 原子(36 条中的 4 条);橙色:v3 提取器从 level 1–4 新得到的 claims(474 条中的 4 条,v2 验真进行中)。每条 = 一个机制 + 条件,不含解法。</span><span class="en">Blue: level-1 atoms kept after the claim-by-claim review (4 of 36); amber: new claims from the v3 extractor on levels 1–4 (4 of 474, v2 verification running). Each = one mechanism + its condition, no solution.</span></p>
</section>

<!-- ===== 6. Status ===== -->
<section id="status">
  <h2><span class="zh">进展</span><span class="en">Progress</span></h2>
  <div class="tablewrap"><table class="booktabs">
    <thead><tr><th>Level</th><th class="num"><span class="zh">局</span><span class="en">Episodes</span></th><th class="num"><span class="zh">清关</span><span class="en">Cleared</span></th><th class="num"><span class="zh">claims (v3)</span><span class="en">Claims (v3)</span></th><th><span class="zh">验真 v2</span><span class="en">Verify v2</span></th><th><span class="zh">过滤</span><span class="en">Filter</span></th></tr></thead>
    <tbody>
      <tr><td>1</td><td class="num">100</td><td class="num">9</td><td class="num">101</td><td><span class="zh">运行中</span><span class="en">running</span></td><td>—</td></tr>
      <tr><td>2</td><td class="num">100</td><td class="num">0</td><td class="num">121</td><td><span class="zh">运行中</span><span class="en">running</span></td><td>—</td></tr>
      <tr><td>3</td><td class="num">100</td><td class="num">0</td><td class="num">128</td><td><span class="zh">运行中</span><span class="en">running</span></td><td>—</td></tr>
      <tr><td>4</td><td class="num">100</td><td class="num">0</td><td class="num">124</td><td><span class="zh">运行中</span><span class="en">running</span></td><td>—</td></tr>
    </tbody>
  </table></div>
  <p class="tabcap"><b><span class="zh">表 2.</span><span class="en">Table 2.</span></b> <span class="zh">知识流水线(四个 level 同一流程)。旧 61 条集经逐条深审:原样可用 4 条,答案型 19 条 → verifier v2 / extractor v3 / filter v2,标准不变。</span><span class="en">Knowledge pipeline (one procedure for all four levels). The old 61-claim set was reviewed claim by claim: 4 usable as written, 19 answer-like → verifier v2 / extractor v3 / filter v2, standard unchanged.</span></p>
  <ul class="tight">
    <li><span class="zh">RL 管线已跑通(每轮:32 局 rollout ≈ 32 min,log-prob + 2 步优化 ≈ 40 min;eval ≈ 33 min / 2 轮;一组 12 轮 ≈ 20 h)。验真 → filter → 合池成最终 𝒦 → 起 sft_first / sft_interleaved / sft_joint。</span><span class="en">RL pipeline runs end to end (per rollout: 32 episodes ≈ 32 min generation, log-prob pass + 2 optimizer steps ≈ 40 min; eval ≈ 33 min per 2 rollouts; one 12-rollout arm ≈ 20 h). Verify → filter → pool the final 𝒦 → launch sft_first / sft_interleaved / sft_joint.</span></li>
    <li><span class="zh">纯 RL 基线需要 π₀ 非零的设定(xhigh 推理或更多局)才有信息量。</span><span class="en">The pure-RL baseline needs a setting with non-zero π₀ (xhigh reasoning or more episodes) to be informative.</span></li>
    <li><span class="zh">第 2 轮(r = 2):把 𝒦₁ 放回上下文再游玩、再提取,看模型能否组合出更高层的知识。</span><span class="en">Round 2 (r = 2): play and extract again with 𝒦₁ in context, to see whether the model composes higher-level knowledge.</span></li>
  </ul>
</section>

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  <span class="mono">~/code/knowledge_learning</span> · <span class="mono">/projects/u6uv/ziyan/outputs/{rl,harness,review,report}</span> · wandb <span class="mono">wangziyan1998/e2k-internalize</span>
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