E2K-40:把验真的可泛化知识内化进权重E2K-40: Internalizing verified, generalizable knowledge into weights

设置Setup

一局的前八步(真实引擎)Eight steps of one episode (real engine)

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1. 0startlevel 1 起始level 1 start
2. 1ACTION6 37 4点左侧色板框 → 选白色click the left colour box → select whiteΔ95
3. 2ACTION5画布已是白色 → 什么都没变canvas already white → nothing changesΔ0
4. 3ACTION6 43 4点右侧色板框 → 选紫色click the right colour box → select purpleΔ95
5. 4ACTION5上半画布涂成紫色paint the top half of the canvas purpleΔ51
6. 5ACTION3涂色器移到左上角applicator moves to the top-left cornerΔ200
7. 6ACTION5左上三角涂成紫色paint the top-left triangle purpleΔ16
8. 7ACTION1角上再"上" → 无效果"up" from a corner → no effectΔ0
9. 8RESET恢复起始back to the startΔ269

图 1.Figure 1. Δ = 该步改变的格子数,是模型能观察到的全部反馈。Δ = cells changed by the step — the only feedback the model can observe.

{{OBS_HEAD}}
  …  (64 rows × 64 integers; {{OBS_LEN}} characters ≈ 8.6k tokens per observation)
{{OBS_TAIL}}

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。The observation the model receives each step: state, levels completed, the integer grid, the available action names — and nothing else.

动机:从自蒸馏到显式、可验证、可组合的知识Motivation: from self-distillation to explicit, verifiable, composable knowledge

SDPO(自蒸馏策略优化)怎么做。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_学生 ∥ π_教师),可再加 RL reward。学生学会"像看到了答案那样"作答。How SDPO (self-distillation policy optimization) works. 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_student ∥ π_teacher) is minimized, optionally with an RL reward. The student learns to answer "as if it had seen the answer".

问题。信号全部来自模型对那个答案的自我反思: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。The problem. All signal comes from the model reflecting on that answer: 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.

我们的想法。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:正确性(在游戏里复现)和泛化性(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。Our idea. 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: correctness (reproduced in the game) and generalization (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.

框架Framework

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。Currently r = 1; the NLL term applies to declarative statements only, never to trajectories.

表 1.Table 1. 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。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.

怎么验真:让代码替模型检验How a claim is verified: code checks the model

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。它不判断 claim 对不对,而是写代码去复现: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 act 去试;计数 reproduced / total,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 set_level(k) 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。The verifier is another session of the same model, given one claim and the past episode journals. It does not judge the claim; it writes code that reproduces it: the claim is split into clauses, each gets a check — counted in the journals, or tried in a fresh episode through act; it records reproduced / total 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 set_level(k). 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.

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。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.

上下文中的知识有效;RL 起点无信号Knowledge in context works; the RL start has no signal

知识长什么样What the knowledge looks like

图 5.Figure 5. 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。Starting boards of the six levels. Same mechanics, different layouts: knowledge that generalizes should still hold on L5–L6.

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。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.

进展Progress

表 2.Table 2. 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。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.

• 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。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.
• 纯 RL 基线需要 π₀ 非零的设定(xhigh 推理或更多局)才有信息量。The pure-RL baseline needs a setting with non-zero π₀ (xhigh reasoning or more episodes) to be informative.
• 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。Round 2 (r = 2): play and extract again with 𝒦₁ in context, to see whether the model composes higher-level knowledge.