generative-thinking

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Generative Thinking — One Move, Committed

生成式思考——专注一种动作

Fixation is the default state. When a generator (human or LLM) has been working on a problem, attention concentrates on the current framing and subsequent ideas tend to be local variations on it. This skill is the interrupt: spend one move stepping sideways, then resume.
The discipline matters more than the move. Pick ONE technique per invocation, run it without second-guessing, and produce explicit reframings or candidate entry points — not a brainstorm list in the same frame.
固着是默认状态。当生成者(人或 LLM)持续处理某个问题时,注意力会集中在当前框架上,后续想法往往只是该框架的局部变体。此 skill 就是一次中断:用一个动作横向迈出一步,然后继续工作。
这种纪律比具体动作更重要。每次调用只选择一种技术,不犹豫地执行,并产出明确的重新表述或候选切入点——而不是在同一框架中列出一份头脑风暴清单。

When to reach for this

何时使用

Claude activates this skill when:
  • The last 2+ iterations are variations of one idea (fixation signal)
  • The user says "widen this", "think bigger", "I'm stuck", "what am I missing", "too narrow", "break out of"
  • A problem is framed as a binary ("X or Y") and neither option is good
  • An agent loop is producing convergent variations — suspect the frame, not the search depth
  • The user explicitly wants a pre-mortem on the framing (not the plan) before committing
Do NOT activate this skill as a default before every consequential task — fixation is the trigger, not stakes. If the current frame is working, let it work.
Claude 在以下情况下启用此 skill:
  • 最近 2 次以上迭代都是同一想法的变体(固着信号)
  • 用户说“拓宽这个(widen this)”“想得更大(think bigger)”“我卡住了(I'm stuck)”“我漏掉了什么(what am I missing)”“范围太窄(too narrow)”“突破当前框架(break out of)”
  • 问题被框定为二选一(“X 或 Y”),而两个选项都不好
  • Agent 循环正在产生趋同的变体——应怀疑框架,而不是搜索深度
  • 用户明确希望在投入执行前,对框架本身(而非计划)进行 pre-mortem
不要把此 skill 作为每项重要任务前的默认流程——触发条件是固着,而不是任务风险。如果当前框架有效,就让它继续发挥作用。

Core discipline

核心纪律

Three rules that apply across every move below. Violations make the output ideation-flavored but structurally identical to what came before.
  1. Generation before evaluation. De Bono's core distinction: lateral thinking cares about movement value, not truth value. A provocation is not a proposal. Evaluate only after the move has produced 3+ candidate framings.
  2. One move, committed. Do not rotate through five techniques as a menu. Pick the move that matches the diagnosis, execute it fully, surface what shook loose, then stop. Menus produce noise; commitment produces distance.
  3. Output framings, not ideas. The deliverable of a generative move is usually a new statement of the problem or a new entry angle, not another solution candidate inside the old frame. If the output could have been produced without the move, the move didn't fire.
Stop condition. Stop when the move has produced 3+ non-trivial framings, or a single framing that reorganizes the problem (one sharp surprise beats five adjacent). Do not keep generating because the list looks short — volume is not the product.
The fire test. After every move, ask: could this output have been produced without the move? If yes, the move did not fire. Either commit harder (push the provocation further, make the reframe more aggressive, re-roll the random word, invert on a different axis) or the move was mismatched to the stuck-pattern — re-diagnose and pick the better-matched move. Re-diagnosis after a miss is not menu-rotation; menu-rotation is cycling through techniques without commitment. One move at a time, each one fully, and if it misses, diagnose why before the next.
Tail sift. The fire test with a number attached. Post-trained models carry a typicality bias: asked for one candidate they return the modal one, and asked for a list they return the top-k modes — a bestseller list, not a sample (Zhang et al. 2025). The 3 framings a move produces are subject to this too. So before evaluating, over-generate — 5 to 8 candidates rather than 3 — and write next to each one the probability, 0 to 1, that a generator still inside the old frame would have produced it. Drop everything above the threshold; the remainder is the move's actual output. Start the threshold at 0.3 and lower it if the survivors still read as adjacent. Writing the number is the mechanism, not decoration: prompts that request a distribution with verbalized probabilities recover diversity that prompts for instances or lists do not, quality holds when the candidates are reasoned rather than listed, and lowering the stated threshold moves output further into the tail. The gain scales with model capability; on a small model the sift adds burden without adding distance.
以下三条规则适用于下方每一种动作。违反这些规则,输出可能带有创意构思的外观,但结构上仍与此前完全相同。
  1. 先生成,后评估。 De Bono 的核心区分:横向思维关注的是思维移动的价值(movement value),而不是真值。Provocation 不是提案。只有在动作产出 3 个以上候选框架后,才进行评估。
  2. 一次只做一个动作,并全情投入。 不要把五种技术轮番当成菜单来展示。选择与诊断最匹配的动作,充分执行,呈现被它“打散出来”的内容,然后停止。菜单只会制造噪音;投入才会产生距离。
  3. 输出框架,而不是点子。 生成式动作的交付物通常是对问题的新表述或新的切入角度,而不是旧框架中的又一个候选方案。如果不使用这个动作也可能产出该结果,就说明动作没有真正生效。
停止条件。 当动作产出 3 个以上非平凡框架,或产出 1 个能够重组问题的框架时停止(一个尖锐的意外发现胜过五个相邻的选项)。不要因为列表看起来不够长就继续生成——数量不是产物。
点火测试(The fire test)。 每次动作后问:不使用这个动作,也可能出现该输出吗? 如果是,动作没有生效。要么更彻底地投入(继续推进 provocation,使 reframe 更激进,重新抽取随机词,改换另一轴进行 inversion),要么该动作与卡住模式不匹配——重新诊断并选择更匹配的动作。失误后的重新诊断不是菜单轮换;菜单轮换是指在没有投入的情况下轮番尝试各种技术。一次只做一个动作,充分执行;若未命中,先诊断原因,再做下一个。
尾部筛选(Tail sift)。 给数字加上标准的点火测试。后训练模型带有典型性偏差(typicality bias):要求一个候选时,它们会返回众数;要求列表时,它们会返回 top-k 模式——那是一份畅销书榜单,而不是一次采样(Zhang et al. 2025)。某个动作产出的 3 个框架同样受此影响。因此,在评估之前要过度生成:生成 5 到 8 个候选,而不是 3 个——并在每个候选旁写下 0 到 1 之间的概率,表示仍处于旧框架中的生成者产出它的可能性。删除所有高于阈值的候选;其余才是该动作真正的输出。阈值从 0.3 开始,如果幸存结果读起来仍然相邻,就继续降低。写下数字是一种机制,不是装饰:要求给出带显式概率的分布,比要求给出实例或列表更能恢复多样性;当候选经过推理而非仅被列出时,质量得以保持;降低明示阈值会让输出进一步进入分布尾部。收益随模型能力而增长;在小模型上,尾部筛选只会增加负担,却不会增加距离。

Diagnostic → Move

诊断 → 动作

Match the stuck-pattern to the move. When unsure, default to Reframe.
If the stuck-pattern is…Reach for…
Framing feels forced ("must be X or Y")Reframe — change the verb, subject, scope, or level
Generator keeps returning near-duplicatesRandom stimulus — force an unrelated concept into the frame
Obvious answer is wrong but you can't see past itProvocation (Po) — state something impossible, extract movement
Iterating on an existing artifactSCAMPER — seven structured transforms
Stuck on "how do we make X succeed?"Inversion — ask "how do we guarantee X fails?" then negate
Problem is defined entirely in one domain's vocabularyStructured analogy — map objects and relations by function into a distant domain, search there
Every solution is blocked by a constraintConstraint play — remove it ("assume magic"), or add an absurd one ("must fit in a tweet")
Two known examples, no theory of the space between/beyond themFamily traversal — name the shared family, walk it to its limits
根据卡住的模式选择动作。不确定时,默认使用 Reframe。
如果卡住的模式是……应采用……
框架显得受限(“必须是 X 或 Y”)Reframe——改变动词、主语、范围或层级
生成器持续返回近似重复项Random stimulus——把一个不相关的概念强行带入框架
明显答案看起来是错的,但无法越过它Provocation (Po)——陈述某种不可能之事,从中提取推进力
正在迭代一个现有产物SCAMPER——七种结构化变换
卡在“如何让 X 成功?”Inversion——先问“如何保证 X 失败?”,再取反
问题完全由某一领域的词汇定义Structured analogy——按功能将对象和关系映射到遥远领域,再到那里搜索
每种解法都被某个约束阻断Constraint play——移除约束(“假设魔法存在”),或添加荒谬约束(“必须能放进一条推文”)
已知两个示例,却没有关于二者之间或之外空间的理论Family traversal——命名它们共享的家族,并一路走到其边界

Reframe

Reframe(问题重构)

The problem-as-stated is rarely the problem-to-solve. Mutate the sentence:
  • Change the verb: "reduce X" → "redistribute X", "time-shift X", "prevent X from mattering"
  • Change the subject: "our team can't ship faster" → "reviewers are the bottleneck" → "the artifact is too reviewable"
  • Change the scope: zoom out (whose problem is this upstream?) or zoom in (which one user, which one minute?)
  • Change the frame: from "problem to fix" to "signal to interpret"
Produce 3 reframings. Fired if: at least one makes the original statement sound naive, or shifts who owns the problem.
按原样表述的问题很少就是真正需要解决的问题。改写这句话:
  • 改变动词:“减少 X”→“重新分配 X”“错开 X 的时间”“防止 X 产生影响”
  • 改变主语:“我们的团队无法更快交付”→“评审人员是瓶颈”→“这个产物太容易评审”
  • 改变范围:向外放大(这上游是谁的问题?)或向内缩小(哪一位用户?哪一分钟?)
  • 改变框架:从“需要修复的问题”变成“需要解读的信号”
产出 3 个 reframe。触发条件: 至少有一个让原始表述显得幼稚,或改变了问题的归属方。

Provocation (Po)

Provocation (Po)(挑衅式刺激)

Edward de Bono's method. Prefix a deliberately wrong, impossible, or absurd statement with
Po:
to signal it is not a proposal — it is a stimulus. Then extract movement: what principle, consequence, or adjacent idea does this surface?
Four recipes (de Bono's formal provocations):
  • Escape: remove an essential feature. Po: the database has no writes.
  • Reversal: flip the causal direction. Po: users pay us to NOT use the product.
  • Exaggeration: push a quantity to the absurd limit. Po: onboarding takes six months.
  • Wishful thinking: assume impossible capability. Po: we know what the user will click next week.
The canonical example: a factory pollutes a river. Po: the factory is downstream of itself. Impossible, but it generates: move intake downstream of discharge. Internal incentive to not pollute. Closed-loop water. The provocation is discarded; the movement stays.
Fired if: the provocation is genuinely impossible or absurd (not merely edgy), AND extracting movement yields a principle that survives translation back to the real constraints. If the "provocation" is a thing you could actually do, it's a proposal, not a Po — push it further.
Edward de Bono 的方法。用
Po:
作前缀,陈述一个故意错误、不可能或荒谬的说法,以表明它不是提案,而是刺激。然后提取推进力:它浮现出什么原则、后果或相邻想法?
四种配方(de Bono 的正式 provocations):
  • Escape(逃离):移除一个必要特征。Po: 数据库没有写入操作。
  • Reversal(反转):颠倒因果方向。Po: 用户付钱让我们不要使用该产品。
  • Exaggeration(夸张):把某个数量推向荒谬极限。Po: 新手引导耗时六个月。
  • Wishful thinking(异想天开):假设一种不可能的能力。Po: 我们知道用户下周会点击什么。
经典示例:一家工厂污染河流。Po: 工厂位于自身的下游。 这不可能,却能生成:将取水口移到排放下游。形成内部不污染的激励。实现闭环用水。Provocation 被丢弃,推进成果保留。
触发条件: 该 provocation 确实不可能或荒谬(而不只是有点尖锐),并且提取推进力后能产生一项可转回现实约束的原则。如果这个“provocation”其实是你真能做的事情,那它就是提案,不是 Po——把它推得更远。

Random stimulus

Random stimulus(随机刺激)

Pick a word, object, or domain with no connection to the problem. Force a connection. The forced-feel is the point — it routes around the habituated pathway.
Template: "How is [problem] like [random]?" then "What does that suggest?"
Sourcing for humans: a random Wikipedia article, a nearby physical object, an Oblique Strategies card, a concept from an unrelated field on the current desk. Commit to the first thing you land on; re-rolling defeats the method.
Sourcing for an LLM agent: an LLM asked directly for a random word does not produce one — the same attention that locked the frame picks a word adjacent to it, and post-training biases the pick toward whatever is typical. Two sources work:
  • External: ask the user for a word, any word; fetch a random Wikipedia article; draw an Oblique Strategy by tool.
  • Internal, hashed — String Seed of Thought (Misaki & Akiba 2025). Write out a long random string (40+ characters, mixed letters, digits and symbols, no visible pattern). Then write out the reduction — sum the character codes, or compute a rolling hash — modulo the size of a pre-listed vocabulary, and take the word at that index.
    references/stimulus-vocabulary.md
    holds 128 nouns from distant domains for exactly this; the Oblique Strategies deck works the same way. Measured: the recipe reaches near-PRNG faithfulness on long-reasoning models, and on open-ended generation it beat both an injected PRNG seed and a random-number tool call, because the string can be re-hashed for several local choices and the derivation is on the page. Two failure modes, both measured: a lazy extraction that reads only the first character (LLM-generated strings have strong positional bias — 947 of 1000 QwQ-32B strings opened with "7"), and skipping the written arithmetic, after which reasoning models hallucinate the result. Use the whole string; write the sum. Models under ~8B cannot execute the reduction reliably — hand them an external source.
Fired if: the connection is genuinely forced (the first 10 seconds feel wrong), and working through the force produces an angle that was not in your prior search space. If the random word feels "relevant" immediately, you re-rolled, picked from attention, or read one character of the seed — get a new one.
选一个与问题毫无关联的词、物体或领域,强行建立联系。刻意的不协调正是重点——它会绕开已经形成习惯的路径。
模板:“[问题]如何像[随机事物]?”,然后问:“这说明了什么?”
人类的取材方式: 随机 Wikipedia 文章、附近的实体物品、一张 Oblique Strategies 卡,或桌面上来自无关领域的概念。承诺使用第一个想到的事物;重新抽取会破坏这种方法。
LLM Agent 的取材方式: 直接要求 LLM 给出一个随机词并不会得到真正随机的结果——正是锁定框架的同一套注意力机制,会选取与框架相邻的词,而后训练偏差又会使选择偏向典型事物。两种来源有效:
  • 外部来源:请用户提供任意一个词;抓取一篇随机 Wikipedia 文章;通过工具抽取一张 Oblique Strategies 卡。
  • 内部哈希方式——String Seed of Thought(Misaki & Akiba 2025)。写出一长串随机字符串(40 个以上字符,混合字母、数字和符号,不呈现可见模式)。然后写出归约过程——对字符码求和,或计算滚动哈希——对预先列出的词汇表大小取模,再取该索引处的词。
    references/stimulus-vocabulary.md
    专门提供了来自遥远领域的 128 个名词;Oblique Strategies 卡组也采用同样方式。实测:这套方法在长推理模型上可达到接近 PRNG 的忠实度;在开放式生成中,它优于注入 PRNG 种子和调用随机数工具,因为同一字符串可重新哈希以支持若干局部选择,而且推导过程保留在页面上。两种实测失败模式:偷懒式提取只读取首字符(LLM 生成的字符串存在很强的位置偏差——1000 个 QwQ-32B 字符串中有 947 个以“7”开头),以及跳过书面算术后推理模型会幻觉出结果。使用整个字符串;写出求和过程。参数低于约 8B 的模型无法可靠执行该归约——为它们提供外部来源。
触发条件: 这种联系确实是强行建立的(最初的 10 秒感觉不对),并且顺着这种强行联系能得出一个此前搜索空间中不存在的角度。如果随机词立刻显得“相关”,说明你重新抽取了、从注意力中挑选了,或只读了种子字符串的一个字符——那就重新来一次。

SCAMPER

SCAMPER

For iterating on an existing artifact. Walk the seven prompts once; do not pick favorites in advance.
  • Substitute — swap a component, material, person, step
  • Combine — merge with something else, including something it competes with
  • Adapt — borrow a mechanism from elsewhere that solves a related problem
  • Modify / magnify / minify — change a dimension, frequency, or weight drastically
  • Put to another use — who else could use this, for what?
  • Eliminate — what happens if this part simply is not there?
  • Reverse / rearrange — swap order, roles, or polarity
Fired if: at least one prompt produced a candidate you would not have reached by asking "what's a better version of this?". If all seven outputs are adjacent polish, the artifact is not the unit of analysis — zoom out and try Reframe.
用于迭代现有产物。依次走完七个提示,不要提前挑选喜欢的方向。
  • Substitute(替换)——替换组件、材料、人员或步骤
  • Combine(组合)——与其他事物合并,包括与竞争对象合并
  • Adapt(适应)——借用其他地方解决相关问题的机制
  • Modify / magnify / minify(修改、放大或缩小)——大幅改变一个维度、频率或权重
  • Put to another use(另作他用)——其他人还能拿它做什么?
  • Eliminate(消除)——如果这个部分根本不存在,会发生什么?
  • Reverse / rearrange(反转或重新排列)——交换顺序、角色或极性
触发条件: 至少一个提示产生了通过“怎样做一个更好的版本?”无法得到的候选。如果七种输出都只是相邻的润色,那么产物就不是分析单元——向外放大并尝试 Reframe。

Inversion

Inversion(逆向思维)

Solve the inverse problem, then negate the solution. Works because failure modes are often more concrete than success paths.
  • "How would I guarantee this fails?" → each failure mode is a protective requirement
  • "What would the worst possible version look like?" → the inverse shape of the good version
  • "If an adversary wanted us to choose X, why?" → surfaces the hidden trap in X
Fired if: inverting surfaced a concrete risk, mechanism, or incentive the forward framing was hiding. If negating the inverted answer gives you the same thing you already had, the inversion was too symmetric — invert on a different axis (goals → incentives, success → unobservable, user → operator).
求解逆问题,再对答案取反。之所以有效,是因为失败模式往往比成功路径更具体。
  • “怎样做才能保证它失败?”→每种失败模式都是一项保护性要求
  • “最糟糕的版本会是什么样?”→好版本的逆向形态
  • “如果对手想让我们选择 X,他为什么要这样做?”→揭示 X 中隐藏的陷阱
触发条件: 逆向过程浮现出正向框架隐藏的具体风险、机制或激励。如果把逆向答案取反后得到的仍是原有答案,说明 inversion 过于对称——换一个轴进行 inversion(目标 → 激励,成功 → 不可观测,用户 → 操作者)。

Structured analogy (perspective shift)

Structured analogy(结构类比,视角转换)

Move the problem into a distant domain by its relational structure, not by asking the distant domain a question. "How would biology solve this?" is the cross-domain baseline in Shen, Druckmann & Zou (2026), and it collapses almost as hard as no domain prompt at all: across 150 generations per problem, about 5% of proposed domains were unique, and solution diversity (Vendi score) was 8.3 against 5.8 for the unconstrained baseline. Explicit structure-mapping scored 90–173% higher on solution diversity, produced solutions judged novel 50–69% of the time against 1.6–38% for the baselines, and reached domains further from the problem. The written mapping is what changes the outcome.
Four steps, after Gentner's structure-mapping theory:
  1. Extract. List the problem's objects with their functional roles, and the relations between them — predicates over two or more objects ("a stationary source releases a substance into a heterogeneous medium"). Attributes of single objects are not mapped.
  2. Map by function. Pick a distant domain and write object ↔ object pairs with the reason each pair holds. "Delivers a payload" is a mapping basis; "is a liquid" is not. Partial coverage is allowed — the analogy needs a subset of the relations, not all of them.
  3. Search the target side. Find an existing, named method in the distant domain that operates on the mapped objects and preserves the shared relations. Search there, not for solutions to the original problem. (Drug delivery ↔ groundwater contamination gave reactive-transport plume models; EEG source localization ↔ seismology gave the double-difference earthquake location algorithm.)
  4. Transfer back. Re-substitute the source objects and state what the method becomes in the original domain.
Domain menu, when step 2 needs a starting point: natural (biology, ecology, geology), trade (kitchen, ER triage, shipping dock), role (CFO, child, historian, adversary), scale (100x, 1/100x).
Fired if: the mapped domain is one the problem's own literature would not cite, AND step 3 returned a named, existing method — not a metaphor. If the object pairs match by resemblance rather than role, or the "method" is the original problem restated in new nouns, the mapping was surface-level; redo step 2 with a further domain.
依据关系结构将问题迁入遥远领域,而不是向遥远领域提出一个问题。“生物学会如何解决这个问题?”是 Shen、Druckmann & Zou(2026)采用的跨领域基线,但它几乎和完全没有领域提示一样容易坍缩:每个问题生成 150 次时,约 5% 的提议领域是独特的;解法多样性(Vendi score)为 8.3,而不受约束的基线为 5.8。显式进行结构映射后,解法多样性提高 90%–173%,有 50%–69% 的解法被判定为新颖,而基线仅为 1.6%–38%;映射所得领域也比原问题领域更遥远。书面映射正是改变结果的关键。
依据 Gentner 的结构映射理论,分四步执行:
  1. 提取(Extract)。 列出问题中的对象及其功能角色,以及对象之间的关系——即作用于两个或更多对象的谓词(“一个静止的源头在异质介质中释放某种物质”)。单个对象的属性不参与映射。
  2. 按功能映射(Map by function)。 选择一个遥远领域,写出对象 ↔ 对象的对象对及每个配对成立的原因。“承载载荷”是映射依据;“是液体”则不是。允许部分覆盖——类比只需要包含部分关系,而非全部关系。
  3. 搜索目标领域(Search the target side)。 在遥远领域中寻找一种现有的、有名称的方法,该方法作用于已映射的对象,并保留共同关系。在那里搜索,而不是直接寻找原问题的解法。(药物递送 ↔ 地下水污染产生了反应输运羽流模型;EEG 源定位 ↔ 地震学产生了双差地震定位算法。)
  4. 迁移回来(Transfer back)。 重新代入源对象,并说明该方法在原始领域中变成了什么。
第 2 步需要一个起点时,可使用以下领域菜单:自然领域(生物学、生态学、地质学)、行业领域(厨房、急诊室分诊、装卸码头)、角色领域(CFO、孩子、历史学家、对手)、尺度领域(100 倍、1/100 倍)。
触发条件: 映射到的领域不会出现在问题自身所属的文献中,并且第 3 步返回了一种现有的、有名称的方法——而不只是隐喻。如果对象对是基于相似性而非功能角色进行匹配,或者所谓的“方法”只是用新名词重述原问题,说明映射只停留在表层——重新执行第 2 步,并选择更遥远的领域。

Constraint play

Constraint play(约束游戏)

Constraints define the solution space. Move them deliberately.
  • Remove: "assume infinite budget / time / compute / permission" — what opens up?
  • Add absurd: "must fit in a tweet", "under $5", "no code", "one meeting only", "physical-only"
  • Invert: the constraint becomes the feature. Limited time → event-driven. Small budget → tiny team as the pitch.
Fired if: a relaxed-constraint solution reveals what you actually value (not just what you'll accept), or an added-constraint solution is sharper than the unconstrained one. If both feel like the same answer with a different budget, the binding constraint is elsewhere — find it.
约束定义了解法空间。刻意地移动约束。
  • 移除:“假设预算、时间、算力或权限无限”——这样会打开什么空间?
  • 添加荒谬约束:“必须能放进一条推文”“预算低于 5 美元”“不能写代码”“只能开一次会”“只能采用实体形式”
  • 反转:让约束变成特性。时间有限 → 事件驱动。预算有限 → 把小团队本身作为卖点。
触发条件: 放宽约束后的解法揭示了你真正重视的东西(而不只是你愿意接受的东西),或者添加约束后的解法比无约束解法更锐利。如果两者感觉仍像同一个答案,只是预算不同,说明真正起作用的约束在别处——把它找出来。

Family traversal

Family traversal(家族遍历)

For when you hold two (or more) related instances and generation keeps orbiting them. The pair is not the object — the parametrized family containing both is. Sub-moves in descending observed yield:
  1. Name the face. State the family or frontier both instances lie on, and its parameter. (Two embedding quantizers → the rate–distortion frontier, parametrized by bits per dimension.) If you cannot name the parameter, you have not found the family yet.
  2. Walk to the limits. Continue past both anchors to the family's extreme points — limits are where members change character. (The 0-bit limit of vector search is ranking by document prior; the zero-distortion limit is exact symbolic addressing — which revealed two "unrelated" projects as endpoints of one frontier.)
  3. Swap the bound object. Name the supporting constraint that walls the family — the bound that cannot be crossed. Since crossing is impossible within the model, change what the constraint binds. (Cannot beat rate–distortion for embeddings → quantize the weights, or the knowledge, instead.)
  4. Probe the chord. Mixtures and blends of the anchors (dithering, ensembles, fusion weights). Lowest yield — blends average rather than extrapolate — but cheap. Run last, not first.
Then sharpen and verify: the traversal's real product is questions precise enough to have derivable answers; the discovery happens in the derivation and a cheap measurement, not in the geometry. (A frontier framing of an addressing scheme implied a capacity law, j² ≤ 2^(significand bits); sixty seconds of numpy confirmed a cliff at exactly N = 4096, closing a four-month-old empirical mystery.) Without this step the move outputs taxonomy, not generation.
Fired if: a limit point or constraint-swap landed outside the prior search space, AND at least one output is a checkable claim. If the output is only a tidy classification of the anchors, the move stalled — push further along the edge or swap the constraint.
Caution: do not equate the interior of the space with novelty. In high dimensions essentially all operation is already extrapolation outside the training hull (Balestriero & LeCun 2021), and mixtures of known points are averages. The generative directions are the limits and the constraint-swaps; the chord is a probe, not a doctrine.
适用于你已经掌握两个或更多相关实例,而生成过程仍不断围绕它们打转的情况。对象不是这两个实例,而是包含它们的参数化家族。
按观察到的产出率从高到低排列各子动作:
  1. 命名所在面(Name the face)。 陈述两个实例共同位于的家族或前沿,以及它的参数。(两个 embedding quantizer → rate–distortion 前沿,以每维 bit 数为参数。)如果无法说出参数,就还没有找到家族。
  2. 走向极限(Walk to the limits)。 越过两个锚点,继续走到家族的极端点——极限正是成员发生性质变化的地方。(向量搜索的 0-bit 极限是按文档先验排序;zero-distortion 极限是精确的符号寻址——这一发现把两个看似无关的项目呈现为同一前沿的两个端点。)
  3. 替换约束对象(Swap the bound object)。 说出为家族设下边界的支撑约束——在当前模型内无法跨越的界限。由于无法在模型内部跨越它,就改变该约束所绑定的对象。(无法让 embeddings 超越 rate–distortion → 转而量化权重或知识。)
  4. 探测弦线(Probe the chord)。 混合和调和锚点(dithering、ensembles、fusion weights)。产出率最低——混合是在求平均,而不是外推——但成本很低,因此最后执行,而不是最先执行。
随后锐化并验证:遍历真正的产物,是足够精确且能够推导出答案的问题;发现发生在推导和一次低成本测量中,而不是几何结构中。(一种关于寻址方案的前沿表述暗示了容量定律 j² ≤ 2^(significand bits);用 NumPy 测量 60 秒,就确认了在 N = 4096 处恰好存在的断崖,从而解开了一个悬而未决四个月的实证谜题。)缺少这一步,动作只会输出分类体系,而不是生成新内容。
触发条件: 某个极限点或约束替换落在先前搜索空间之外,并且至少一个输出是可检验的主张。如果输出只是对锚点进行了整洁分类,动作便已停滞——沿边缘继续推进,或替换约束。
注意:不要把空间内部等同于新颖性。在高维空间中,几乎所有操作实际上都已经是训练凸包之外的外推(Balestriero & LeCun 2021),而已知点的混合只是平均值。生成方向是极限与约束替换;弦只是探针,不是信条。

Applying the skill to an agent's own reasoning

将此 skill 应用于 Agent 自身的推理

LLM agents exhibit a context-bound analog of functional fixedness: attention concentrates on current framing and generates variations of it. A second mechanism compounds it and does not depend on context: preference data favors familiar text, so post-training sharpens the policy toward the modal continuation for any prompt (Zhang et al. 2025, Theorem D.1) — which is why "give me five alternatives" returns five near-neighbors even in a fresh context. Signals this is happening:
  • The nth iteration has the same structure as the first
  • The agent has rejected the same class of option three times with similar reasoning
  • The plan has a step labeled "brainstorm" that is producing adjacent bullets
When detected, the fix is the same: pick one move from the diagnostic table, execute it on the agent's own current framing, and explicitly write out the new framing(s) before resuming work. The write-out is essential — a framing that stays implicit in attention gets re-absorbed into the previous frame.
LLM Agent 会表现出一种与上下文绑定的功能固着类比:注意力集中在当前框架上,并生成其中的变体。第二种机制会加剧这一问题,且不依赖上下文:偏好数据偏爱熟悉的文本,因此后训练会让策略在面对任何提示时都更加偏向最典型的续写(Zhang et al. 2025, Theorem D.1)——这就是为什么“给我五个替代方案”会返回五个近邻选项,即便处于全新上下文中。出现以下信号即说明正在发生:
  • 第 n 次迭代与第一次具有相同结构
  • Agent 已经用相似理由拒绝同一类选项三次
  • 计划中有一个名为“头脑风暴”的步骤,却只产出彼此相邻的项目符号
检测到这些信号时,修复方法相同:从诊断表中选择一个动作,对 Agent 自身的当前框架执行,并在继续工作前明确写出新的框架。书面输出至关重要——如果一个框架始终隐含在注意力中,就会再次被旧框架吸收。

What this skill does NOT do

此 skill 不做什么

  • Does not evaluate. Pair with challenging after generation if the artifact is high-stakes.
  • Does not do MECE coverage. Use tiling-tree for exhaustive partitioning.
  • Does not synthesize multiple viewpoints. Use convening-experts for collaborative multi-role panels.
  • Does not produce long idea lists. A three-reframe output with one surprising move beats a fifty-item brainstorm in the original frame.
  • 不进行评估。 如果产物 stakes 较高,请在生成之后搭配使用 challenging。
  • 不进行 MECE 覆盖。 如需穷尽式分区,请使用 tiling-tree。
  • 不综合多个观点。 如需多角色协作面板,请使用 convening-experts。
  • 不生成长篇点子列表。 一个包含意外动作的 3 个 reframe 输出,胜过旧框架中的 50 项头脑风暴。

Canonical references (progressive disclosure)

标准参考资料(渐进式披露)

Load these only when the user wants depth on a specific technique.
  • Lateral thinking, provocation, Po, random stimulus — Edward de Bono. Primary: Wikipedia: Lateral thinking, Wikipedia: Po. Essay: de Bono, "Serious Creativity". Books: Lateral Thinking (1970), Serious Creativity (1992).
  • SCAMPER — Bob Eberle, SCAMPER: Games for Imagination Development (1971), built on Alex Osborn's Applied Imagination (1953) checklist. Summary: Wikipedia: SCAMPER.
  • Oblique Strategies — Brian Eno & Peter Schmidt (1974–2001, five editions). Summary: Wikipedia: Oblique Strategies. Full deck: mattrickard.com/list-of-all-oblique-strategies. Draw one at random when reaching for random stimulus.
  • Functional fixedness (the cognitive bias this skill counters) — Karl Duncker, originally Zur Psychologie des produktiven Denkens (1935); English translation On Problem-Solving (1945), doi:10.1037/h0093599. The candle problem is the canonical demonstration.
  • Extrapolation vs interpolation in high dimensions (why "interior = novelty" is wrong) — Balestriero, Pesenti & LeCun, "Learning in High Dimension Always Amounts to Extrapolation," arXiv:2110.09485.
  • Typicality bias and mode collapse; verbalized-probability prompting (the tail sift) — Zhang, Yu, Chong, Sicilia, Tomz, Manning & Shi, "Verbalized Sampling: How to Mitigate Mode Collapse and Unlock LLM Diversity," arXiv:2510.01171. Distribution-level prompts with probabilities raised creative-writing diversity 1.6–2.1× over direct prompting; a threshold in the prompt tunes how far into the tail; gains grow with model scale.
  • String Seed of Thought (the hashed internal random stimulus) — Misaki & Akiba, Sakana AI, "String Seed of Thought: Prompting LLMs for Distribution-Faithful and Diverse Generation," arXiv:2510.21150. Total-variation distance to the target distribution shrinks with string length even under autoregressive correlation (Thm 4.2); §D.5 for the first-character failure, §D.6 for the comparison against injected seeds and tool calls.
  • Structure-mapping theory of analogy — Gentner, "Structure-Mapping: A Theoretical Framework for Analogy," Cognitive Science 7(2), 1983, doi:10.1207/s15516709cog0702_3. Relations map, attributes do not.
  • Analogical reasoning as a diversity engine (the structured-analogy procedure) — Shen, Druckmann & Zou, Stanford, "Unlocking LLM Creativity in Science through Analogical Reasoning," arXiv:2605.11258. Extraction and search prompts in §G.1; four AR-generated methods implemented and benchmarked in biomedicine.
  • Design fixation and generative-AI specific failure modes — Wadinambiarachchi, Kelly, Pareek, Zhou & Velloso, "The Effects of Generative AI on Design Fixation and Divergent Thinking," CHI 2024, paper 380, doi:10.1145/3613904.3642919 (arXiv:2403.11164). N=60 visual ideation experiment: participants with AI image-generator support showed higher fixation on the initial example, and lower fluency, variety, and originality than the no-support baseline. Directly relevant when the fixation is coming from an LLM's own prior outputs.
仅当用户希望深入了解某项具体技术时,才加载以下内容。
  • Lateral thinking、provocation、Po、random stimulus——Edward de Bono。主要来源:Wikipedia: Lateral thinking、Wikipedia: Po。文章:de Bono, “Serious Creativity”。书籍:Lateral Thinking(1970)、Serious Creativity(1992)。
  • SCAMPER——Bob Eberle,SCAMPER: Games for Imagination Development(1971),基于 Alex Osborn 的 Applied Imagination(1953)检查清单。摘要:Wikipedia: SCAMPER。
  • Oblique Strategies——Brian Eno 与 Peter Schmidt(1974–2001,共五版)。摘要:Wikipedia: Oblique Strategies。完整卡组:mattrickad.com/list-of-all-oblique-strategies。使用随机刺激时抽取一张。
  • Functional fixedness(此 skill 所对抗的认知偏差)——Karl Duncker,原始论文为 Zur Psychologie des produktiven Denkens(1935);英译本 On Problem-Solving(1945),doi:10.1037/h0093599。蜡烛问题是经典演示。
  • 高维空间中的外推与内插(为何“内部 = 新颖”是错误的)——Balestriero、Pesenti 与 LeCun,“Learning in High Dimension Always Amounts to Extrapolation,” arXiv:2110.09485。
  • 典型性偏差与模式坍缩;显式概率提示(尾部筛选)——Zhang、Yu、Chong、Sicilia、Tomz、Manning 与 Shi,“Verbalized Sampling: How to Mitigate Mode Collapse and Unlock LLM Diversity,” arXiv:2510.01171。分布级提示配合概率,可将创意写作多样性提升至直接提示的 1.6–2.1 倍;提示中的阈值可调节输出进入尾部的程度;收益随模型规模增长。
  • String Seed of Thought(哈希式内部随机刺激)——Misaki 与 Akiba,Sakana AI,“String Seed of Thought: Prompting LLMs for Distribution-Faithful and Diverse Generation,” arXiv:2510.21150。在满足自回归相关性的情况下,与目标分布的总变差距离会随字符串长度缩短(Thm 4.2);§D.5 介绍首字符失败问题,§D.6 比较自注入种子与工具调用。
  • 类比的结构映射理论——Gentner,“Structure-Mapping: A Theoretical Framework for Analogy,” Cognitive Science 7(2), 1983,doi:10.1207/s15516709cog0702_3。映射的是关系,而不是属性。
  • 作为多样性引擎的类比推理(结构类比流程)——Shen、Druckmann 与 Zou,Stanford,“Unlocking LLM Creativity in Science through Analogical Reasoning,” arXiv:2605.11258。提取与搜索提示见 §G.1;四种由 AR 生成的方法已在生物医学领域实现并完成基准测试。
  • 设计固着与生成式 AI 特有的失败模式——Wadinambiarachchi、Kelly、Pareek、Zhou 与 Velloso,“The Effects of Generative AI on Design Fixation and Divergent Thinking,” CHI 2024,论文 380,doi:10.1145/3613904.3642919(arXiv:2403.11164)。N=60 的视觉构思实验:获得 AI 图像生成器支持的参与者,对初始示例表现出更高的固着程度,其流畅性、多样性和原创性均低于无支持条件的基线。当固着来自 LLM 自身先前的输出时,这一点尤其相关。

Quick-reference card

快速参考卡

DIAGNOSE: What kind of stuck?
  → framing forced        : REFRAME
  → near-duplicates       : RANDOM STIMULUS
  → can't see past obvious: PROVOCATION (Po)
  → iterating an artifact : SCAMPER
  → chasing success       : INVERSION
  → one domain vocabulary : STRUCTURED ANALOGY
  → blocked by constraint : CONSTRAINT PLAY
  → two examples, no theory: FAMILY TRAVERSAL

DISCIPLINE:
  1. Generation before evaluation
  2. One move, committed
  3. Output framings, not ideas
  TAIL SIFT: over-generate 5-8, tag P(old frame reaches it), drop > 0.3

STOP when: 3+ non-trivial framings produced, or one surprising framing that reorganizes the problem.
DIAGNOSE: What kind of stuck?
  → framing forced        : REFRAME
  → near-duplicates       : RANDOM STIMULUS
  → can't see past obvious: PROVOCATION (Po)
  → iterating an artifact : SCAMPER
  → chasing success       : INVERSION
  → one domain vocabulary : STRUCTURED ANALOGY
  → blocked by constraint : CONSTRAINT PLAY
  → two examples, no theory: FAMILY TRAVERSAL

DISCIPLINE:
  1. Generation before evaluation
  2. One move, committed
  3. Output framings, not ideas
  TAIL SIFT: over-generate 5-8, tag P(old frame reaches it), drop > 0.3

STOP when: 3+ non-trivial framings produced, or one surprising framing that reorganizes the problem.