摘要：自我改进的 Agent 必须决定保留哪些新技能。在实践中，它通常会保留能够获得高奖励、说服评判模型或压缩其技能库的技能，即使这些技能是错误的。在答案不必绝对精确时，这或许尚可；但对于交易记录表中的合计数，答案要么正确，要么错误。我们提出一个更难的问题：Agent 能否在没有奖励、没有评判者、也没有标准答案的情况下，扩展自身的计算能力，同时仍保证答案精确无误？一个参数冻结的模型基于一门小型、精确的领域特定语言（DSL）运行两个嵌套循环。内循环仅在两个独立编写的表达式对每条记录的计算结果都一致时，才回答新问题。外循环则自行发现缺失的能力并为其编写算子；只有当第二个独立实现与之结果一致，且结果遵守守恒定律时，才接纳该算子，整个过程无需真实答案。内循环使可回答问题集合扩大至约三倍；外循环则从互不重叠的初始集合出发实现自我扩展，创造出初始闭包之外的算子；不进行归纳的对照组无法回答任何新问题。在独立参考实现的检验下，准入规则在实验中表现可靠：它拒绝了全部 138 个存在缺陷的算子变体，其中还包括由不同模型家族编写的变体；相比之下，领域内常依赖的“能运行即接纳”、自一致性和压缩信号会接纳其中大多数变体。同一机制未经修改即可在另外两个具有不同数据模式的领域——业务账本问答和临床就诊问答——实现自我扩展，使其可回答问题集合分别增长十余倍和近二十倍。该循环也能跨模型家族迁移：使用其他提议模型运行时，准入机制仍然可靠，不同模型家族实现的自我扩展程度相近，只有归纳产出量随各提议模型对 DSL 的熟练程度而变化。

Abstract:A self-improving agent has to decide which new skills to keep, and in practice it keeps whatever earns a high reward, convinces a judge model, or compresses its library, even when the skill is wrong. That is fine until the answers have to be exactly right: over a table of transactions, a total is either right or wrong. We ask a harder question: can an agent grow what it can compute with no reward, no judge, and no answer key, and still be exactly right? A single frozen model runs two nested loops over a small, exact domain-specific language (DSL). The inner loop answers new questions only when two independently written expressions agree on every record. The outer loop discovers its own missing capability and authors an operator for it, admitted only when an independent second implementation agrees and the result obeys a conservation law, all without ground truth. The inner loop roughly triples the answerable-question set, and the outer loop self-extends on disjoint starting sets, inventing operators outside the starting closure; a no-induction control answers none of the new questions. The admission rule is empirically sound: it rejects 138 of 138 buggy operator variants under an independent reference, even one written by a different model family, where the admit-if-it-runs, self-consistency, and compression signals the field relies on admit most of them. Unmodified, the same mechanism self-extends on two further domains with unrelated schemas, business-ledger and clinical-encounter question answering, growing their answerable sets more than tenfold and nearly twentyfold. The loop transfers across model families too: run with further proposers, the gate stays sound and independent families self-extend comparably, with only the induction yield tracking each proposer's DSL fluency.