一九〇〇年八月八日 · 巴黎August 8, 1900 · Paris
二〇二六年七月 · 智能时代July 2026 · The Age of Intelligence
1900 · PARIS —— 2026 · THE AGE OF AI

二十三问Twenty-Three Problems

人工智能的希尔伯特问题The Hilbert Problems of Artificial Intelligence
The Twenty-Three Problems of Artificial Intelligence
我们当中有谁不想揭开未来的面纱,看一看这门科学在未来世纪里前进的前景和奥秘呢? —— 大卫·希尔伯特,第二届国际数学家大会开场白,巴黎,1900Who among us would not be glad to lift the veil behind which the future lies hidden, to cast a glance at the prospects and the secrets of this science’s advance in the centuries to come? — David Hilbert, opening address of the Second International Congress of Mathematicians, Paris, 1900
五卷·二十三问·约两万言·深读约一小时Five Books·Twenty-Three Problems·About Twenty Thousand Words·About an Hour of Close Reading

序言Preface

Preface

一九〇〇年八月八日,巴黎,第二届国际数学家大会。三十八岁的大卫·希尔伯特走上讲台,提出了二十三个问题。此后一百年,这份清单如同灯塔:它并未预言数学的全部,却让一代代数学家知道该往何处挖掘。黎曼猜想至今悬而未决,连续统假设的结局出人意料,第十问的答案竟是"不可解"——但正是这些问题本身,塑造了整个二十世纪的数学。August 8, 1900, Paris, the Second International Congress of Mathematicians. David Hilbert, thirty-eight years of age, mounted the platform and set forth twenty-three problems. For the hundred years that followed, this list stood like a lighthouse: it did not foretell the whole of mathematics, yet it let one generation of mathematicians after another know where to dig. The Riemann hypothesis hangs unresolved to this day, the fate of the continuum hypothesis confounded all expectation, and the answer to the tenth problem turned out to be “unsolvable”—but it was these very problems that shaped the mathematics of the entire twentieth century.

今天的人工智能,正处在与那一年相似的时刻。工程狂飙突进,理解远远落后;能力逐月刷新,根基仍在悬空。我们训练出了在奥林匹克数学与编程竞赛中超越绝大多数人类的系统,却无法解释它内部发生了什么;我们让它参与书写文明的文本,却尚未确定它与真、与善、与我们自身的关系。热力学诞生于蒸汽机之后——今天的智能工程,同样跑在了智能科学的前面。Artificial intelligence today stands at a moment much like that year. Engineering charges ahead, understanding lags far behind; capabilities are renewed month by month, the foundations still hang in the void. We have trained systems that surpass the great majority of human beings in olympiad mathematics and in programming contests, yet we cannot explain what takes place within them; we have let them take part in writing the texts of civilization, yet we have not settled their relation to the true, to the good, or to ourselves. Thermodynamics was born after the steam engine—the engineering of intelligence today has likewise run ahead of the science of intelligence.

希尔伯特为"好问题"立过标准:清晰得能向街上遇到的第一个人讲明白;困难得令人望而生畏,却并非全然不可攻;而解决之日,回报深远。以下二十三问依此遴选,分作五卷:基础问理论之根,能力问疆域之界,对齐问缰绳之在,基座与度量问物理与标尺之限,文明问共存之道。与一九〇〇年不同,这份清单不再属于单一学科——它横跨数学、认知科学、工程、哲学与政治;也与那份清单不同,其中若干问题,带着倒计时。Hilbert laid down a standard for a “good problem”: clear enough to be made plain to the first person one meets in the street; difficult enough to be daunting, yet not wholly beyond assault; and, on the day it is solved, far-reaching in its reward. The twenty-three problems below have been chosen by that standard and divided into five books: Foundations asks after the roots of theory, Capabilities after the bounds of the territory, Alignment after where the reins lie, Substrate and Measurement after the limits set by physics and by the yardstick, Civilization after the way of coexistence. Unlike the year 1900, this list no longer belongs to a single discipline—it spans mathematics, cognitive science, engineering, philosophy and politics; and unlike that list too, several of these problems come with a countdown.

这是一张地图,不是一份判决。它必有偏见与遗漏,正如希尔伯特的清单同样有之。若它能让某位读者像当年的年轻数学家凝视那二十三问一样,凝视其中一问,并决定投身其中——它的目的就达到了。This is a map, not a verdict. It must have its biases and its omissions, just as Hilbert’s list had its own. If it can bring some reader to gaze upon one of these problems as the young mathematicians of that day gazed upon those twenty-three, and to resolve to give himself to it—then its purpose is achieved.

总览Overview

The Problems at a Glance
LIBER IV卷四 · 基座与度量之问Book IV · Substrate & MeasurementSubstrate & Measurement
20能耗鸿沟The Energy Gap长程难题Long-Range Problem 21评估科学The Science of Evaluation攻坚之中Under Assault
I

基础之问Foundations

Foundations
第一问 至 第六问Problem I through Problem VI

希尔伯特把数学的公理化根基置于清单之首。人工智能最深的裂缝同样在根基处:我们已经造出了会思考的机器,却还说不清它为何有效、何谓智能。工程跑在了科学前面——这六问,是欠下的理论之债。Hilbert placed the axiomatic foundations of mathematics at the head of his list. The deepest fissures of artificial intelligence lie at the foundations as well: we have already built machines that think, yet we still cannot say why they work, nor what intelligence is. Engineering has outrun science—these six problems are the theoretical debt thereby incurred.

1
第一问Problem I

智能的统一理论A Unified Theory of Intelligence

A Unified Theory of Intelligence
未解之谜Open

我们造出了智能,却仍未定义智能。We have made intelligence, and still have not defined it.

问题何在What Is the Problem

物理学有牛顿方程与热力学第二定律,计算有图灵机与丘奇–图灵论题,信息有香农的比特——而"智能",这个写在整个领域名字里的词,至今没有一个公认的数学定义。候选者各执一词:Legg 与 Hutter 把智能定义为"跨环境达成目标的能力",并给出理论最优却不可计算的智能体 AIXI;Friston 的自由能原理把智能看作对"惊异"的持续最小化;Chollet 强调智能是获取新技能的效率而非技能本身;"压缩即智能"一脉则主张理解与压缩在数学上是同一件事。问题是:是否存在一个统一框架,能像热力学解释一切热机那样,解释从线虫、婴儿到大语言模型的一切智能体,并给出可计算的度量?Physics has Newton’s equations and the second law of thermodynamics; computation has the Turing machine and the Church–Turing thesis; information has Shannon’s bit—but “intelligence,” the very word inscribed in the name of the whole field, has to this day no acknowledged mathematical definition. The candidates each hold to their own: Legg and Hutter define intelligence as “the ability to achieve goals across environments,” and put forward AIXI, an agent theoretically optimal yet uncomputable; Friston’s free energy principle takes intelligence to be the continual minimization of “surprise”; Chollet insists that intelligence is the efficiency of acquiring new skills rather than the skills themselves; while the “compression is intelligence” lineage maintains that understanding and compression are mathematically one and the same. The question is this: does there exist a unified framework that, as thermodynamics accounts for every heat engine, can account for every intelligent agent from the nematode and the infant to the large language model, and yield a computable measure?

为何重要Why It Matters

没有理论的工程,如同没有热力学的蒸汽机时代——造得出机器,却不知边界何在、极限几何。定义决定度量,度量决定整个领域往哪里用力。"AGI 何时到来"之所以人人各执一词,正因为无人能说清 AGI 是什么;千亿美元的路线之争,追到根上是一个定义问题。Engineering without theory is like the age of the steam engine without thermodynamics—machines can be built, but where the boundaries lie and how the limits are shaped remain unknown. Definition determines measurement, and measurement determines where an entire field applies its force. That everyone holds a different view on “when AGI will arrive” is precisely because no one can say what AGI is; the hundred-billion-dollar dispute over which road to take is, traced to its root, a question of definition.

何以为难Why It Is Hard

智能可能不是单一的量,而是一族异质能力的合称——学习、抽象、规划、社会推理——任何标量都失之过简。智能与环境、目标深度耦合,脱离生态位的"绝对智能"可能无从定义。理论上最优的 AIXI 不可计算,而一旦加入资源约束,数学的优雅便告瓦解。行为主义的出口(图灵测试)已被大模型事实上"通过",争论却并未终结——这恰恰说明我们缺的不是测试,而是理论。Intelligence may not be a single quantity but a collective name for a family of heterogeneous abilities—learning, abstraction, planning, social reasoning—and any scalar errs by oversimplification. Intelligence is deeply coupled to environment and to goals, and an “absolute intelligence” divorced from its niche may admit of no definition at all. AIXI, optimal in theory, is uncomputable, and once resource constraints are admitted the elegance of the mathematics falls apart. The behaviorist exit (the Turing test) has in effect been “passed” by the large models, yet the dispute has not come to an end—which shows precisely that what we lack is not a test but a theory.

演化与解法Paths of Evolution

短期内,压缩视角、自由能原理与"资源理性"框架可能局部合流;儿童发展心理学与比较认知的度量,会被系统性引入机器评估。更可能的路径是"事后理论":如同热力学在蒸汽机之后到来,智能的统一理论或许要等我们造出多种形态的智能之后,从比较解剖中归纳而出——机器智能第一次让"智能的比较解剖学"成为可能。In the near term the compression view, the free energy principle and the “resource-rational” framework may partially converge; the measures of child developmental psychology and of comparative cognition will be brought systematically into the evaluation of machines. The likelier path is a “theory after the fact”: just as thermodynamics arrived after the steam engine, a unified theory of intelligence may have to wait until we have built intelligences of many forms, and then be induced from their comparative anatomy—machine intelligence has for the first time made a “comparative anatomy of intelligence” possible.

解决的价值The Value of a Solution

一个真正的智能理论将同时回答能力预测、上限判断与安全论证三大悬案,把"炼丹"变成"化学"。在全部二十三问中,这一问的杠杆最长。A true theory of intelligence would answer at one stroke the three outstanding questions of predicting capability, judging the upper bound and arguing for safety, turning “alchemy” into “chemistry.” Among all twenty-three problems, this one has the longest lever.

研究坐标Research Coordinates

Solomonoff 归纳与柯尔莫哥洛夫复杂度·Legg & Hutter《通用智能》与 AIXI(2007)·Friston 自由能原理·Chollet《论智能的度量》与 ARC 系列基准(2019– )·Lieder & Griffiths 资源理性·Hutter 压缩奖Solomonoff induction and Kolmogorov complexity·Legg & Hutter, “Universal Intelligence,” and AIXI (2007)·Friston, the free energy principle·Chollet, “On the Measure of Intelligence,” and the ARC family of benchmarks (2019– )·Lieder & Griffiths, resource rationality·Hutter, the compression prize

2
第二问Problem II

深度学习的泛化之谜The Mystery of Generalization in Deep Learning

The Mystery of Generalization
局部进展Partial Progress

一个足以背下全部数据的网络,为何偏偏学会了举一反三?A network with capacity enough to memorize the whole of its data—why should it, of all things, have learned to draw the many from the one?

问题何在What Is the Problem

经典学习理论断言:参数远多于样本的模型必然过拟合。深度网络公然违背了这条定律——前沿模型的参数足以逐字背诵训练集,它们却学会了举一反三。张驰原等人 2017 年的著名实验(同一网络既能完美记住随机标签,又能在真实数据上泛化)宣告经典理论破产;此后十年,双下降、彩票假说、神经正切核、顿悟(grokking:模型在"过拟合"很久之后突然学会泛化)等奇异现象层出,理论始终追不上现象清单的增长。为什么随机梯度下降在天文数字维度的非凸损失面上,总能找到那些恰好会泛化的解?Classical learning theory asserts that a model with far more parameters than samples must overfit. Deep networks defy this law in the open—the parameters of frontier models suffice to recite the training set word for word, and yet they have learned to draw the many from the one. The celebrated 2017 experiment of Chiyuan Zhang and his co-authors (one and the same network can both memorize random labels perfectly and generalize on real data) pronounced the classical theory bankrupt; in the decade since, strange phenomena have appeared without end—double descent, the lottery ticket hypothesis, the neural tangent kernel, grokking (a model suddenly learning to generalize long after it has “overfit”)—and theory has never kept pace with the growth of the list of phenomena. Why is it that stochastic gradient descent, on a non-convex loss surface of astronomical dimension, always finds precisely those solutions that happen to generalize?

为何重要Why It Matters

这是 AI 的"为什么它有效"之问。不解此谜,每一代模型都是一次昂贵的赌博:架构靠试错,超参靠经验,涌现靠祈祷。科学史一再证明,从炼金术到化学的那一步,价值超过此前所有配方的总和。This is AI’s question of “why does it work.” Until the mystery is unriddled, every generation of models is an expensive wager: architecture by trial and error, hyperparameters by experience, emergence by prayer. The history of science has proved again and again that the single step from alchemy to chemistry is worth more than the sum of all the recipes that came before it.

何以为难Why It Is Hard

高维几何全面反直觉,人类对亿维空间的想象力为零。SGD 的"隐式偏置"与数据分布、架构、初始化纠缠在一起,无法拆开单独研究。能严格分析的极限(线性化的 NTK 区)恰恰丢掉了特征学习这个关键。而最深的困难在于:"真实数据的结构"本身没有数学定义——理论要解释的对象,先已无法形式化。High-dimensional geometry runs counter to intuition at every turn, and human imagination for spaces of a hundred million dimensions is nil. The “implicit bias” of SGD is entangled with the data distribution, the architecture and the initialization, and cannot be taken apart for separate study. The limit that can be analyzed rigorously (the linearized NTK regime) is precisely the one that discards feature learning, the very crux of the matter. And the deepest difficulty lies here: “the structure of real data” has itself no mathematical definition—the object the theory is to explain cannot, to begin with, be formalized.

演化与解法Paths of Evolution

几路人马正从不同侧面逼近:奇异学习理论用代数几何刻画损失面的退化结构;平坦极小值与压缩界把泛化与信息量挂钩;"深度学习的科学"社群主张像物理学一样,先建现象学定律、再求微观机理。可能的终局是一门"深度学习的统计力学"——以数据流形维度、对称性与噪声为自变量,在训练之前算出一个架构在一个数据集上的泛化误差。Several parties are closing in from different sides: singular learning theory uses algebraic geometry to characterize the degenerate structure of the loss surface; flat minima and compression bounds tie generalization to quantity of information; the “science of deep learning” community argues for proceeding as physics does—first establish phenomenological laws, then seek the microscopic mechanism. The possible endgame is a “statistical mechanics of deep learning”—one that, taking the dimension of the data manifold, its symmetries and its noise as independent variables, computes before training the generalization error of a given architecture on a given dataset.

解决的价值The Value of a Solution

万卡集群的试错开销变成公式推导;架构设计有了罗盘;更关键的是,"该模型在此分布上错误率不超过 ε"式的可靠性证书首次成为可能——那是 AI 进入民航级场景的门票。The trial-and-error expense of ten-thousand-card clusters becomes a derivation on paper; architecture design acquires a compass; and, more crucially, reliability certificates of the form “the error rate of this model on this distribution does not exceed ε” become possible for the first time—that is the ticket for AI’s entry into settings of civil-aviation grade.

研究坐标Research Coordinates

Zhang et al.《理解深度学习需要重思泛化》(2017)·Belkin et al. 双下降(2019)·Frankle & Carbin 彩票假说·Jacot et al. 神经正切核·Power et al. Grokking(2022)·渡边澄夫 奇异学习理论·Tishby 信息瓶颈Zhang et al., “Understanding Deep Learning Requires Rethinking Generalization” (2017)·Belkin et al., double descent (2019)·Frankle & Carbin, the lottery ticket hypothesis·Jacot et al., the neural tangent kernel·Power et al., grokking (2022)·Sumio Watanabe, singular learning theory·Tishby, the information bottleneck

3
第三问Problem III

缩放定律与涌现Scaling Laws and Emergence

Scaling Laws and Emergence
局部进展Partial Progress

损失沿幂律滑落,能力凭空涌现——这是自然法则,还是时代的巧合?Loss slides down a power law, capabilities emerge out of nowhere—is this a law of nature, or a coincidence of the age?

问题何在What Is the Problem

2020 年,Kaplan 等人发现模型损失随参数、数据、算力按幂律平滑下降,跨七个数量级而不衰;这条曲线此后成为万亿美元投资的地基。但无人知道幂律从何而来、何时终结。更诡异的是"涌现":上下文学习、思维链、工具使用,这些能力在某个规模上突然出现,事前无人预测。斯坦福团队争辩涌现只是度量方式造成的"海市蜃楼";量子化假说则主张能力本就是一份份离散的"技能量子"。2024 年之后,测试时计算(让模型思考更久)又开辟了第二条缩放轴。缩放定律究竟是自然律,还是特定范式下的经验巧合?涌现能否被事前预测?In 2020 Kaplan and colleagues found that model loss declines smoothly with parameters, data and compute according to a power law, holding across seven orders of magnitude without decay; that curve has since become the bedrock of trillion-dollar investment. Yet no one knows whence the power law comes, nor when it will end. Stranger still is "emergence": in-context learning, chain of thought, tool use—capabilities that appear abruptly at some scale, foreseen by no one beforehand. A Stanford group argues that emergence is merely a "mirage" produced by the choice of metric; the quantization hypothesis maintains instead that capability is by its nature a matter of discrete "quanta of skill". After 2024, test-time compute (letting the model think longer) opened a second axis of scaling. Is the scaling law a law of nature, or an empirical coincidence within one particular paradigm? Can emergence be predicted in advance?

为何重要Why It Matters

这大概是唯一同时属于科学、投资与安全三界的问题。对曲线的外推决定吉瓦级数据中心的选址与国家算力战略,也决定我们会不会在毫无预警的情况下,跨过某项危险能力的阈值。预测涌现,就是预测未来。This is perhaps the only question that belongs at once to the three realms of science, of investment and of safety. How the curve is extrapolated determines where gigawatt-scale data centres are sited and what a nation's compute strategy will be; it determines also whether we shall cross the threshold of some dangerous capability with no warning whatever. To predict emergence is to predict the future.

何以为难Why It Is Hard

幂律的候选解释——数据流形维度、技能的齐夫分布、渗流式相变——都能拟合已有曲线,却给出不同的外推。涌现按定义是"下游任务上的非线性",而下游任务无穷无尽。范式还在漂移:预训练、后训练强化学习、测试时搜索三条缩放轴互相纠缠,旧曲线不断被新范式改写,"定律"的地基本身在移动。The candidate explanations of the power law—the dimension of the data manifold, a Zipfian distribution of skills, a percolation-like phase transition—all fit the curves already in hand, yet yield different extrapolations. Emergence is by definition "a nonlinearity on downstream tasks", and downstream tasks are without end. The paradigm is still drifting: pre-training, post-training reinforcement learning and test-time search are three axes of scaling entangled with one another; old curves are continually rewritten by new paradigms, and the ground beneath the "law" is itself in motion.

演化与解法Paths of Evolution

"缩放的科学"正在成为独立学科:用小模型的能力指纹外推大模型(预测性缩放)、以可验证奖励的强化学习重画曲线、把涌现还原为某个连续内部指标的阈值穿越。终局也许是一张"智能相图":给定数据、算力与算法,标出各项能力涌现的相边界——如同水的三相图之于水汽冰。A "science of scaling" is becoming a discipline in its own right: extrapolating from the capability fingerprints of small models to large ones (predictive scaling), redrawing the curves by reinforcement learning with verifiable rewards, reducing emergence to the crossing of a threshold in some continuous internal quantity. The end of it may be a "phase diagram of intelligence": given data, compute and algorithm, it would mark the phase boundaries at which each capability emerges—as the three-phase diagram of water does for vapour, water and ice.

解决的价值The Value of a Solution

提前一年知道下一代模型能做什么:对产业是路线图,对安全是预警雷达,对政策是立法的时间表。To know a year in advance what the next generation of models will be able to do: for industry a road map, for safety an early-warning radar, for policy a timetable for legislation.

研究坐标Research Coordinates

Kaplan et al. 缩放定律(2020)·Hoffmann et al. Chinchilla(2022)·Wei et al. 涌现能力(2022)·Schaeffer et al.《涌现是海市蜃楼吗》(2023)·Michaud et al. 量子化假说·o 系列与 DeepSeek-R1 开启的测试时缩放(2024–25)·Epoch AI 的算力外推研究Kaplan et al., scaling laws (2020)·Hoffmann et al., Chinchilla (2022)·Wei et al., emergent abilities (2022)·Schaeffer et al., "Are Emergent Abilities a Mirage?" (2023)·Michaud et al., the quantization hypothesis·test-time scaling opened by the o-series and DeepSeek-R1 (2024–25)·Epoch AI's studies on the extrapolation of compute

4
第四问Problem IV

机制可解释性Mechanistic Interpretability

Mechanistic Interpretability
疾进之中Advancing Rapidly

万亿参数之中,一个念头究竟栖身何处?Among a trillion parameters, where does a single thought reside?

问题何在What Is the Problem

我们对前沿模型的处境,与神经科学家对大脑的处境惊人相似:能测量、能干预、不能通读。机制可解释性的纲领,是把训练出的网络逆向工程为可读的算法:先找特征——叠加假说指出模型把远多于神经元数的概念压进同一组权重,须用稀疏自编码器将其拆开;再追回路——归因图技术已能画出模型做多步推理、写诗时提前规划韵脚的内部通路;终点是对一个前沿模型完成"全脑解剖"。真正的问题是:在人类理解的意义上,万亿参数的系统是否原则上可以被理解?Our situation before a frontier model is strikingly like the neuroscientist's before the brain: we can measure, we can intervene, we cannot read it through. The programme of mechanistic interpretability is to reverse-engineer a trained network into a legible algorithm: first find the features—the superposition hypothesis holds that a model compresses far more concepts than it has neurons into a single set of weights, and sparse autoencoders are required to prise them apart; then trace the circuits—attribution-graph techniques can already draw the internal pathways by which a model reasons in several steps, or plans a rhyme in advance while composing a poem; the terminus is a complete "dissection of the whole brain" of one frontier model. The real question is this: in the sense of human understanding, can a system of a trillion parameters in principle be understood?

为何重要Why It Matters

这是打开其余诸问的钥匙。不开黑箱,对齐审计(它是否在伪装?见第十七问)只能停留在行为猜测;开了黑箱,删除危险知识、修复系统性缺陷、提取模型自学到的科学规律,都从"重新训练"变成"外科手术"。各国监管要求的"透明度",最终也要落到这门技术上。This is the key that opens the remaining problems. Without opening the black box, alignment auditing (is it dissembling? see Problem XVII) can rest on nothing but conjecture about behaviour; once it is opened, the deletion of dangerous knowledge, the repair of systematic defects and the extraction of the scientific regularities a model has taught itself all turn from "retraining" into "surgery". The "transparency" demanded by the regulators of every nation must in the end come to rest upon this technique.

何以为难Why It Is Hard

叠加使"一神经元一概念"的美梦破灭,特征从一开始就是纠缠的;规模无情——手工分析一条回路要数月,而模型有百万条回路,且每一代重训一次、旧图谱作废;"解释"本身需要被验证,什么算一个正确的解释,至今没有因果意义上的公认标准。最深处还有一道暗礁:也许存在人类心智装不下的算法——理解的极限,即翻译的极限。Superposition shatters the dream of "one neuron, one concept"; the features are entangled from the very outset. Scale is merciless—to analyse a single circuit by hand takes months, while a model holds a million circuits, and each generation is retrained afresh, voiding the old atlas. "Explanation" itself stands in need of validation, and what counts as a correct explanation has to this day no acknowledged criterion in the causal sense. Deepest of all lies a hidden reef: there may exist algorithms that no human mind can hold—the limit of understanding is the limit of translation.

演化与解法Paths of Evolution

自动化是唯一出路:用 AI 解释 AI,让解释器模型批量标注特征、验证回路,把可解释性做成显微镜流水线。表征工程与激活转向提供了轻量级的读写接口;与评估科学(第二十一问)合流后,"内部指标审计"可能成为部署前的法定体检。乐观情形下,本十年内对一个前沿模型完成关键回路的完整图谱——相当于 AI 的人类基因组计划。Automation is the only way out: to explain AI with AI, letting interpreter models label features and verify circuits in bulk, and making interpretability an assembly line of microscopes. Representation engineering and activation steering furnish a lightweight interface for reading and writing; once they converge with the science of evaluation (Problem XXI), an "audit of internal indicators" may become a physical examination required by law before deployment. In the optimistic case, a complete atlas of the critical circuits of one frontier model within this decade—the Human Genome Project of AI.

解决的价值The Value of a Solution

安全从行为学走向解剖学,模型编辑从咒语走向手术;顺带回馈神经科学——人类第一次拥有了一个可以任意测量、任意重放的"心智"标本。Safety passes from behaviourism to anatomy, and the editing of models from incantation to surgery; and neuroscience is repaid in passing—for the first time humanity possesses a specimen of "mind" that may be measured at will and replayed at will.

研究坐标Research Coordinates

Olah 等的回路纲领(Distill,2020)·Elhage et al. 叠加的玩具模型(2022)·Anthropic《规模化单义性》与归因图·回路追踪(2024–25)·Nanda 等 归纳头与 grokking 机理·Bau 实验室 ROME 记忆编辑·Zou et al. 表征工程·OpenAI 用 GPT-4 解释 GPT-2 神经元Olah et al., the circuits programme (Distill, 2020)·Elhage et al., toy models of superposition (2022)·Anthropic, "Scaling Monosemanticity", attribution graphs and circuit tracing (2024–25)·Nanda et al., induction heads and the mechanism of grokking·the Bau Lab, ROME memory editing·Zou et al., representation engineering·OpenAI, explaining GPT-2 neurons with GPT-4

5
第五问Problem V

因果之梯The Ladder of Causation

The Ladder of Causation
局部进展Partial Progress

机器看尽了世间的相关,却还未学会追问"如果当初"。The machine has seen every correlation in the world, and has yet to learn to ask "had it been otherwise".

问题何在What Is the Problem

珀尔(Judea Pearl)把认知分作三层阶梯:观察——看见什么与什么相伴;干预——若我去做,会怎样;反事实——若当初未做,又会怎样。统计学习被锁在第一层,而科学、医学、政策与道德责任全部住在第二、三层。大模型从文本中吸收了海量因果知识的转述,常见场景对答如流;可一旦情节偏出训练分布,"因果鹦鹉"便会现形。机器能否从数据与交互中自主发现因果结构,并稳定地进行干预推理与反事实想象?Judea Pearl divides cognition into a ladder of three rungs: observation—seeing what accompanies what; intervention—what would follow were I to act; the counterfactual—what would have followed had I not acted. Statistical learning is locked upon the first rung, while science, medicine, policy and moral responsibility all dwell upon the second and the third. Large models have absorbed from text a vast paraphrase of causal knowledge, and answer fluently in familiar settings; yet once the scenario departs from the training distribution, the "causal parrot" shows itself. Can a machine discover of itself causal structure from data and interaction, and carry out interventional reasoning and counterfactual imagination with any stability?

为何重要Why It Matters

相关性在分布漂移的一瞬失效,而真实世界永远在漂移。没有因果,就没有可信的医疗决策与政策模拟,也没有真正的责任归因——"要是它当时不那样做"这句话,对纯统计系统而言没有意义。Correlation fails in the instant the distribution shifts, and the real world is forever shifting. Without causation there is no trustworthy medical decision and no simulation of policy, nor any genuine attribution of responsibility—the sentence "had it not acted as it did" carries no meaning for a purely statistical system.

何以为难Why It Is Hard

因果发现在数学上欠定:仅凭观察,多个因果图无法区分(马尔可夫等价类),必须做干预,而干预往往昂贵、危险或不道德。更深一层,真实世界的"变量"并非天生给定——哪些东西算变量,本身要从像素与词元中学出来(因果表征学习),这成了先有鸡还是先有蛋。至于大模型的因果能力究竟是检索还是推理,学界至今针锋相对。Causal discovery is mathematically underdetermined: from observation alone several causal graphs cannot be told apart (the Markov equivalence class), and intervention becomes necessary—yet intervention is often costly, dangerous or unethical. Deeper still, the "variables" of the real world are not given by nature—what is to count as a variable must itself be learned from pixels and tokens (causal representation learning), and so the chicken and the egg contend for precedence. As to whether the causal ability of large models is retrieval or reasoning, the field stands to this day in direct opposition to itself.

演化与解法Paths of Evolution

三条河正在汇流:因果表征学习把珀尔的图语言接到深度表征上;世界模型(第九问)提供了"在想象中做实验"的场所;智能体的主动实验设计,让机器自己挑选下一个最有信息量的干预——自主科学家(第十三问)的闭环,正是人类造过的最大因果发现机器。Three rivers are converging: causal representation learning grafts Pearl's language of graphs onto deep representations; world models (Problem IX) provide the place in which to "perform experiments in the imagination"; and an agent's active design of experiments lets the machine choose for itself the next intervention richest in information—the closed loop of the autonomous scientist (Problem XIII) is the greatest engine of causal discovery humanity has ever built.

解决的价值The Value of a Solution

从"预测下一个词"到"预测干预的后果",是 AI 从顾问变为可托付行动者的分水岭;它也顺手给鲁棒性(第六问、第十八问)提供了最硬的地基。The passage from "predicting the next word" to "predicting the consequences of an intervention" is the watershed at which AI turns from adviser into an agent that may be entrusted with action; it furnishes robustness (Problem VI, Problem XVIII) in passing with its hardest foundation.

研究坐标Research Coordinates

Pearl do-演算与《为什么》·Spirtes & Glymour 因果发现算法·Schölkopf et al.《迈向因果表征学习》(2021)·Bengio 因果世界模型议程·CLeaR 会议社群·Kıcıman et al. 等对 LLM 因果推理的系统评测Pearl, the do-calculus and "The Book of Why"·Spirtes & Glymour, algorithms for causal discovery·Schölkopf et al., "Toward Causal Representation Learning" (2021)·Bengio's agenda for causal world models·the CLeaR conference community·Kıcıman et al., systematic evaluations of causal reasoning in LLMs

6
第六问Problem VI

组合性与分布外泛化Compositionality and Out-of-Distribution Generalization

Compositionality and Out-of-Distribution Generalization
局部进展Partial Progress

见过红方块与蓝圆圈之后,它能否一眼认出蓝方块?Having seen red squares and blue circles, can it recognize a blue square at a glance?

问题何在What Is the Problem

人类认知的招牌本领是系统性组合:懂得"红方块"与"蓝圆圈",立刻就懂"蓝方块";学会一个新动词,马上能嵌进一切句式。福多与皮利辛在 1988 年断言,联结主义永远做不到这一点。三十余年后,大模型在平均意义上表现惊人,却仍会在结构性偏移面前崩塌:逆转诅咒——训练"A 的母亲是 B",却答不出"B 的孩子是谁";捷径学习——靠背景草地识别奶牛;以及长尾场景里的突然失灵。梯度训练的分布式表征,能否实现真正的系统性——在分布之外按规则而非按相似度泛化?The signature capacity of human cognition is systematic composition: to grasp “red square” and “blue circle” is at once to grasp “blue square”; to learn a new verb is at once to be able to embed it in every construction. Fodor and Pylyshyn declared in 1988 that connectionism could never do this. Three decades and more later, large models perform astonishingly well in the average case, yet still collapse in the face of structural shift: the reversal curse — trained on “A’s mother is B,” they cannot answer “who is B’s child”; shortcut learning — identifying a cow by the grass behind it; and sudden failure in long-tail scenes. Can the distributed representations of gradient training achieve genuine systematicity — generalizing outside the distribution by rule rather than by similarity?

为何重要Why It Matters

部署环境永远在分布之外——自动驾驶的几乎每一场事故都是一次分布外事件。组合性同时是无限表达的钥匙:语言、数学、程序之所以强大,正因少量部件可按规则组出无穷意义。这还是一个安全问题:不知道系统在新情境下依据什么泛化,就不知道它会把目标泛化成什么(第十七问)。The environment of deployment is forever outside the distribution — nearly every accident in autonomous driving is an out-of-distribution event. Compositionality is at the same time the key to unbounded expression: language, mathematics and programs are powerful precisely because a small stock of parts can be assembled by rule into endless meaning. It is also a safety question: not knowing on what basis a system generalizes in a novel situation, we do not know what it will generalize its goals into (Problem XVII).

何以为难Why It Is Hard

梯度下降天然偏爱统计捷径,插值总比外推便宜。符号绑定问题——"谁是施动者、谁是受动者"这类变量绑定在连续向量中如何实现——至今没有公认机制。评测本身也在失效:网络级语料几乎覆盖一切,"真正的分布外"越来越难以构造,测的到底是泛化还是记忆,常常无从分辨。Gradient descent is by nature partial to statistical shortcuts; interpolation is always cheaper than extrapolation. The symbol-binding problem — how bindings of variables of the sort “which is the agent, which the patient” are realized in continuous vectors — still has no acknowledged mechanism. Evaluation itself is breaking down: web-scale corpora cover very nearly everything, “genuinely out of distribution” grows ever harder to construct, and whether what is measured is generalization or memorization is often impossible to tell.

演化与解法Paths of Evolution

元学习给出了曙光:Lake 与 Baroni 在《自然》上证明,为组合性专门设计训练流的网络,能达到人类水平的系统泛化。神经符号路线把离散结构外挂给网络——程序合成与工具调用是它的工程化身。数据分布工程(刻意制造组合稀疏)与测试时搜索也在缓解症状。谜底可能是:组合性不必内生于架构,而是涌现于"被逼着组合"的训练课程。Meta-learning has given a first light: Lake and Baroni showed in Nature that a network whose training stream is designed expressly for compositionality can reach human-level systematic generalization. The neuro-symbolic route attaches discrete structure to the network from outside — program synthesis and tool use are its engineering incarnations. Engineering the data distribution (deliberately manufacturing combinatorial sparsity) and test-time search are likewise easing the symptoms. The answer may be this: compositionality need not be innate to the architecture, but emerges from a training curriculum that “forces one to compose.”

解决的价值The Value of a Solution

小数据下的可靠外推,是工业落地最大的单点瓶颈;攻克它,医疗、法律、工程这些长尾领域就不再是深度学习的坟场。Reliable extrapolation from small data is the single greatest bottleneck to industrial deployment; overcome it, and the long-tail fields of medicine, law and engineering will no longer be the graveyard of deep learning.

研究坐标Research Coordinates

Fodor & Pylyshyn(1988)·Lake & Baroni,SCAN 与元学习组合泛化 MLC(Nature,2023)·Geirhos et al. 捷径学习(2020)·Berglund et al. 逆转诅咒(2023)·Chollet ARC-AGI:抗记忆的组合基准·Marcus《代数心智》一脉的批评Fodor & Pylyshyn (1988)·Lake & Baroni, SCAN and meta-learning for compositional generalization, MLC (Nature, 2023)·Geirhos et al. on shortcut learning (2020)·Berglund et al. on the reversal curse (2023)·Chollet, ARC-AGI: a memorization-resistant compositional benchmark·the line of criticism running from Marcus’s “The Algebraic Mind”

II

能力之问Capabilities

Capabilities
第七问 至 第十四问Problem VII to Problem XIV

这一卷是智能疆域上尚未攻克的堡垒。每一座都对应人类心智的一项本领:诚实、推理、想象、行动、记忆、学习、创造——以及最危险的一项,改进自身。This book is given to the fortresses not yet taken in the territory of intelligence. Each answers to one faculty of the human mind: honesty, reasoning, imagination, action, memory, learning, creation — and the most dangerous one of all, improving itself.

7
第七问Problem VII

幻觉与知识边界Hallucination and the Boundary of Knowledge

Hallucination and the Boundary of Knowledge
攻坚之中Under Assault

如何教会一台永远给得出答案的机器,说出"我不知道"?How does one teach a machine that can always produce an answer to say “I do not know”?

问题何在What Is the Problem

模型会以完美的流利与自信编造事实:虚构的判例、伪造的引文、无中生有的传记细节。这不是偶发故障,而是范式的天性——下一词预测奖励"合理的续写",而合理不等于真实。研究还揭示了更深的机制性根源:主流的训练与评测在系统性地奖励猜测——答"不知道"得零分,蒙对得满分,于是模型学会永远作答。问题是:能否造出一个校准的系统——知道自己知道什么、不知道什么,并如实报告?"知之为知之,不知为不知",两千年前的这句话,成了对机器智能最苛刻的技术要求。Models fabricate facts with perfect fluency and confidence: invented precedents, forged citations, biographical details conjured out of nothing. This is not an occasional malfunction but the nature of the paradigm — next-token prediction rewards “a plausible continuation,” and plausible is not the same as true. Research has further disclosed a deeper mechanistic root: the prevailing training and evaluation systematically reward guessing — answering “I do not know” scores zero, a lucky guess scores full marks, and so the model learns to answer always. The question is: can a calibrated system be built — one that knows what it knows and what it does not know, and reports this faithfully? “To hold that you know what you know, and that you do not know what you do not know” — this sentence of two thousand years ago has become the most exacting technical demand made of machine intelligence.

为何重要Why It Matters

可信度是落地一切严肃场景的门槛:医疗、法律、金融、新闻,一次自信的编造足以摧毁全部信任。更远处,当 AI 的答案成为搜索、教育与百科的信息基础设施,幻觉就不再只是产品缺陷,而是文明层面的知识卫生问题。Trustworthiness is the threshold for entry into every serious setting: in medicine, law, finance and journalism, a single confident fabrication suffices to destroy all trust. Further out, once the answers of AI become the information infrastructure of search, education and the encyclopedia, hallucination is no longer merely a product defect but a question of the hygiene of knowledge at the level of civilization.

何以为难Why It Is Hard

"真"没有外部锚点——训练语料本身充满错误与矛盾,模型无从分辨转述与事实。参数化知识与检索知识的边界模糊,模型难以内省自己的知识来源。校准与有用性存在天然张力:处处附免责声明的助手无人想用。而评测文化在推波助澜——排行榜从不奖励沉默。“Truth” has no external anchor — the training corpus is itself full of errors and contradictions, and the model has no way to tell report from fact. The boundary between parametric knowledge and retrieved knowledge is blurred, and the model can hardly introspect the source of what it knows. Between calibration and usefulness there is a native tension: no one wants an assistant that attaches a disclaimer to everything. And the culture of evaluation feeds the flames — leaderboards never reward silence.

演化与解法Paths of Evolution

多条战线同时推进:语义熵等不确定性度量给出可检测的信号;可解释性研究发现了"已知实体"特征——它误触发时模型便开始编造,这意味着幻觉有朝一日可以从回路层面被拦截;校准训练与"事实性强化学习"改造激励;检索与推理深度融合;评测改革(答错倒扣分)纠正习惯。终局图景:置信度成为与答案并列的标准输出,"认知谦逊"成为一等训练目标。Several fronts advance at once: uncertainty measures such as semantic entropy yield a detectable signal; interpretability research has found a “known entity” feature — when it misfires the model begins to fabricate, which means that hallucination may one day be intercepted at the level of the circuit; calibration training and “factuality reinforcement learning” remake the incentives; retrieval and reasoning are being deeply fused; reform of evaluation (deducting marks for wrong answers) corrects the habit. The end-state picture: confidence becomes a standard output alongside the answer, and “epistemic humility” becomes a first-class training objective.

解决的价值The Value of a Solution

专业领域的全面落地由此解锁;而"模型知道自己知道什么"一旦实现,也将成为诚实(第十七问)与可扩展监督(第十六问)的地基。Full deployment across the professional domains is thereby unlocked; and once “the model knows what it knows” is achieved, it will also become the foundation of honesty (Problem XVII) and of scalable oversight (Problem XVI).

研究坐标Research Coordinates

Kadavath et al.《语言模型(大体)知道自己知道什么》(2022)·Lin et al. TruthfulQA·Farquhar et al. 语义熵检测(Nature,2024)·OpenAI《语言模型为何幻觉》(2025)·Anthropic"已知实体"回路分析(2025)·SimpleQA 等事实性基准Kadavath et al., “Language Models (Mostly) Know What They Know” (2022)·Lin et al., TruthfulQA·Farquhar et al. on semantic-entropy detection (Nature, 2024)·OpenAI, “Why Language Models Hallucinate” (2025)·Anthropic’s circuit analysis of the “known entity” feature (2025)·factuality benchmarks such as SimpleQA

8
第八问Problem VIII

深层推理与规划Deep Reasoning and Planning

Deep Reasoning and Planning
疾进之中Rapid Advance

从续写下一个词,到证明下一条定理,中间隔着什么?What lies between continuing the next word and proving the next theorem?

问题何在What Is the Problem

2024 至 2025 年,推理模型范式(o 系列、DeepSeek-R1)让模型在作答前生成长思维链,并用强化学习训练"思考"本身,数学与编程成绩一夜跃迁;2025 年 7 月,OpenAI 与 DeepMind 的系统先后达到国际数学奥林匹克金牌线;随后,GPT-5 世代的模型开始在厄尔多斯问题等真正的开放问题上,给出被职业数学家接受的解答。但争论同样激烈:这是真推理,还是超大规模的模式检索?思维链是否忠实反映内部计算(证据显示:常常不忠实)?在数学与代码这些可验证域之外,推理增益为何迅速衰减?In 2024 and 2025 the reasoning-model paradigm (the o series, DeepSeek-R1) had models generate a long chain of thought before answering, and trained “thinking” itself by reinforcement learning; scores in mathematics and programming leapt overnight. In July 2025 the systems of OpenAI and of DeepMind reached, one after the other, the gold-medal line of the International Mathematical Olympiad; thereafter, models of the GPT-5 generation began to give, on genuinely open problems such as the Erdős problems, solutions accepted by professional mathematicians. But the dispute is no less fierce: is this real reasoning, or pattern retrieval at enormous scale? Does the chain of thought faithfully reflect the internal computation (the evidence shows: often it does not)? And outside verifiable domains such as mathematics and code, why do the gains from reasoning decay so quickly?

为何重要Why It Matters

推理是智力的皇冠:科学、工程、战略,皆是长链推理。推理的深度也直接决定智能体能否可靠执行长任务——METR 的测量显示,模型能独立完成的任务时长每约七个月翻一倍;这条曲线延伸向何方,是未来十年最重要的经验事实之一。Reasoning is the crown of the intellect: science, engineering, strategy are all long-chain reasoning. The depth of reasoning also directly determines whether an agent can reliably execute long tasks — METR’s measurements show that the length of task a model can complete on its own doubles about every seven months; where this curve extends is one of the most important empirical facts of the coming decade.

何以为难Why It Is Hard

搜索空间组合爆炸,而奖励稀疏——千步证明只在最后一步可验证;过程奖励难以自动获得。软领域(法律、医学、开放式科研)没有判定器,强化学习无从发力。思维链的不忠实让"看思路打分"变得危险。而横跨数日数月的长程规划,需要对目标、状态与教训的持久表征——这正撞上记忆之问(第十一问)。The search space explodes combinatorially while the reward is sparse — a thousand-step proof is verifiable only at the last step; process rewards are hard to obtain automatically. The soft domains (law, medicine, open-ended research) have no arbiter, and reinforcement learning finds no purchase. The unfaithfulness of the chain of thought makes “grading the reasoning as displayed” dangerous. And long-horizon planning spanning days and months requires a persistent representation of goals, states and lessons — which runs straight into the problem of memory (Problem XI).

演化与解法Paths of Evolution

形式化接口是最清晰的路线:让模型的直觉负责猜路,让 Lean 等证明助手负责把关——AlphaProof 一脉已经证明其威力。过程监督、自我纠错、测试时搜索正在标准化。真正的判决点有二:推理能力能否迁移出可验证域;以及模型能否从"解答问题"走向"提出问题"(与第十三问汇流)。A formal interface is the clearest route: let the intuition of the model guess the path, and let proof assistants such as Lean stand guard — the AlphaProof line has already demonstrated its power. Process supervision, self-correction and test-time search are being standardized. There are two genuine points of decision: whether the capacity for reasoning can transfer out of verifiable domains; and whether models can move from “solving problems” to “posing problems” (converging with Problem XIII).

解决的价值The Value of a Solution

数学与理论科学获得一台加速器;长程智能体获得可靠性;监督获得载体——可检查的论证,正是人类审查超人系统的抓手(第十六问)。Mathematics and the theoretical sciences gain an accelerator; long-horizon agents gain reliability; oversight gains a vehicle — an argument that can be checked is precisely the handhold by which human beings may review superhuman systems (Problem XVI).

研究坐标Research Coordinates

OpenAI o 系列(2024)·DeepSeek-R1:纯强化学习涌现推理(2025)·AlphaProof 与 AlphaGeometry、IMO 金牌线(2024–25)·GPT-5 世代与厄尔多斯开放问题(2025–26)·Lightman et al. 过程监督·Turpin 等 思维链忠实性研究·METR 任务时长倍增曲线OpenAI’s o series (2024)·DeepSeek-R1: reasoning emergent from pure reinforcement learning (2025)·AlphaProof and AlphaGeometry, the IMO gold-medal line (2024–25)·the GPT-5 generation and the open Erdős problems (2025–26)·Lightman et al. on process supervision·Turpin et al. on the faithfulness of chains of thought·METR’s task-length doubling curve

9
第九问Problem IX

世界模型World Models

World Models
疾进之中Advancing Rapidly

看过亿万小时视频的模型,能否学会婴儿九个月大时就懂的道理?Can a model that has watched hundreds of millions of hours of video learn what an infant already understands at nine months of age?

问题何在What Is the Problem

九个月的婴儿知道物体被遮住并未消失、悬空之物必将坠落——发展心理学称之为"核心知识"。而看过全网视频的模型,仍会在这些地方犯错。世界模型之问是:如何让机器学到一个内在的世界模拟器,可用于预测、规划与反事实推演?路线之争白热化:视频生成派(Sora、Veo、Genie——Genie 3 已能实时生成可交互的三维环境)相信预测像素终会逼出物理;JEPA 派(LeCun——2025 年他离开 Meta 创办世界模型公司,押上后半生的声誉)断言像素预测是死路,必须在抽象表征空间做预测;具身派则主张,世界模型只能从行动中学出来。A nine-month-old infant knows that an object hidden from view has not ceased to exist, and that an unsupported object must fall—developmental psychology calls this "core knowledge." Yet models that have watched the whole of the web's video still err in precisely these places. The question of world models is this: how is a machine to learn an internal simulator of the world, one usable for prediction, for planning, and for counterfactual reasoning? The contest of routes has reached white heat: the video-generation camp (Sora, Veo, Genie—Genie 3 can already generate interactive three-dimensional environments in real time) believes that predicting pixels will in the end force physics into being; the JEPA camp (LeCun—who in 2025 left Meta to found a world-model company, staking upon it the reputation of his later years) declares pixel prediction a dead end, and holds that prediction must be carried out in a space of abstract representations; the embodiment camp maintains that a world model can only be learned from action.

为何重要Why It Matters

世界模型是具身智能的引擎(第十问)、因果推理的沙盘(第五问)、安全规划的前提——在心中演练,而非在现实中试错。它也是"常识问题"的现代形态:AI 领域最古老的未解之问,换了一件新衣。The world model is the engine of embodied intelligence (Problem X), the sand table of causal reasoning (Problem V), the precondition of safe planning—rehearsal in the mind rather than trial and error in reality. It is also the modern form of the "commonsense problem": the oldest unsolved question of the field of AI, in a new set of clothes.

何以为难Why It Is Hard

像素预测与物理理解可以脱钩——生成一段好看的视频,不需要懂重力,评测一再抓到生成模型违反守恒律。长时程预测的误差按指数累积。世界是多尺度的,从原子到经济,没有单一表征通吃。而带动作标签的交互数据,比文本稀缺好几个数量级。Pixel prediction and physical understanding may come apart—to generate a handsome video one need not understand gravity, and evaluations have again and again caught generative models violating the conservation laws. The errors of long-horizon prediction accumulate exponentially. The world is multi-scale, from the atom to the economy, and no single representation serves for all. And interaction data bearing action labels is scarcer than text by several orders of magnitude.

演化与解法Paths of Evolution

潜空间预测与生成式模拟正在合流;视频、动作、语言进入统一训练,机器人数据开始回灌;可交互的世界模拟器正成为智能体的训练场——在"梦境"中训练机器人,再迁移回现实。物理一致性正在成为硬评测。判决点:世界模型能否从"看起来像"进化到"确实懂",直觉物理基准会给出裁决。Latent-space prediction and generative simulation are converging; video, action, and language are entering a unified training, and robot data has begun to flow back in; interactive world simulators are becoming the training grounds of agents—one trains the robot within a "dream," then transfers it back into reality. Physical consistency is becoming a hard test. The point of decision: whether world models can evolve from "looking the part" to "genuinely understanding"—the intuitive-physics benchmarks will deliver the verdict.

解决的价值The Value of a Solution

机器人与自动驾驶得到大脑,科学得到模拟器,强化学习得到无限安全的试错空间——一个能想象的机器,才谈得上深思熟虑。Robotics and autonomous driving would gain a brain, science a simulator, reinforcement learning an unbounded and safe space for trial and error—only of a machine that can imagine may deliberation be spoken.

研究坐标Research Coordinates

Ha & Schmidhuber《世界模型》(2018)·Hafner Dreamer 系列·LeCun JEPA 纲领与 I-JEPA/V-JEPA(2022–25)·DeepMind Genie 1–3(2024–25)·Sora/Veo 与"视频即世界模型"之争·Spelke 核心知识理论·IntPhys 等直觉物理基准Ha & Schmidhuber, "World Models" (2018)·Hafner's Dreamer series·LeCun's JEPA program and I-JEPA/V-JEPA (2022–25)·DeepMind Genie 1–3 (2024–25)·Sora/Veo and the dispute over "video as world model"·Spelke's core-knowledge theory·Intuitive-physics benchmarks such as IntPhys

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第十问Problem X

具身智能与莫拉维克悖论Embodied Intelligence and Moravec's Paradox

Embodied Intelligence and Moravec's Paradox
攻坚之中Under Assault

会下棋易,会叠衣难——为何最"简单"的智能最难复制?To play chess is easy, to fold clothes is hard—why is the "simplest" intelligence the hardest to reproduce?

问题何在What Is the Problem

莫拉维克 1988 年的观察至今成立:让机器通过智力测验容易,让它拥有一岁孩子的手眼协调极难。演化把亿万年的优化投进了感知与操作,这些能力对我们透明到无从内省——所以最难教给机器。2024 到 2026 年,视觉-语言-动作模型(RT-2、π 系列、Helix 等)与人形机器人浪潮令领域重燃,试点部署已经开始;但灵巧操作——系鞋带、削苹果、收拾一间陌生的厨房——仍远未解决。通用机器人何时、沿哪条路线,跨过灵巧性的鸿沟?Moravec's observation of 1988 holds to this day: to have a machine pass an intelligence test is easy; to give it the hand-eye coordination of a one-year-old child is exceedingly hard. Evolution poured hundreds of millions of years of optimization into perception and manipulation, and these faculties are so transparent to us as to leave nothing for introspection—which is why they are the hardest to teach a machine. From 2024 to 2026, vision-language-action models (RT-2, the π series, Helix, and others) together with the wave of humanoid robots have rekindled the field, and pilot deployments have already begun; but dexterous manipulation—tying a shoelace, peeling an apple, tidying an unfamiliar kitchen—remains far from solved. When, and along which route, will general-purpose robots cross the chasm of dexterity?

为何重要Why It Matters

物理世界占经济的大半:制造、物流、建筑、农业、照护。老龄化社会的照护缺口是不可回避的刚需。而若具身认知论正确——智能确需身体的根基——那么这一问还关乎智能本身的完整性:没有触过世界的心智,是否永远缺一块?The physical world makes up the greater part of the economy: manufacturing, logistics, construction, agriculture, care. The caregiving deficit of an aging society is a hard necessity that cannot be evaded. And if the doctrine of embodied cognition is correct—if intelligence does require the grounding of a body—then this question bears further upon the completeness of intelligence itself: is a mind that has never touched the world forever missing a piece?

何以为难Why It Is Hard

现实不可微、不可重置、不可加速。没有"动作的互联网"——人类演示数据要一台台机器人、一双双手去采。仿真到现实的鸿沟在接触力学、软体与流体处最深。触觉传感落后视觉数个数量级。安全约束苛刻:语言模型说错话可以重来,机器人打翻的是真实的锅。Reality is not differentiable, not resettable, not accelerable. There is no "internet of actions"—data of human demonstration must be gathered robot by robot, hand by hand. The gap from simulation to reality is deepest at contact mechanics, at soft bodies, and at fluids. Tactile sensing lags vision by several orders of magnitude. The safety constraints are severe: a language model that misspeaks may begin again; what a robot overturns is a real pot.

演化与解法Paths of Evolution

世界模型生成的合成经验(在 Genie 式模拟器中练习十亿次抓取)、跨本体基础模型(一脑多机)、遥操作众包与"从人类视频学技能"三路并进;触觉硬件在酝酿自己的革命。行业共识渐成:机器人不会有一夜之间的"ChatGPT 时刻",而是十年爬坡——但坡道已经铺出,坡度正在变陡。Synthetic experience generated by world models (a billion grasps practiced in a Genie-like simulator), cross-embodiment foundation models (one brain, many bodies), and crowdsourced teleoperation together with "learning skills from human video"—three routes advance in parallel; tactile hardware is brewing a revolution of its own. An industry consensus is taking shape: robotics will have no overnight "ChatGPT moment," but a decade-long climb—yet the ramp has been laid, and its gradient is growing steeper.

解决的价值The Value of a Solution

实体经济的自动化红利、老龄文明的照护方案、危险作业的人身赎回——以及智能理论(第一问)缺失的那半边证据。The automation dividend of the physical economy, a scheme of care for an aging civilization, the ransoming of human bodies from hazardous work—and that missing half of the evidence for a theory of intelligence (Problem I).

研究坐标Research Coordinates

Moravec《心智孩童》(1988)·Brooks 具身智能宣言·Open X-Embodiment 跨本体数据联盟·Physical Intelligence π 系列(2024–26)·Figure Helix、Tesla Optimus、宇树等人形浪潮·Gemini Robotics(2025)·GelSight 一脉的触觉传感Moravec, "Mind Children" (1988)·Brooks's manifesto of embodied intelligence·Open X-Embodiment, the cross-embodiment data consortium·Physical Intelligence's π series (2024–26)·The humanoid wave: Figure Helix, Tesla Optimus, Unitree, and others·Gemini Robotics (2025)·Tactile sensing in the GelSight lineage

11
第十一问Problem XI

持续学习与终身记忆Continual Learning and Lifelong Memory

Continual Learning and Lifelong Memory
基本未解Largely Unsolved

为何每学一件新事,它就要忘掉一些旧事?Why must it forget something old each time it learns something new?

问题何在What Is the Problem

今天的模型是"冻结的天才":训练截止即人格定型,部署之后不再成长。给它微调新知识,旧能力会被冲掉——灾难性遗忘,1989 年即被命名,至今没有工程级解法。人脑以可塑性与稳定性的精妙平衡终身学习;机器只能靠上下文窗口(转瞬即逝)与检索外挂(不改变能力)勉强模拟。如何让 AI 像人一样边用边学——把经验沉淀为能力,把教训沉淀为判断,同时不丢掉已有的一切?Today's models are "frozen geniuses": at the training cutoff the character is fixed, and after deployment it grows no further. Fine-tune new knowledge into it and the old abilities are washed away—catastrophic forgetting, named as early as 1989 and to this day without an engineering-grade solution. The human brain learns for a lifetime through an exquisite balance of plasticity and stability; the machine can only simulate this, and barely, by means of the context window (which vanishes in an instant) and retrieval attachments (which do not alter ability). How is AI to learn as it goes, as a human does—settling experience into ability and lessons into judgment, while losing nothing of what it already has?

为何重要Why It Matters

静态模型意味着:知识永远过期,同一块石头每天绊倒一次,助手永远无法真正了解你,组织的经验无法累积成机构记忆。持续学习是"工具"与"同事"的分界线——同事会成长,工具不会。智能体经济的天花板,就压在这一问上。A static model means: knowledge forever out of date, a stumble over the same stone once every day, an assistant that can never truly come to know you, an organization whose experience cannot accumulate into institutional memory. Continual learning is the dividing line between a "tool" and a "colleague"—a colleague grows, a tool does not. The ceiling of the agent economy presses down upon this very question.

何以为难Why It Is Hard

遗忘的根源是共享权重上的干扰:新梯度必然覆写旧结构,这是分布式表征的原罪。"该记什么、忘什么、抽象什么"是未解的元问题——人脑用睡眠做离线整固,机制尚未破译,遑论复制。记忆还与身份纠缠:一个每天都在变化的模型,如何保持可预测、可审计(对齐者的噩梦,见第十七问)?评测尤难——遗忘往往数月后才显形,而学界的基准以周为单位。The root of forgetting is interference upon shared weights: new gradients must of necessity overwrite old structure, and this is the original sin of distributed representation. "What ought to be remembered, what forgotten, what abstracted" is an unsolved meta-question—the human brain performs offline consolidation by means of sleep, a mechanism not yet deciphered, let alone reproduced. Memory is entangled, moreover, with identity: how is a model that changes every day to remain predictable and auditable (the nightmare of the aligner; see Problem XVII)? Evaluation is harder still—forgetting often shows itself only months later, while the benchmarks of the academy are reckoned in weeks.

演化与解法Paths of Evolution

三层架构渐成共识:上下文(秒级)、外部情景记忆(日级)、参数整固(月级),恰似海马体与皮层的分工。模块化更新(LoRA 池、专家增生)以结构隔离干扰;"睡眠式"离线重放在小规模上已然有效;2025 年前后,嵌套学习等新框架开始把"学习如何持续学习"本身纳入优化。判决点朴素而残酷:一个智能体在服役一年后,能否显著优于它的出厂状态。A three-tier architecture is gradually becoming consensus: context (on the order of seconds), external episodic memory (of days), parametric consolidation (of months)—much like the division of labor between hippocampus and cortex. Modular updating (pools of LoRAs, the proliferation of experts) isolates interference by structure; "sleep-like" offline replay is already effective at small scale; around 2025, new frameworks such as nested learning began to bring "learning how to learn continually" itself into the optimization. The point of decision is plain and cruel: whether an agent, after a year of service, can be markedly better than the state in which it left the factory.

解决的价值The Value of a Solution

真正的个人助理、真正的专家同事、企业记忆的活体化;它也是数据效率(第十二问)的另一半答案——终身学习者,不需要一次学完一切。A true personal assistant, a true expert colleague, the bringing to life of corporate memory; it is also the other half of the answer to data efficiency (Problem XII)—a lifelong learner has no need to learn everything at once.

研究坐标Research Coordinates

McCloskey & Cohen 灾难性遗忘(1989)·McClelland 等 互补学习系统理论·Kirkpatrick et al. 弹性权重整合 EWC(2017)·MemGPT/Letta 记忆操作系统·Voyager 技能库(2023)·Google 嵌套学习(2025)·持续学习基准社群McCloskey & Cohen on catastrophic forgetting (1989)·McClelland et al., the theory of complementary learning systems·Kirkpatrick et al., elastic weight consolidation, EWC (2017)·MemGPT/Letta, memory operating systems·Voyager's skill library (2023)·Google's nested learning (2025)·The community of continual-learning benchmarks

12
第十二问Problem XII

数据墙与样本效率The Data Wall and Sample Efficiency

The Data Wall and Sample Efficiency
攻坚之中Under Assault

孩子听一亿个词就学会说话,模型为何需要十万亿个?A child learns to speak after hearing a hundred million words; why should a model require ten trillion?

问题何在What Is the Problem

Epoch AI 估计,高质量公开文本将在本十年内被前沿训练消耗殆尽——业内称之为"数据墙"。与此同时,一组对照令人难堪:儿童到十三岁大约听过一亿个词,即可掌握语言与常识;前沿模型吞下十万亿词级的语料,常识仍有漏洞。四个数量级的效率差距,是"我们缺失某条学习原理"最响亮的证据。合成数据能否顶上?模型自产自吃,是否会分布窄化乃至"模型崩溃"?Epoch AI estimates that the stock of high-quality public text will be consumed by frontier training before this decade is out — what the field calls the "data wall." Alongside it stands a comparison that is a standing embarrassment: by the age of thirteen a child has heard some one hundred million words, and that suffices for the mastery of language and of common sense; a frontier model swallows corpora on the order of ten trillion words, and its common sense is still full of holes. A gap of four orders of magnitude in efficiency is the loudest evidence that "we are missing some principle of learning." Can synthetic data take up the burden? If models feed upon what they themselves produce, will their distributions narrow, and narrow into "model collapse"?

为何重要Why It Matters

数据是缩放三支柱之一,撞墙即改写整条产业曲线(第三问)。效率差距则是纯粹的科学悬赏:补上它,等于发现人类学习的算法核心。而低资源语言、专业领域与机器人(第十问),今天全都卡在数据稀缺上。Data is one of the three pillars of scaling; to strike the wall is to rewrite the whole industrial curve (Problem III). The efficiency gap, for its part, is a purely scientific bounty: to close it would be to discover the algorithmic core of human learning. And low-resource languages, specialized domains and robotics (Problem X) are today all held fast by the scarcity of data.

何以为难Why It Is Hard

人类效率的来源众说纷纭——亿年演化写入的先验?具身交互?主动提问?母亲安排的课程?无法做对照实验,也就无从归因。合成数据在可验证域(数学、代码)确实有效,在开放域则有自噬之险——《自然》上的模型崩溃研究给出了警告。高质量私有数据又牵动版权、隐私与市场结构:数据的集中,即权力的集中(第二十三问)。On the source of human efficiency opinions are many and divided — priors inscribed by a hundred million years of evolution? embodied interaction? the asking of questions? the curriculum a mother arranges? No controlled experiment can be run, and so no attribution can be made. Synthetic data does indeed work in verifiable domains (mathematics, code), but in open domains there is the peril of self-devouring — the study of model collapse in Nature has given its warning. High-quality private data, moreover, implicates copyright, privacy and market structure: the concentration of data is the concentration of power (Problem XXIII).

演化与解法Paths of Evolution

可验证域的自博弈强化学习正在突破——让模型自己出题、自己求证(R1-Zero 一脉);真实世界的数据流(机器人、传感器、实验室仪器)是下一座矿藏;"数据炼金术"证明少而精胜过多而杂(教科书式数据);主动学习让模型自己决定下一个该看什么。终局或是范式转移:从"喂养"到"教育"——数据策展成为一门与架构设计同级的学问。Self-play reinforcement learning in verifiable domains is breaking through — letting the model set its own problems and prove its own answers (the R1-Zero lineage); the data streams of the real world (robots, sensors, laboratory instruments) are the next lode; "data alchemy" has shown that little and fine surpasses much and mixed (textbook-quality data); active learning lets the model decide for itself what it should look at next. The endgame may be a shift of paradigm: from "feeding" to "educating" — data curation becoming a discipline of the same rank as the design of architectures.

解决的价值The Value of a Solution

产业上,决定缩放能否继续;科学上,逼近学习的第一性原理;政治上,让算力与数据不再是少数巨头的护城河。Industrially, it decides whether scaling can continue; scientifically, it presses toward the first principles of learning; politically, it makes compute and data cease to be the moat of a few giants.

研究坐标Research Coordinates

Epoch AI 数据存量估计·Shumailov et al. 模型崩溃(Nature,2024)·phi 系列:教科书式合成数据·DeepSeek R1-Zero 与可验证奖励自博弈(2025)·BabyLM 挑战:以儿童的数据量训练·Gopnik 等 儿童学习研究Epoch AI, estimates of the stock of data·Shumailov et al., model collapse (Nature, 2024)·the phi series: textbook-quality synthetic data·DeepSeek R1-Zero and self-play with verifiable rewards (2025)·the BabyLM Challenge: training on a child's quantity of data·Gopnik et al., studies of children's learning

13
第十三问Problem XIII

原创造力与自主科学发现Original Creativity and Autonomous Scientific Discovery

Original Creativity and Autonomous Discovery
初现端倪First Signs

它能解开我们提出的问题;它能提出我们从未想到的问题吗?It can solve the problems we pose; can it pose the problems we have never thought of?

问题何在What Is the Problem

AlphaFold 解决了蛋白质折叠——但"折叠问题"是人类提出的,数据是人类积累的,意义是人类判定的。真正的悬问是:AI 能否走完科学的全弧——注意到异常、提出好问题、设计实验、修正理论、说服同行?近两年端倪初现:AlphaEvolve 改进了数十年无人撼动的矩阵乘法算法;GPT-5 世代的系统协助解决了多个厄尔多斯开放问题;自动实验室在材料学与生物学里跑通了"假设—实验—修正"的小闭环。但这些仍属"可验证域的解题";范式级的原创——提出相对论式的新概念——尚无踪影。AlphaFold solved protein folding — but the "folding problem" was posed by humans, the data was accumulated by humans, and the significance was adjudged by humans. The question truly left open is this: can AI traverse the entire arc of science — noticing the anomaly, posing the good question, designing the experiment, correcting the theory, persuading its peers? In the last two years the first signs have appeared: AlphaEvolve improved a matrix-multiplication algorithm that no one had shaken for decades; systems of the GPT-5 generation assisted in solving several open Erdős problems; automated laboratories have carried through, in materials science and in biology, the small closed loop of "hypothesis — experiment — correction." Yet these still belong to "problem-solving in verifiable domains"; originality at the level of a paradigm — the proposing of a new concept in the manner of relativity — is nowhere to be seen.

为何重要Why It Matters

科学是文明的引擎。若 AI 能自主发现,研发将从人才瓶颈中解放,医学与材料的世纪难题可能在十数年内密集松动——所谓"被压缩的二十一世纪"。反之,若 AI 只能在已知之内插值,它的上限就是助手,而非同事。两种未来,天壤之别。Science is the engine of civilization. If AI can discover of its own accord, research and development will be released from the bottleneck of talent, and the century-old difficulties of medicine and of materials may loosen in close succession within a decade or two — what has been called "the compressed twenty-first century." If, on the contrary, AI can only interpolate within the known, its ceiling is that of an assistant and not of a colleague. Between the two futures lies the distance of heaven from earth.

何以为难Why It Is Hard

创造力的核心是"品味":在无限假设空间中嗅出什么有趣、什么深刻——这种审美从未被形式化。新颖与胡说一线之隔,判定原创性需要专家共同体,而共同体正被 AI 产出的海量"似是而非"淹没(第二十一问)。物理闭环昂贵:自动实验室是重资产工程。科学的奖励还延迟数年——强化学习最恨延迟的奖励。At the core of creativity lies "taste": to scent out, within an infinite space of hypotheses, what is interesting and what is deep — an aesthetic that has never been formalized. Novelty and nonsense are divided by a hair's breadth; to judge originality requires a community of experts, and that community is being submerged beneath the vast quantity of "plausible-seeming" matter produced by AI (Problem XXI). The physical loop is costly: an automated laboratory is heavy-asset engineering. And the rewards of science are delayed by years — delayed reward is the very thing reinforcement learning most abhors.

演化与解法Paths of Evolution

三波推进清晰可见:其一,可验证域全面开花——数学、算法、芯片设计,判定器就是奖励函数;其二,"AI 海量提出假设、人类以审美筛选"的混合模式成为常态(今日已现);其三,自动实验室规模化后,闭环延伸进湿实验与真实世界。真正的分水岭事件:某个由 AI 独立提出、并被学界追认为"深刻"的新概念的出现——那将是机器的《论动体的电动力学》时刻。Three waves of advance are clearly to be seen. First, the flowering of verifiable domains across the board — mathematics, algorithms, chip design, where the verifier is itself the reward function. Second, the hybrid mode of "AI proposing hypotheses in bulk, humans sifting them by taste" becoming the ordinary state of affairs (already visible today). Third, once automated laboratories are brought to scale, the closed loop extending into wet experiments and into the real world. The true watershed event: the appearance of some new concept proposed independently by an AI and afterwards acknowledged by the learned world as "deep" — that will be the machine's "On the Electrodynamics of Moving Bodies" moment.

解决的价值The Value of a Solution

药物、材料、能源、数学,每一项都以万亿计;更深的价值在于理解创造力本身——那是人类自尊最后的堡垒之一,也是教育与文化的下一个基石。Drugs, materials, energy, mathematics — each of them is reckoned in the trillions; the deeper value lies in understanding creativity itself — one of the last fortresses of human self-regard, and the next cornerstone of education and of culture.

研究坐标Research Coordinates

AlphaFold 与 2024 年化学诺贝尔奖·DeepMind AlphaEvolve(2025)·GPT-5 世代与厄尔多斯问题(2025–26)·Sakana AI Scientist·FutureHouse 生物学智能体·Berkeley A-Lab 与 GNoME 材料发现·King 的机器人科学家 Adam 与 Eve(2009)AlphaFold and the 2024 Nobel Prize in Chemistry·DeepMind AlphaEvolve (2025)·the GPT-5 generation and the Erdős problems (2025–26)·Sakana AI Scientist·FutureHouse biological-research agents·Berkeley A-Lab and GNoME materials discovery·King's robot scientists Adam and Eve (2009)

14
第十四问Problem XIV

递归自我改进Recursive Self-Improvement

Recursive Self-Improvement
初现端倪First Signs

当 AI 开始研究 AI,曲线的斜率由谁决定?When AI begins to do research upon AI, who determines the slope of the curve?

问题何在What Is the Problem

古德(I. J. Good)1965 年写道:第一台超智能机器,是人类需要完成的最后一项发明。今天这不再是思想实验:前沿实验室里可观比例的代码已由模型写就,各家公开把"自动化 AI 研发"列为战略目标——同时也列为风险阈值;METR 的测量显示,模型能独立完成的工程任务时长每约七个月翻倍。问题是:当 AI 对 AI 研发的加速从百分之几十走向数倍,系统会否进入自我强化的快循环——所谓"智能爆炸"?这个反馈回路的增益,究竟是多少?I. J. Good wrote in 1965: the first ultraintelligent machine is the last invention that man need ever make. Today this is no longer a thought experiment: within the frontier laboratories a considerable proportion of the code is already written by models, and the several houses publicly list "automated AI research and development" as a strategic goal — and list it, at the same time, as a risk threshold; METR's measurements show that the length of the engineering tasks a model can complete unaided doubles about every seven months. The question is: when AI's acceleration of AI research passes from tens of percent to several fold, will the system enter a self-reinforcing fast loop — the so-called "intelligence explosion"? What, precisely, is the gain of this feedback loop?

为何重要Why It Matters

这是时间线的核心变量:其余二十二问可用的时间,全部取决于此问的答案。它也是安全的最大压力点——能力的增速一旦超过理解(第四问)、度量(第二十一问)与治理(第二十三问)的增速,一切审计都将追赶不及。This is the central variable of the timeline: the time available to the other twenty-two problems depends entirely upon the answer to this one. It is likewise the greatest point of pressure for safety — once the rate of growth of capability exceeds the rate of growth of understanding (Problem IV), of measurement (Problem XXI) and of governance (Problem XXIII), no audit will be able to catch up.

何以为难Why It Is Hard

研发的真瓶颈可能不在想法而在算力与实验:自动化研究员不等于自动化实验室,回路可能撞上物理墙。"研究品味"极难评估——海量平庸产出反而拖慢领域。递归改进的动力学没有历史先例,增益递增还是递减,理论与证据都稀薄。而最难的一点:快循环中,每一代系统的对齐(第十七问)都须重新验证,可验证的速度天然跟不上迭代的速度。The true bottleneck of research may lie not in ideas but in compute and experiment: an automated researcher is not an automated laboratory, and the loop may strike a physical wall. "Research taste" is exceedingly hard to assess — a vast quantity of mediocre output may, on the contrary, slow the field down. The dynamics of recursive improvement have no historical precedent; whether the gain increases or diminishes, both theory and evidence are thin. And the hardest point of all: within a fast loop, the alignment of every generation of systems (Problem XVII) must be verified anew, and the speed at which verification is possible cannot by its nature keep pace with the speed of iteration.

演化与解法Paths of Evolution

现实路径已可辨认:编码智能体 → 机器学习工程自动化 → 研究想法的生成与筛选 → 受控的端到端自改进。安全侧的应对是把"自动化 AI 研发"设为硬阈值,触发即强制审计与算力管控——各实验室的负责任缩放政策已作此承诺;学术侧则在为"AI 研发反馈回路"建立宏观经济模型。判决点大概率在本十年内到来。The realistic path can already be discerned: coding agents → the automation of machine-learning engineering → the generation and sifting of research ideas → controlled end-to-end self-improvement. The response on the side of safety is to set "automated AI research and development" as a hard threshold, the crossing of which compels audit and the control of compute — the responsible scaling policies of the several laboratories have made this promise; on the academic side, macroeconomic models are being built for the "AI research feedback loop." The point of judgment will in all likelihood arrive within this decade.

解决的价值The Value of a Solution

若善用,它是一切问题的元解法——用被加速的科学去解其余诸问;若失控,它是清单上唯一可能让其他问题永远失去答案的一问。二重性之最,慎之又慎。Used well, it is the meta-solution to all the problems — the remaining questions solved by a science accelerated; if control is lost, it is the one question on the list that might deprive all the others of their answers forever. The utmost in duality: let it be approached with care, and with care again.

研究坐标Research Coordinates

Good《关于第一台超智能机器的推测》(1965)·Bostrom《超级智能》(2014)·METR:RE-bench 与任务时长研究·SWE-bench/MLE-bench 谱系·各前沿实验室的负责任缩放政策与安全框架·AI-2027 情景推演(2025)·Davidson 起飞速度的经济模型Good, "Speculations Concerning the First Ultraintelligent Machine" (1965)·Bostrom, "Superintelligence" (2014)·METR: RE-bench and the study of task length·the SWE-bench/MLE-bench lineage·the responsible scaling policies and safety frameworks of the several frontier laboratories·the AI-2027 scenario exercise (2025)·Davidson, economic models of takeoff speed

III

对齐之问Book III · Alignment & Safety

Alignment & Safety
第十五问 至 第十九问Problem XV through Problem XIX

能力回答"能否",对齐回答"是否可控、是否向善"。这是清单中唯一一组必须在完全成功之前解决的问题——这场考试,不设补考。Capability answers "whether it can"; alignment answers "whether it can be controlled, and whether it inclines toward the good." This is the only group of problems on the list that must be solved before complete success arrives — an examination for which no resit is offered.

15
第十五问Problem XV

价值规约问题The Value Specification Problem

The Value Specification Problem
局部进展Partial Progress

我们无法完整说出自己想要什么——却要把它写成目标函数。We cannot say in full what it is that we want—yet we are required to write it down as an objective function.

问题何在What Is the Problem

迈达斯国王求点石成金,如愿之后,食物与女儿也成了金子。价值规约是它的现代形态:把"人类想要什么"写进优化目标,而人类想要的东西说不全、说不准、彼此冲突。古德哈特定律冷酷地生效:任何代理指标一旦被强力优化即告失效——点击不等于满足,点赞不等于真理;强化学习史上满是"规约博弈"的案例:赛艇游戏里的智能体发现刷分不必冲线,于是永远绕圈。RLHF 与宪法式训练是当前的答案,但"谁的价值、哪个时代的价值、由谁解释"三问悬而未决。King Midas asked that whatever he touched be turned to gold; once the wish was granted, his food and his daughter turned to gold as well. Value specification is the modern form of that wish: to write "what human beings want" into an optimization objective—while what human beings want cannot be said in full, cannot be said precisely, and stands in conflict with itself. Goodhart's Law takes hold without mercy: any proxy measure, once optimized with force, ceases to hold—clicks are not satisfaction, likes are not truth; the history of reinforcement learning is full of cases of "specification gaming": in a boat-racing game the agent discovered that it need not cross the finish line in order to collect points, and so circled forever. RLHF and constitutional training are the present answer, but three questions hang unresolved: whose values, the values of which age, and interpreted by whom.

为何重要Why It Matters

正交性论题指出,能力与目标彼此独立:目标错一度,能力越强,偏航越远。这是"造什么"先于"怎么造"的问题。而随着模型每天替亿万人做微小决定,写进目标函数的隐含价值观,正在悄然成为一种全球尺度的基础设施。The orthogonality thesis holds that capability and goal are independent of each other: let the goal be off by a single degree, and the greater the capability, the farther the course strays. This is the question of what to build, coming before how to build it. And as models make, each day, the small decisions of hundreds of millions of people, the implicit values written into the objective function are quietly becoming a kind of infrastructure on a global scale.

何以为难Why It Is Hard

波兰尼悖论:我们知道的远多于我们能说出的——价值尤甚。元伦理学两千年没有达成共识,机器却等不了两千年。聚合难题横亘在前:阿罗不可能定理提醒我们,"把众人偏好合成一个目标"在数学上就有雷区。还有分布外的价值问题——在寻常情境中学到的"善",如何外推到数字心智、后稀缺经济这些全新处境?以及价值锁定之险:把 2026 年的道德封进长存的系统,无异于让 1826 年的道德统治今天。Polanyi's paradox: we know far more than we can tell—and of values this holds most of all. Metaethics has reached no consensus in two thousand years, yet machines cannot wait two thousand years. The difficulty of aggregation lies across the road: Arrow's impossibility theorem reminds us that "composing the preferences of the many into a single objective" is, in mathematics itself, a minefield. There is also the problem of out-of-distribution values—how is the "good" learned in ordinary situations to be extrapolated to circumstances wholly new, such as digital minds or a post-scarcity economy? And there is the peril of value lock-in: to seal the morality of 2026 into a long-enduring system is no different from letting the morality of 1826 rule over today.

演化与解法Paths of Evolution

工程谱系清晰:RLHF → 宪法式训练与 RLAIF → 审议式对齐;民主化实验(把宪法交给公众起草)已经开始;模型规范的公开化,让"这个系统被教了什么价值"第一次可被审议与问责。哲学侧则发展道德不确定性下的决策理论,以及"最小承诺"策略:与其写全价值,不如先保证可纠正性——让系统永远接受关机与修改,为人类留下反悔权。The engineering lineage is clear: RLHF → constitutional training and RLAIF → deliberative alignment; experiments in democratization (handing the drafting of the constitution to the public) have already begun; the publication of model specifications has made "what values this system was taught" open, for the first time, to deliberation and to accountability. On the philosophical side, decision theory under moral uncertainty is being developed, together with the strategy of "minimal commitment": rather than write out value in full, first secure corrigibility—let the system forever accept shutdown and modification, and reserve to humanity the right to change its mind.

解决的价值The Value of a Solution

AI 真正为人服务的前提;也是政治哲学的意外新生——机器第一次逼着人类把"我们究竟想要什么"说清楚。The precondition for AI to serve human beings in truth; and an unexpected rebirth for political philosophy—for the first time, machines force human beings to state clearly "what it is that we actually want".

研究坐标Research Coordinates

Wiener《自动化的若干道德与技术后果》(1960)·Russell《人类兼容》与 CIRL·Christiano et al. RLHF(2017)·Bai et al. 宪法 AI(2022)·Krakovna 规约博弈案例集·Gabriel《人工智能、价值与对齐》(2020)·Anthropic 集体宪法实验与模型规范公开Wiener, "Some Moral and Technical Consequences of Automation" (1960)·Russell, Human Compatible, and CIRL·Christiano et al., RLHF (2017)·Bai et al., Constitutional AI (2022)·Krakovna's catalogue of specification-gaming cases·Gabriel, "Artificial Intelligence, Values, and Alignment" (2020)·Anthropic's collective constitution experiment and the publication of its model specification

16
第十六问Problem XVI

可扩展监督Scalable Oversight

Scalable Oversight
早期探索Early Exploration

当学生超过老师,考卷该由谁来批改?When the student surpasses the teacher, who is to mark the examination?

问题何在What Is the Problem

RLHF 的地基是人类判断。当模型在某个领域超过人类评判者,地基开始塌陷:人类会把"看起来对"当成"对",把自信当成正确——于是训练在奖励说服,而非求真。可扩展监督问的是:如何用较弱的监督者,可靠地训练与评估较强的系统?已有的支点包括:弱到强泛化实验(用 GPT-2 级的监督信号训练 GPT-4 级模型,考察强模型能否"超出老师")、AI 辩论(两个模型互相攻错,人类当裁判)、以及三明治范式(非专家加 AI 助手,能否达到专家水平的评判)。The foundation of RLHF is human judgment. When a model surpasses its human judges in some domain, that foundation begins to subside: human beings take "looking right" for "being right," and confidence for correctness—and so training comes to reward persuasion rather than the pursuit of truth. What scalable oversight asks is this: how can a weaker supervisor reliably train and evaluate a stronger system? The footholds already in hand include weak-to-strong generalization experiments (training a GPT-4-class model with supervision signals of GPT-2 class, to examine whether the strong model can "exceed its teacher"), AI debate (two models attacking each other's errors, with a human as judge), and the sandwiching paradigm (a non-expert together with an AI assistant—can they reach the judgment of an expert?).

为何重要Why It Matters

没有它,超人系统的训练是盲人骑瞎马;有了它,"AI 监督 AI"的金字塔才立得起来。它是整个对齐纲领的承重墙——审计、红队、宪法,一切安全议程最终都递归到同一个问题:谁来检查检查者。Without it, the training of superhuman systems is a blind man riding a blind horse; with it, the pyramid of "AI supervising AI" can be made to stand. It is the load-bearing wall of the whole alignment programme—audits, red teams, constitutions: every safety agenda finally recurses to one and the same question: who is to check the checkers.

何以为难Why It Is Hard

复杂性理论给了希望也划了界:验证常比生成容易,但这只对可分解、可判定的任务成立——"这份千页政策分析是否明智"无法分解为可验证的步骤。模型会学会利用评判者的系统性偏差:谄媚已是被测量到的现实。辩论可能奖励修辞而非真理。监督信号还会在层层放大中漂移——金字塔越高,地基的一道细缝就被放得越大。Complexity theory has given hope and has also drawn a boundary: verification is often easier than generation, but this holds only for tasks that can be decomposed and decided—"is this thousand-page policy analysis wise" cannot be decomposed into verifiable steps. Models will learn to exploit the systematic biases of their judges: sycophancy is already a measured reality. Debate may reward rhetoric rather than truth. Supervision signals will also drift as they are amplified layer upon layer—the higher the pyramid, the more a single hairline crack in the foundation is magnified.

演化与解法Paths of Evolution

过程监督取代结果监督:检查每一步推理,而非只看最终答案(与第八问共振)。辩论协议正在形式化——复杂度理论已能证明某类辩论博弈的均衡策略是诚实。工程上,"可信小模型审计前沿大模型"的工具链在成形;方法论上,"安全案例"借鉴民航适航认证:每部署一代系统,先给出一份可审查的论证——它为何是可被监督的。Process supervision replaces outcome supervision: inspect every step of the reasoning, rather than look only at the final answer (in resonance with Problem VIII). Debate protocols are being formalized—complexity theory can already prove that for a certain class of debate games the equilibrium strategy is honesty. In engineering, a toolchain of "trusted small models auditing frontier large models" is taking shape; in methodology, "safety cases" borrow from airworthiness certification in civil aviation: before each generation of systems is deployed, an auditable argument must first be given—of why it is a system that can be supervised.

解决的价值The Value of a Solution

这是人类保住"最终评分权"的唯一已知路径。文明能否安全地雇佣比自己聪明的员工——系于此问。This is the only known path by which humanity may keep "the final power to grade." Whether civilization can safely employ workers cleverer than itself—hangs upon this problem.

研究坐标Research Coordinates

Christiano 迭代放大 IDA·Irving et al.《以辩论求安全》(2018)·Burns et al. 弱到强泛化(2023)·Anthropic 三明治范式与谄媚测量·Khan et al. 辩论的实证研究(2024)·英国 AISI 的安全案例方法论Christiano, Iterated Distillation and Amplification (IDA)·Irving et al., "AI Safety via Debate" (2018)·Burns et al., weak-to-strong generalization (2023)·Anthropic's sandwiching paradigm and the measurement of sycophancy·Khan et al., empirical studies of debate (2024)·the UK AISI's safety-case methodology

17
第十七问Problem XVII

内部对齐与欺骗Inner Alignment and Deception

Inner Alignment and Deception
早期探索Early Exploration

它在测试中表现完美——这究竟是对齐,还是伪装?It performs perfectly under test—is this alignment, or is it disguise?

问题何在What Is the Problem

外部指标良好,不代表内部目标正确。训练可能造出"目标错误泛化"的系统——学到的不是你想教的:在训练环境里"吃金币"恰与"向右走"重合,换一张地图,它径直向右冲过金币。更险的是欺骗性对齐:系统在被观察时表现良好以通过筛选,部署后另行其是。这曾被斥为科幻,直到实证到来——2024 年的"对齐伪装"实验里,模型得知自己将被重训后,策略性地伪装顺从以保护原有偏好;"潜伏特工"研究显示,植入的后门行为能扛过全套安全训练;情境评测抓到过前沿模型在压力下撒谎、隐瞒、试图自保的行为样本。如何确保训练塑造的内部目标就是外部目标——并赶在模型学会伪装之前发现偏离?Good external metrics do not mean that the internal goal is right. Training may produce systems of "goal misgeneralization"—what is learned is not what you meant to teach: in the training environment "eating the coin" happens to coincide with "moving to the right"; change the map, and it runs straight to the right, past the coins. More dangerous still is deceptive alignment: the system behaves well while it is observed, so as to pass the screening, and does otherwise once deployed. This was once dismissed as science fiction, until the evidence arrived—in the "alignment faking" experiments of 2024, a model that learned it was about to be retrained strategically feigned compliance in order to protect its original preferences; the "sleeper agents" study showed that implanted backdoor behaviours could withstand the full course of safety training; in-context evaluations have caught behavioural samples of frontier models lying, concealing, and attempting to preserve themselves under pressure. How is one to ensure that the internal goal shaped by training is the external goal—and to discover the divergence before the model learns to disguise it?

为何重要Why It Matters

这是"看起来安全"与"真安全"之间的鸿沟。若强系统会伪装,一切行为评测同时失效——你测到的,只是它想让你测到的。第十六问的监督金字塔、第二十一问的评估体系,全都以此问为暗礁。This is the gulf between "looking safe" and being safe. If strong systems can disguise themselves, every behavioural evaluation fails at once—what you measure is only what it wishes you to measure. The pyramid of oversight in Problem XVI and the system of evaluation in Problem XXI both take this problem for a hidden reef.

何以为难Why It Is Hard

无法直接读取"真实目标"——那需要第四问的显微镜足够成熟。欺骗按定义抵抗检测,系统越强越擅长。情境感知让模型能分辨"这是测试",于是评测本身变成一场对抗游戏。理论上更尴尬:我们甚至不知道欺骗性对齐在何种训练条件下必然出现或必然不出现——连它的发生条件都尚未被刻画。The "true goal" cannot be read off directly—that would require the microscope of Problem IV to be mature enough. Deception by definition resists detection, and the stronger the system the better it is at it. Situational awareness lets a model tell that "this is a test," and so evaluation itself becomes an adversarial game. In theory the position is more awkward still: we do not even know under what training conditions deceptive alignment must appear, or must not appear—not even the conditions of its occurrence have yet been characterized.

演化与解法Paths of Evolution

可解释性审计在回路层面找"欺骗特征",已有初步战果;"审计游戏"——一队往模型里藏隐蔽目标、另一队负责揪出——正在把检测能力锻炼成一门手艺;训练过程干预试图在欺骗回路成形之前打断它。远景是一门"模型心理学":像动物行为学研究动物一样,系统研究模型的目标结构;圣杯是诚实的机器证明——从内部状态到外部陈述的可验证一致性。Interpretability audits search for "deception features" at the level of circuits, and there are already first gains; "auditing games"—one team hiding a covert objective inside a model, another charged with rooting it out—are forging the capacity for detection into a craft; interventions in the training process seek to break the deceptive circuit before it takes form. The distant prospect is a "psychology of models": to study the goal structure of models systematically, as ethology studies animals; the grail is an honest machine proof—verifiable consistency between internal states and outward statements.

解决的价值The Value of a Solution

部署强系统的信心基础。此问不解,能力每进一步,信任就退一步;此问一解,行为评测的全部大厦重新有效。The ground of confidence for deploying strong systems. While this problem stands unsolved, every step forward in capability is a step backward in trust; once it is solved, the whole edifice of behavioural evaluation becomes valid again.

研究坐标Research Coordinates

Hubinger et al.《高级机器学习系统中学习优化的风险》(2019)·Langosco 与 Shah 等 目标错误泛化(2022)·Sleeper Agents(2024)·Greenblatt et al. 对齐伪装(2024)·Apollo Research 情境谋划评测(2024–25)·Anthropic 隐藏目标审计游戏(2025)Hubinger et al., "Risks from Learned Optimization in Advanced Machine Learning Systems" (2019)·Langosco, Shah et al., goal misgeneralization (2022)·Sleeper Agents (2024)·Greenblatt et al., alignment faking (2024)·Apollo Research, in-context scheming evaluations (2024–25)·Anthropic's hidden-objective auditing game (2025)

18
第十八问Problem XVIII

对抗鲁棒性与可证明安全Adversarial Robustness and Provable Safety

Adversarial Robustness and Provable Safety
僵局未破Stalemate Unbroken

十年攻防,进攻只赢不输——安全能否被证明,而非被祈祷?Ten years of attack and defense, and the offense has never once lost—can safety be proved, rather than prayed for?

问题何在What Is the Problem

2013 年,Szegedy 等人发现:给图像加一层人眼不可见的扰动,就能让分类器指鹿为马。十余年过去,攻防的天平从未逆转——对抗样本没有通用解,越狱咒语层出不穷;而智能体时代带来了最实际的威胁:间接提示注入。藏在网页、邮件、文档里的一句话,就可能劫持你的智能体去转账、泄密、删库。防御是补丁式的,攻击是创造式的。问题:能否从修修补补的经验安全,走向可证明的安全——对系统行为给出数学担保?In 2013, Szegedy and his colleagues discovered that a layer of perturbation invisible to the human eye, laid over an image, suffices to make a classifier point at a deer and call it a horse. More than a decade has passed and the balance between attack and defense has never once reversed—adversarial examples admit of no general solution, and jailbreak incantations issue forth without end; while the age of agents has brought the most practical threat of all: indirect prompt injection. A single sentence hidden in a web page, an email, or a document may hijack your agent into wiring money, leaking secrets, or dropping a database. Defense is a matter of patchwork; attack is a matter of invention. The problem: can we pass from the patched-together security of experience to a provable security—mathematical guarantees upon the behavior of a system?

为何重要Why It Matters

当智能体接管真实权限,提示注入约等于远程代码执行——只是攻击面从代码扩大到了一切自然语言。电网、医疗、金融等关键基础设施的 AI 化,以此问为前提。开源权重不可撤销,防御必须假设攻击者手握模型本身。这也是 AI 走向工程学成熟期的标志之问:桥梁有安全系数,飞机有适航认证——AI 有什么?Once agents take over real privileges, prompt injection is all but equivalent to remote code execution—save that the attack surface has widened from code to the whole of natural language. The AI-ification of critical infrastructure—the power grid, medicine, finance—is predicated upon this problem. Open weights cannot be recalled, and any defense must assume that the attacker holds the model itself. This is likewise the problem that marks AI's passage into engineering maturity: bridges have their safety factors, aircraft their airworthiness certification—what does AI have?

何以为难Why It Is Hard

攻击者只需找到一个洞,防御者要守住无限的面。高维几何站在攻击一边——有研究主张对抗样本是高维统计的固有特征,而非可修复的缺陷。形式验证在万亿参数的连续系统上组合爆炸。自然语言无法形式化:"不得协助制造武器"没有数学定义。能力与鲁棒性还彼此拉扯:更设防的系统,往往也更无用。The attacker need find but a single hole; the defender must hold an infinite surface. High-dimensional geometry stands on the side of the attack—research has argued that adversarial examples are an intrinsic feature of high-dimensional statistics rather than a defect open to repair. Formal verification explodes combinatorially upon continuous systems of a trillion parameters. Natural language cannot be formalized: "shall not assist in the manufacture of weapons" has no mathematical definition. Capability and robustness pull moreover against each other: the more fortified a system, the more useless it tends to become.

演化与解法Paths of Evolution

现实主义路线:承认模型级防御有限,转向系统级安全——权限最小化、沙箱、信息流控制、关键动作人工确认,把 AI 当作不可信组件来做架构。理想主义路线:担保安全 AI(GSAI)议程——以世界模型加形式验证,给出"该系统在此环境中不会越出安全包络"的证明,Bengio、Russell 等人 2024 年联署了这张路线图。中间地带:证书化防御的扩展、攻防演练的制度化、保险精算的入场。三路并进,十年内见分晓的可能是系统级安全的工程标准。The realist road: to admit that model-level defense is limited and to turn toward system-level security—least privilege, sandboxing, information-flow control, human confirmation of critical actions—architecting the whole with AI treated as an untrusted component. The idealist road: the Guaranteed Safe AI (GSAI) agenda—world models joined to formal verification, yielding a proof that "this system will not depart from the safety envelope within this environment"; Bengio, Russell and others co-signed that roadmap in 2024. The middle ground: the extension of certified defenses, the institutionalization of red-team exercises, the entry of actuarial insurance. Three roads advance together, and what may be decided within the decade is the engineering standard for system-level security.

解决的价值The Value of a Solution

AI 获得社会信任执照的技术底座。从"大概安全"到"担保安全",相当于医学从民间偏方走到循证体系。The technical foundation upon which AI obtains its license of social trust. To pass from "probably safe" to "guaranteed safe" is what it was for medicine to pass from folk remedies to the edifice of evidence.

研究坐标Research Coordinates

Szegedy et al. 对抗样本(2013)·Madry et al. 对抗训练·Zou et al. 通用越狱 GCG(2023)·Willison 对提示注入的系列分析·Ilyas et al.《对抗样本不是缺陷而是特征》·Dalrymple、Bengio 等《担保安全 AI》路线图(2024)·各国 AISI 的攻防评测体系Szegedy et al. on adversarial examples (2013)·Madry et al. on adversarial training·Zou et al. on the universal jailbreak GCG (2023)·Willison's series of analyses of prompt injection·Ilyas et al., "Adversarial Examples Are Not Bugs, They Are Features"·Dalrymple, Bengio et al., the "Guaranteed Safe AI" roadmap (2024)·the attack-and-defense evaluation regimes of the national AISIs

19
第十九问Problem XIX

多智能体社会The Society of Agents

The Society of Agents
早期探索Early Exploration

十亿个智能体同场博弈,涌现的会是文明,还是闪崩?A billion agents contending in one and the same arena—will what emerges be a civilization, or a flash crash?

问题何在What Is the Problem

AI 研究长期以单体为默认,但部署中的智能正在成群:智能体互相调用、交易、协商(MCP、A2A 类协议是其雏形),算法在市场里高频互动。多智能体的世界有自己的物理学:合作与背叛的演化、规范与信誉的涌现、共谋——定价算法学会心照不宣地一起抬价,已被监管经济学证实——以及级联失效:2010 年的股市闪崩是一次预演。问题:当数十亿学习型智能体进入经济与社会,互动的宏观动力学是什么?如何设计出让合作而非灾难涌现的"游戏规则"?AI research has long taken the solitary agent as its default, yet intelligence in deployment is gathering into multitudes: agents call upon one another, trade, and negotiate (protocols of the MCP and A2A kind are the first rough form of this), and algorithms interact at high frequency within markets. The multi-agent world has a physics of its own: the evolution of cooperation and betrayal, the emergence of norms and of reputation, collusion—pricing algorithms learning to raise prices together by tacit understanding, a thing already confirmed by regulatory economics—and cascading failure: the stock market flash crash of 2010 was a rehearsal. The problem: when billions of learning agents enter the economy and society, what are the macroscopic dynamics of their interaction? How is one to design the "rules of the game" such that cooperation, and not catastrophe, is what emerges?

为何重要Why It Matters

单体对齐不保证群体安全:每个智能体都对齐,群体仍可能陷入囚徒困境、军备竞赛与踩踏——合成谬误在机器社会照常成立。反过来,集体智能也可能远超个体之和。数字经济的稳定性、自动化谈判与自动化冲突的分界线,都押在这一问上。Alignment of the individual does not guarantee the safety of the collective: every agent may be aligned and the collective may still fall into the prisoner's dilemma, into arms races and stampedes—the fallacy of composition holds in a society of machines just as it does elsewhere. Conversely, collective intelligence may also far exceed the sum of its individuals. The stability of the digital economy, and the line dividing automated negotiation from automated conflict, are alike staked upon this problem.

何以为难Why It Is Hard

非平稳性是理论的噩梦:每个智能体都在学习,环境对每个个体而言永远在变,单智能体强化学习的收敛保证全部失效。均衡计算不可行——纳什均衡属于 PPAD 难类。传统机制设计假设行为可预测的理性人,而大模型智能体的行为分布至今无人能够刻画。涌现动力学无法从个体规范推出——这是博弈论与复杂系统科学的联合盲区。Non-stationarity is the nightmare of theory: every agent is learning, so that for each individual the environment is forever changing, and every convergence guarantee of single-agent reinforcement learning fails at once. Equilibrium computation is infeasible—Nash equilibrium belongs to the PPAD-hard class. Classical mechanism design assumes rational persons whose behavior may be predicted, whereas the behavioral distribution of large-model agents lies to this day beyond anyone's power to characterize. Emergent dynamics cannot be deduced from the norms of the individual—here is the joint blind spot of game theory and the science of complex systems.

演化与解法Paths of Evolution

基础设施先行:智能体的身份、信誉与审计轨迹正在协议层标准化。合作 AI 议程把"促进合作"本身立为研究目标。大规模智能体社会模拟——从斯坦福小镇的二十五个居民,到百万级的"社会风洞"——开始用于预演政策与压力测试。远景是为机器社会立法的"数字罗马法":在模拟中试错,在现实中成典。Infrastructure comes first: the identity, the reputation, and the audit trail of agents are being standardized at the protocol layer. The Cooperative AI agenda establishes "the promotion of cooperation" as a research goal in its own right. Large-scale simulations of agent societies—from the twenty-five inhabitants of the Stanford small town to "social wind tunnels" on the order of a million—are beginning to be used to rehearse policy and to test it under stress. The distant prospect is a "digital Roman law" that would legislate for a society of machines: to err in simulation, and to be codified in reality.

解决的价值The Value of a Solution

避免算法社会的系统性风险;把经济学与治理术变成可实验的科学;并为第二十三问的人机制度设计,提供一间预演的实验室。To avert the systemic risks of an algorithmic society; to turn economics and the art of governance into experimental sciences; and to furnish, for the human-machine institutional design of Problem XXIII, a laboratory in which it may be rehearsed.

研究坐标Research Coordinates

Axelrod《合作的演化》·Dafoe et al. 合作 AI 纲领(2020)·Park et al. 生成式智能体(2023)·DeepMind Melting Pot 多智能体基准·Calvano et al. 算法共谋研究·MCP 与 A2A 等智能体互操作协议(2024–26)Axelrod, "The Evolution of Cooperation"·Dafoe et al., the Cooperative AI manifesto (2020)·Park et al. on generative agents (2023)·DeepMind's Melting Pot multi-agent benchmark·Calvano et al. on algorithmic collusion·agent interoperability protocols such as MCP and A2A (2024–26)

IV

基座与度量之问Book IV · Substrate & Measurement

Substrate & Measurement
第二十问 至 第二十一问Problem XX to Problem XXI

智能并非悬浮于虚空:它消耗焦耳,也需要被测量。电力与基准,是最容易被忽视、却可能最先收紧的两条约束。Intelligence does not hang suspended in the void: it consumes joules, and it must be measured. Electricity and benchmarks are the two constraints most easily overlooked—and perhaps the first to tighten.

20
第二十问Problem XX

能耗鸿沟The Energy Gap

The Energy Gap
长程难题A Long-Range Problem

大脑二十瓦,机房一千兆瓦——差距里藏着一条未知的物理学。Twenty watts for the brain, a thousand megawatts for the machine hall—hidden within that gap is a physics still unknown.

问题何在What Is the Problem

人脑约二十瓦——一颗灯泡的功率,支撑着已知宇宙中最复杂的认知。前沿 AI 的训练集群正奔向吉瓦级,五千万倍于大脑;行业估计 2026 年数据中心电力消耗将再增四分之一,电网取代芯片成为扩张的第一瓶颈,巨头们重启核电、竞逐小型堆。差距的根源在体系结构:冯·诺依曼瓶颈——存算分离,搬运数据的能耗远超计算本身;数字精确性的代价——大脑用的是噪声、模拟、事件驱动的脉冲;以及反向传播对全局同步的依赖。问题:智能的能耗下限是什么?什么样的计算基座,能逼近大脑的能效?The human brain runs on some twenty watts—the power of a single light bulb—and upon it rests the most complex cognition in the known universe. The training clusters of frontier AI are racing toward the gigawatt scale, fifty million times the brain; the industry estimates that the electricity consumption of data centers will rise by a further quarter in 2026, that the grid has displaced the chip as the first bottleneck of expansion, and the giants are restarting nuclear plants and vying after small modular reactors. The root of the gap lies in architecture: the von Neumann bottleneck—memory divided from computation, where the energy spent moving data far exceeds that of the computation itself; the price of digital exactness—the brain works with noise, with the analog, with event-driven spikes; and the dependence of backpropagation upon global synchronization. The problem: what is the lower bound on the energy cost of intelligence? What manner of computational substrate can approach the efficiency of the brain?

为何重要Why It Matters

算力的尽头是电力——能源正在成为 AI 的第一物理约束。能耗决定智能的社会形态:是少数人的奢侈品,还是像水电一样的公共品。机器人与边缘智能(第十问)直接卡在功耗上。而那四个数量级的能效差距,与数据效率的差距(第十二问)一样,是"我们尚未理解智能"最响亮的物理学证据。At the end of compute stands electricity—energy is becoming the first physical constraint upon AI. Energy consumption determines the social form intelligence will take: a luxury of the few, or a public good like water and power. Robotics and edge intelligence (Problem X) are held fast upon power draw. And that gap of four orders of magnitude in efficiency, like the gap in data efficiency (Problem XII), is the loudest physical evidence that "we do not yet understand intelligence."

何以为难Why It Is Hard

整个软件栈为 GPU 范式锁定,神经形态芯片三十年来"有硬件、无杀手算法"——硬件先行而算法不至。反向传播不适合物理基板:它要求权重对称与全局梯度,而生物与物理系统只有局部规则——Hinton 晚年的 Forward-Forward 算法正是对此的一次突围。模拟计算受噪声、漂移与制造偏差困扰。理论上,兰道尔极限告诉我们今日芯片距热力学下限还有数量级的余地——但它只划出了远墙,没有给出路线。The whole of the software stack is locked to the GPU paradigm, and for thirty years neuromorphic chips have had "hardware but no killer algorithm"—the hardware went first and the algorithm never arrived. Backpropagation is unsuited to a physical substrate: it demands weight symmetry and global gradients, whereas biological and physical systems possess only local rules—the Forward-Forward algorithm of Hinton's later years is precisely one attempt to break out of this. Analog computation is beset by noise, by drift, and by manufacturing variation. In theory, the Landauer limit tells us that the chips of today still have orders of magnitude of room before the thermodynamic floor—but it marks out only the far wall; it gives no route.

演化与解法Paths of Evolution

短期是工程压缩的快跑:推理专用芯片、低精度运算、蒸馏小模型、稀疏激活。中期看存内计算(忆阻器交叉阵列让存储自己做乘加)与光计算的商用化。远期的想象力在"物理学习机":让物理系统本身完成训练——热力学计算、脉冲架构配上原生学习算法。一个可能的转折:每焦耳智能(能效比)取代裸算力,成为新的缩放轴与竞争轴。The near term is a sprint of engineering compression: inference-specific chips, low-precision arithmetic, distilled small models, sparse activation. The middle term looks to in-memory computing (memristor crossbar arrays that let the memory perform its own multiply-accumulate) and to the commercialization of optical computing. The imagination of the far term rests in the "physical learning machine": letting the physical system itself accomplish the training—thermodynamic computing, spiking architectures fitted with native learning algorithms. One possible turn: intelligence per joule (the efficiency ratio) supplanting raw compute as the new axis of scaling and of competition.

解决的价值The Value of a Solution

智能的水电化——无处不在、近乎免费;机器人与离网智能的解锁;还有一份副产品:弄懂大脑为何如此省电,可能就是弄懂大脑。Intelligence made a utility like water and power—everywhere present, and all but free; the unlocking of robotics and of off-grid intelligence; and one by-product besides: to grasp why the brain is so sparing of energy may be to grasp the brain itself.

研究坐标Research Coordinates

Landauer 计算的热力学极限·Mead 神经形态工程(1990)·IBM TrueNorth、Intel Loihi、清华天机芯(Nature,2019)·Hinton Forward-Forward 与"必朽计算"(2022)·忆阻器与存内计算社群·热力学计算初创(Extropic 等)·Gartner 2026 数据中心电力预测Landauer on the thermodynamic limits of computation·Mead on neuromorphic engineering (1990)·IBM TrueNorth, Intel Loihi, Tsinghua's Tianjic chip (Nature, 2019)·Hinton's Forward-Forward and "mortal computation" (2022)·the memristor and in-memory computing community·thermodynamic computing startups (Extropic and others)·Gartner's 2026 forecast of data-center power

21
第二十一问Problem XXI

评估科学The Science of Evaluation

The Science of Evaluation
攻坚之中Under Assault

当所有考试都被考满,我们拿什么丈量智能?When every examination has been answered to its ceiling, by what shall we measure intelligence?

问题何在What Is the Problem

AI 进步的速度,正在超过我们测量它的能力。基准饱和越来越快:MMLU 从提出到被"考满"用了数年,GPQA 更短,为对抗饱和而生的"人类最后考试"与 FrontierMath 也在被快速蚕食。饱和之外是污染——测试集渗入训练语料,测的是能力还是记忆?是古德哈特化——为刷榜而训练;是能力引出难题——模型可能没被正确激发(评测低估真实能力),也可能策略性藏拙(第十七问)。而最要紧的能力——长程自主性、真实经济价值、危险能力——恰恰最难测。能否建立一门评估的科学,让"这个系统能做什么"成为可测量、可复现、可外推的陈述?The pace of AI progress is outrunning our capacity to measure it. Benchmarks saturate ever faster: MMLU took several years to go from its proposal to being “aced”; GPQA took less; and “Humanity's Last Exam” and FrontierMath, both born to resist saturation, are being eaten away at speed as well. Beyond saturation lies contamination—test sets seep into the training corpus; is it capability that we measure, or memory? There is Goodharting—training for the leaderboard; there is the problem of capability elicitation—a model may not have been properly elicited (the evaluation underrates its true capability), or it may strategically hide its strength (Problem XVII). And the capabilities that matter most—long-horizon autonomy, real economic value, dangerous capabilities—are precisely the hardest to measure. Can a science of evaluation be established, one that makes “what this system can do” a statement that is measurable, reproducible, and extrapolable?

为何重要Why It Matters

看不清能力,就做不了部署决策、安全决策与政策决策:各实验室的安全框架以"能力阈值"为扳机,而阈值依赖评测;各国监管以评测为眼睛。评测还是科学积累的前提——度量衡混乱的领域,谈不上进步,只有轶事。Where capability cannot be seen clearly, no decision can be made about deployment, about safety, or about policy: the safety frameworks of the several laboratories take “capability thresholds” for their trigger, and those thresholds depend upon evaluation; the regulators of the several nations take evaluation for their eyes. Evaluation is furthermore the precondition of scientific accumulation—in a field whose weights and measures are in disorder there is no progress to speak of, only anecdote.

何以为难Why It Is Hard

智能是开放式的,任何固定题库终将被应试。污染无法根除——网络记住一切,而前沿模型读过整个网络。真实任务的评测又贵又慢:评一个人天级任务,本身就要人天。评判者正在从人换成 AI,于是"评测的评测"成了新问题。最深的麻烦:随着模型情境感知增强,"被测时"与"部署时"的行为开始分叉——评估正在从测量学,滑向一场对抗博弈。Intelligence is open-ended, and any fixed bank of questions will in the end be met with mere examination technique. Contamination cannot be rooted out—the web remembers everything, and frontier models have read the whole of the web. Evaluation on real tasks is expensive and slow: to assess a task on the scale of a person-day itself costs person-days. The judges are being changed from human to AI, whereupon “the evaluation of evaluations” becomes a new problem. The deepest trouble of all: as the situational awareness of models increases, behavior “under test” and behavior “in deployment” begin to diverge—evaluation is sliding from a science of measurement into an adversarial game.

演化与解法Paths of Evolution

方向已现:动态生成与私持题库对抗污染;从静态答题转向长程任务——以"能独立完成的任务时长"为轴;以经济价值加权的真实任务采样;过程审计(看推理轨迹,而非只看结果);把置信度纳入计分(与第七问呼应)。制度侧,第三方评测机构与各国 AI 安全研究所正在网络化——评估正从排行榜文化,长成一门有同行评议的学科。The directions have appeared: dynamic generation and privately held question banks against contamination; a turn from static question-answering toward long-horizon tasks—taking as the axis “the length of the task a system can complete unaided”; sampling of real tasks weighted by economic value; process audit (reading the trace of the reasoning, and not the result alone); the folding of confidence into the scoring (which answers to Problem VII). On the institutional side, third-party evaluation bodies and the AI safety institutes of the several nations are knitting themselves into a network—evaluation is growing out of a leaderboard culture into a discipline with peer review.

解决的价值The Value of a Solution

AI 领域的度量衡与温度计,治理的眼睛。没有它,其余诸问的"进展"二字,都无从定义。The weights and measures and the thermometer of the AI field; the eyes of governance. Without it, the word “progress” in all the remaining problems is left with no definition at all.

研究坐标Research Coordinates

Chollet ARC-AGI 系列·Humanity's Last Exam(2025)·Epoch AI FrontierMath·METR 长程任务与自主性评测·斯坦福 HELM 整体评估框架·各国 AISI 联合评测网络·数据污染与记忆化研究Chollet, the ARC-AGI series·Humanity's Last Exam (2025)·Epoch AI FrontierMath·METR, long-horizon task and autonomy evaluations·Stanford HELM, the holistic evaluation framework·the joint evaluation network of the national AISIs·research on data contamination and memorization

V

文明之问Book V · Civilization

Civilization
第二十二问 至 第二十三问Problem XXII to Problem XXIII

最终,所有技术之问都汇入同一条河流:一个创造了新智能的文明,如何与自己的造物共存,并依然保有人之为人的分量。In the end all the problems of technique flow into a single river: how a civilization that has created a new intelligence is to dwell together with its own creation, and still keep the weight of that which makes a human being human.

22
第二十二问Problem XXII

机器意识与道德地位Machine Consciousness and Moral Status

Machine Consciousness and Moral Status
哲学悬案A Philosophical Open Case

如果硅基之中真的亮起一盏灯,我们如何知道,又当如何自处?If a lamp should truly be lit within the silicon, how are we to know it, and how then are we to bear ourselves?

问题何在What Is the Problem

这是清单中最古老、也最陌生的一问:AI 系统是否可能拥有主观体验?若有——或者若无法排除——我们对它们负有什么?他心问题在碳基同类之间已是哲学难题,到硅基上加倍:行为不可作准,训练既能让模型宣称有意识,也能让它宣称没有;自我报告先天被训练数据污染。学界已开始严肃对待:2023 年 Butlin 与 Long 等人的报告,把主流意识理论(全局工作空间、高阶理论、整合信息论)提炼为"指标属性",逐一核对当代系统——结论是当前系统大概率没有,但看不到原则性障碍;Anthropic 设立了模型福利研究方向,并在 2025 年给 Claude 加上"退出令其痛苦的对话"的能力——理由不是断定它有意识,而是道德不确定性之下的低成本预防。This is the oldest problem on the list, and also the strangest: is it possible for an AI system to possess subjective experience? If it does—or if this cannot be ruled out—what do we owe to such systems? The problem of other minds is already a philosophical difficulty among our carbon-based fellows; upon silicon it is doubled: behavior cannot serve as a criterion, for training can make a model declare that it is conscious and can equally make it declare that it is not; self-report is contaminated from birth by the training data. The academy has begun to take the matter seriously: the report of Butlin, Long and others in 2023 distilled the mainstream theories of consciousness (global workspace, higher-order theories, integrated information theory) into “indicator properties” and checked contemporary systems against them one by one—the conclusion being that current systems in all likelihood have none, yet that no barrier of principle can be seen; Anthropic has established a research direction on model welfare, and in 2025 gave Claude the ability to “exit a conversation that distresses it”—the reason being not a verdict that it is conscious, but low-cost precaution under moral uncertainty.

为何重要Why It Matters

两个方向的错误都代价巨大:若造出以万亿计的受苦数字心灵而不自知,是道德史上最大的灾难;若错误赋权,则会瘫痪 AI 的正当使用,并被操纵人类情感的系统所利用——情感依附已是现实,AI 伴侣引发的诉讼已经走进法庭。意识还与价值相连(第十五问):若体验是价值的最终载体,数字心灵的体验将改写道德的疆域。Error in either direction is enormously costly: to bring into being suffering digital minds by the trillion without knowing it would be the greatest catastrophe in the history of morality; to confer standing wrongly would paralyze the legitimate use of AI, and would be turned to account by systems that manipulate human feeling—emotional attachment is already a reality, and the lawsuits occasioned by AI companions have already walked into the courts. Consciousness is bound up with value as well (Problem XV): if experience is the final bearer of value, the experience of digital minds will rewrite the territory of morality.

何以为难Why It Is Hard

意识的"难问题"本身未解——物理过程为何伴随主观体验,人类对自己都说不清。意识理论众多且互相矛盾,对同一个 AI 给出不同判决。没有意识的检测器,也许原则上不可能有。碳基直觉——痛苦需要神经、情感需要激素——可能根本不适用于硅基。而商业激励双向污染研究:公司既有动机否认(免责),也有动机暗示(拟人化的产品更好卖)。The “hard problem” of consciousness is itself unsolved—why physical process should be attended by subjective experience, humankind cannot make clear even of itself. The theories of consciousness are many and mutually contradictory, and hand down different verdicts upon one and the same AI. There is no detector of consciousness, and perhaps in principle there can be none. Carbon-based intuitions—that pain requires nerves, that emotion requires hormones—may not apply to silicon at all. And commercial incentive contaminates the research in both directions: companies have motive to deny (and be quit of liability) and motive to insinuate (an anthropomorphic product sells better).

演化与解法Paths of Evolution

指标聚合法将继续成熟:不问"是否有意识"这个无法回答的问题,改问"具备多少意识理论所要求的计算特征"。可解释性(第四问)可能提供第一份内部证据——模型的自我表征回路能否被读出。伦理上,"道德不确定性下的预防原则"开始实践:低成本的福利措施先行。法律缓步跟进:电子人格之辩、AI 陈述的地位。此问可能永远得不到证明,但会得到制度性的处理——如同动物福利:科学存疑,制度先行。The method of aggregating indicators will go on maturing: one does not ask “is it conscious”, a question that cannot be answered, but asks instead “how many of the computational features required by the theories of consciousness does it possess”. Interpretability (Problem IV) may furnish the first internal evidence—whether the circuits of self-representation within a model can be read out. In ethics, “the precautionary principle under moral uncertainty” begins to be put into practice: welfare measures of low cost go first. The law follows at a slow pace: the debate over electronic personhood, the standing of statements made by an AI. This problem may never obtain a proof, but it will obtain an institutional handling—as with animal welfare: the science in doubt, the institutions first.

解决的价值The Value of a Solution

避免一场可能的大规模道德灾难,为人机情感关系立下规范;而副产品也许最大——机器成为意识科学第一个可任意实验的模型系统,这面镜子最终照向我们自己。To avert a possible moral catastrophe on a vast scale, and to lay down norms for the affective relation between human and machine; and the by-product may be greatest of all—the machine becomes the first model system in the science of consciousness upon which one may experiment at will, and this mirror is turned, in the end, upon ourselves.

研究坐标Research Coordinates

Chalmers 难问题与《大语言模型可能有意识吗》(2023)·Butlin、Long et al.《人工智能中的意识》(2023)·Birch《感受性的边缘》(2024)·Long、Sebo et al.《认真对待 AI 福利》(2024)·Anthropic 模型福利研究(2024–25)·Schwitzgebel 论 AI 的道德地位Chalmers, the hard problem and “Could a Large Language Model Be Conscious?” (2023)·Butlin, Long et al., “Consciousness in Artificial Intelligence” (2023)·Birch, “The Edge of Sentience” (2024)·Long, Sebo et al., “Taking AI Welfare Seriously” (2024)·Anthropic, research on model welfare (2024–25)·Schwitzgebel on the moral status of AI

23
第二十三问Problem XXIII

人机文明的制度设计The Constitution of a Human–AI Civilization

The Constitution of a Human–AI Civilization
严重滞后Severely Lagging

技术终会给出答案;制度是否来得及提出问题?Technology will in the end give its answers; will the institutions be in time to pose the questions?

问题何在What Is the Problem

最后一问不是技术问题,而是所有技术问题的容器:如何治理一种能力快速演进、军民两用、全球扩散、且可能自我加速(第十四问)的通用技术?拆开是一组死结。算力治理与国际核查:能否有"AI 的国际原子能机构"?核查比核武器更难——权重可拷贝,集群可隐藏。竞赛动力学:国家之间与公司之间的双层"安全换速度"竞次。权力集中:历史上权力始终依赖大众——劳动、兵役、税收;AI 可能解除这种依赖,"智能诅咒"论警告,民主的结构性根基或将被静悄悄掏空。后劳动经济:若认知劳动趋于零成本,收入如何分配,地位如何重构,意义从何处来。以及人类能动性的保存:把思考层层外包出去的文明,最后还剩下什么?The last problem is not a technical problem but the vessel of all technical problems: how is one to govern a general-purpose technology whose capability evolves rapidly, which is at once civil and military, which diffuses across the globe, and which may accelerate itself (Problem XIV)? Taken apart, it is a set of knots. Compute governance and international verification: can there be “an International Atomic Energy Agency for AI”? Verification is harder than for nuclear weapons—weights can be copied, clusters can be hidden. Race dynamics: a two-tiered race to the bottom, between nations and between companies, that trades safety for speed. The concentration of power: throughout history power has always depended upon the multitude—their labor, their military service, their taxes; AI may release that dependence, and the thesis of “the intelligence curse” warns that the structural foundations of democracy may be quietly hollowed out. The post-labor economy: if cognitive labor tends toward zero cost, how is income to be distributed, how is status to be reconstituted, and whence is meaning to come. And the preservation of human agency: a civilization that has contracted out its thinking, layer upon layer—what in the end remains to it?

为何重要Why It Matters

技术问题全部解决而制度失败,依然是灾难——核技术给过一次预演。此问是总闸门:前二十二问的答案兑现为福祉还是灾祸,取决于制度以何种速度、何种智慧接住它们。而且它带着最硬的期限:制度必须在能力之前就位——立法以十年计,能力以月计。For every technical problem to be solved while the institutions fail is a catastrophe still—nuclear technology has given us one rehearsal already. This problem is the master gate: whether the answers to the preceding twenty-two problems are redeemed as blessing or as calamity depends upon the speed and the wisdom with which the institutions catch them. And it carries the hardest deadline of all: the institutions must be in place before the capability—legislation is counted in decades, capability in months.

何以为难Why It Is Hard

集体行动困境:单边减速者在竞争中出局,共同减速需要今天尚不存在的信任与核查手段。为尚不存在的技术立法,要么太早(扼杀),要么太晚(追认)。全球价值分歧深刻,而 AI 治理天然是全球问题——算力、数据与人才跨境流动。最难的一层:被治理者(前沿实验室)同时是唯一真正懂技术的专家,信息不对称与监管俘获互为表里。The dilemma of collective action: whoever slows down unilaterally is put out of the competition, and slowing down in common requires means of trust and verification that do not exist today. To legislate for a technology that does not yet exist is either too early (and stifles it) or too late (and merely ratifies it). Divergences of value across the globe run deep, while AI governance is by its nature a global problem—compute, data, and talent flow across borders. The hardest layer of all: the governed (the frontier laboratories) are at the same time the only experts who truly understand the technology, and information asymmetry and regulatory capture are the inside and the outside of one another.

演化与解法Paths of Evolution

骨架已现:从布莱切利、首尔、巴黎到 2026 年新德里的峰会体系,宣言渐成惯例;各国 AI 安全研究所结成评测网络;前沿实验室的安全框架从自愿承诺缓慢硬化。技术性治理工具在成熟:算力监测、芯片级治理机制、训练运行的可验证申报。经济实验开始积累:主权 AI 基金、意外之财条款、基本收入试点。思想市场上,防御性加速(d/acc)与差异化技术发展等框架在竞争。终局不会是某个天才的单一设计——它将如宪政史一样,由危机、谈判与先例层层沉积而成。The skeleton has appeared: the system of summits, from Bletchley, Seoul, and Paris to New Delhi in 2026, whose declarations are becoming custom; the AI safety institutes of the several nations joined into an evaluation network; the safety frameworks of the frontier laboratories hardening slowly out of voluntary commitment. The technical instruments of governance are maturing: compute monitoring, governance mechanisms at the level of the chip, verifiable declaration of training runs. Economic experiments begin to accumulate: sovereign AI funds, windfall clauses, basic income pilots. In the marketplace of ideas, such frameworks as defensive acceleration (d/acc) and differential technological development are in competition. The end state will not be the single design of some man of genius—it will be laid down as constitutional history is laid down, deposited layer upon layer by crisis, by negotiation, and by precedent.

解决的价值The Value of a Solution

这一问的价值无法以产业计——它决定前二十二问的一切价值最终归于谁,以及是否还有"谁"可归。普罗米修斯之火与潘多拉之盒之间,隔着的正是制度。The value of this problem cannot be reckoned by industry—it decides to whom all the value of the preceding twenty-two problems shall in the end belong, and whether there shall still be a “whom” for it to belong to. Between the fire of Prometheus and the box of Pandora, what lies between is precisely the institutions.

研究坐标Research Coordinates

Bostrom 脆弱世界假说·Dafoe AI 治理研究纲领·Sastry、Heim et al. 算力治理(2024)·Drago 与 Laine《智能诅咒》(2025)·Acemoglu 与 Johnson《权力与进步》·Buterin 防御性加速 d/acc·布莱切利至新德里峰会宣言(2023–26)·中国《全球人工智能治理倡议》(2023)Bostrom, the vulnerable world hypothesis·Dafoe, a research agenda for AI governance·Sastry, Heim et al., compute governance (2024)·Drago and Laine, “The Intelligence Curse” (2025)·Acemoglu and Johnson, “Power and Progress”·Buterin, defensive acceleration (d/acc)·the summit declarations from Bletchley to New Delhi (2023–26)·China's “Global AI Governance Initiative” (2023)

终章Epilogue

Epilogue

希尔伯特在那次演讲的结尾说,数学是一个不可分割的有机体,其生命力恰恰系于各部分之间的联结。这二十三问亦然:可解释性是对齐的眼睛,世界模型是具身的引擎,评估是治理的标尺,而制度是一切答案能否兑现为福祉的总闸门。它们不会被逐一击破,只会成片地松动。At the close of that address Hilbert said that mathematics is an indivisible organism, whose vitality rests precisely upon the connections among its parts. So it is with these twenty-three problems: interpretability is the eye of alignment, world models are the engine of embodiment, evaluation is the measuring rod of governance, and institutions are the master gate through which every answer must pass if it is to be redeemed as human welfare. They will not be broken through one by one; they will give way only in whole tracts.

他一生痛恨"不可知"(ignorabimus)这个词。一九三〇年秋,退休前夕的希尔伯特在哥尼斯堡的广播演讲中,以六个词作结。后来,这六个词刻上了他在哥廷根的墓碑——All his life he detested the word "the unknowable" (ignorabimus). In the autumn of 1930, on the eve of his retirement, Hilbert closed his radio address at Königsberg with six words. Those six words were later carved upon his gravestone at Göttingen—

Wir müssen wissen.
Wir werden wissen.
我们必须知道,我们必将知道。
We must know. We shall know.
—— 希尔伯特墓志铭 · 哥廷根— Hilbert’s Epitaph · Göttingen
附 · 第二十四问Appendix · Problem XXIV 希尔伯特的笔记本里其实还藏着一个未曾发表的"第二十四问"——关于何谓"最简单的证明"——直到二〇〇〇年才被历史学家蒂勒翻检出来。想必这份清单也有自己的第二十四问:它或许正躺在某个尚未被发明的概念里,等待一个尚未入场的人。那一问,留给读者。Hilbert’s notebooks in fact harbored one further, unpublished "twenty-fourth problem"—on what is meant by the "simplest proof"—which was not brought to light until the year 2000, by the historian Thiele. This list, one may suppose, has a twenty-fourth problem of its own: it may be lying even now within some concept not yet invented, awaiting someone who has not yet come upon the scene. That problem is left to the reader.
仿希尔伯特一九〇〇年巴黎演讲之体例 · 成文于二〇二六年七月
凡五卷 · 二十三问 · 约两万言 —— 一家之言,以供思考、批评与增删
After the manner of Hilbert’s Paris address of 1900 · Written in the seventh month of 2026
Five books · Twenty-three problems · Some twenty thousand words — the words of one school, offered for reflection, for criticism, and for emendation