立委NLP频道

1.1 训练与推断的二分

机器学习系统存在两个核心阶段：

- 训练时间（Training Time）：参数空间Θ的优化过程，目标函数为误差最小化 minL(θ;D_train)
- 推断时间（Inference Time）：固定参数θ时对新样本x_test的条件分布预测p(y|x_test;θ)

大语言模型(LLM)领域的最新进展显示，通过引入思维链(CoT)机制，推断阶段的计算量（test time compute）显著增长，也收获了相应的智能提升。

1.2 逻辑学视角

Inference 对应概率模型中的推断过程，本质是大数据压缩后的经验性模式归纳。在传统的符号逻辑语境下，Reasoning 特指演绎推理的符号化过程，但考察当下的LLM推理模型，reasoning 最多只是对逻辑演绎的符号化模拟，本质上仍然是概率模型的推断（inference）生成。溯因在大模型范式下，其实现启发式推测的手段也还是大数据压缩后的经验性（逆向）模式归纳。总之，生成式AI大模型以不变应万变，各种思考推理过程一律采用下一词元预测（Next Token Prediction）形式的推断实现。生成机理不变，但 input-output 函数范式变了。

1.2 认知科学视角的函数范式

Kahneman在《思考，快与慢》中提出的双系统理论为理解大脑行为提供新视角：

- System 1（快思考）：直觉式响应 input→output，对应大模型 seq2seq 函数式生成模式

output=F(input)

- System 2（慢思考）：反思性推理 input→[Think]→output，体现为CoT (ChainofThought) 驱动的两阶段函数生成模式

CoT=F(input) & output=F(input+CoT)

大模型 F 的底层逻辑不变，但强化学习启动了思维链外化（CoT），搭建了应对复杂问题（input）的信息桥梁CoT，增加了大模型推断output的可解释性，最重要地，大幅提升了复杂问题的解决智能。

1.3 推理模型的计算-智能增长关系

强化学习赋能的推理模型新范式呈现的新 scaling law 是怎样的呢？并无定论，一切刚刚开始，经验法则需要时间测量。

例如，当test time compute增加10倍时：
- 推理准确率提升多少？
- 响应延迟增长多少？

`

1.4 答问

「蔡江滨l六问：早安，能否理解为cot的生成是推断inference ，根据cot生成的具体内容是推理？@wei li 」

cot+answer 的区分是人为的格式区分，对于ntp GPT 模型，它们都是概率性 inference 生成的 response

如果这个response 是针对理工类推理题目，那么这种 inference 是对于人类 reasoning，尤其是演绎（ deduction）的模拟，但不是严格意义上的逻辑演绎。

如果是创作类任务，inference 中的 CoT 就是 planning/pondering 等思考过程， inference 中的answer就是生成结果，都谈不上逻辑推理。

reasoning model 这个实命名也不准确，还不如叫思考模型、思维链模型、慢思维模型、意识流模型、内心独白模型、小九九模型，总之就是 system 2，与传统的 system 1 模型比，只是多了个 CoT。

【原文】

• 生成式AI学习中容易混淆的几个术语

test time / reasoning / inference 辨析

推理模型是当前生成式AI的主流热点，带火了一个热词（buzz word）叫 test time compute，咱们就先从它谈起。

从模型开发者视角，test time（测试时间） 针对的是 training time （训练时间）。众所周知，这是机器学习的两个阶段，一个是在线，一个是离线。训练模型好比是软件开发；测试模型就是软件测试。模型测试阶段就是常说的（在线）推理（inference）阶段，所以 test time 又叫 inference time。

问题是，中文翻译“推理”对应了英文两个词：inference 和 reasoning，业内人士很多人是认为后者才是推理正解，而前者是错译（misnomer），合适的翻译是“推断”。但“推理”的一词二用已经混淆并流行了很久，社区习惯上不一定能改过来。但对于后学，还是要辨析清楚才好。

test time compute 之所以流行，是因为大模型领域近几个月的“范式转变”。社区依据预训练scaling law原来一直聚焦基座大模型的做大做强，但发现大算力带来大智能的效益递减，进入了平台期。于是把重心转移到后训练的强化学习，发展了一种称为 System 2 慢思维模式的推理模型。这种推理模型最大的特点就是运行起来慢了，原来的秒回现在是慢了几拍才回复，消耗了更多在线时间和在线推断的算力（即 test/inference time compute）。

按常理，在线计算量增加，模型运行慢了，听上去是在退步，而不是进步。但好消息是，模型对于复杂问题的处理智能飙升。时间换质量，当然应该看好这个新方向。慢思维推理模型的成就，就好比人类的三思而后行。一般而言，凡事喜欢琢磨的人，比不假思索就行动的人，更有智慧，也更加靠谱。学会了慢思维（术语叫思维链）的大模型亦是如此。

模型训练阶段，无论是预训练还是后训练，都是离线进行的，迭代循环，在改变模型的参数，模型并未成形，属于开发进行时。而 test time 说的是模型已经完成阶段。严格说，test time 是内部试运行阶段，让 QA（quality assurance）部门在上线发布前做测试。但现在谈 test time compute，已经不分内部测试还是用户使用，所以更准确的术语还是 inference time compute。

白老师说：

Inference当初译成推理就错，真的推理Reasoning不来还则罢了，这回真的来了，将错就错都难。

我说：

不知是不是下意识，以前一直有意无意地把 inference 与统计预测关联得更紧，而把 reasoning 与符号演绎（deduction）划了等号。前者是统计性的，后者是确定性的。（概率性）推断就是（统计性）预测，statistical inference。不知道受到了什么的暗中影响。

老友尼克说：

本意也差不多是这个意思。reasoning是偏deduction的。

大模型的术语最早借自于统计，统计中区分建模与inference两个阶段，大模型训练相当于建模。统计中inference翻译为“推断”。简中自媒体乱翻导致业界人也瞎起哄，好像上海电影译制厂把中国两代人的英文发音都带偏了。

但是定理证明community也用inference，好多会都以此冠名，所以很难把inference与reasoning完全隔开。相对讲，reasoning更偏deduction，最好的办法是在可能引起歧义时括号英文。

abduction在逻辑里是美国实用主义的特定叫法，源自Peirce。这个意思是把建模和inference合到一起的意思，就是Solomonoff Induction的不严谨的哲学说法。inference出错时，再去修正模型，the whole nine yard。在Kolmogorov Complexity中，inference被称为logic depth 。。。

其实，inference time 口语中也叫 running time 或 runtime，其他的近义词和关联词还有很多： test-time，real time，decoding time, prediction time, service time, execution time, on-the-fly computing time ...

【外一篇：推理范式演进中的概念】

1.1 训练与推断的二分

机器学习系统存在两个核心阶段：

- 训练时间（Training Time）：参数空间Θ的优化过程，目标函数为误差最小化 minL(θ;D_train)
- 推断时间（Inference Time）：固定参数θ时对新样本x_test的条件分布预测p(y|x_test;θ)

大语言模型(LLM)领域的最新进展显示，通过引入思维链(CoT)机制，推断阶段的计算量（test time compute）显著增长。

1.2 逻辑学视角

在传统的符号逻辑语境下，Reasoning 特指演绎推理的符号化过程，但考察当下的LLM推理模型，reasoning 最多只是对逻辑演绎的符号化模拟，本质上仍然是概率模型的推断（inference）生成；而Inference对应概率模型中的推断过程，本质是大数据压缩后的经验性模式归纳。溯因在大模型范式下，实现启发式推测的手段也还是大数据压缩后的经验性（逆势）模式归纳。总之，生成式AI大模型以不变应万变，各种思考推理过程一律采用下一词元预测（Next Token Prediction）的 inference 实现。

1.2 认知科学维度

Kahneman在《思考，快与慢》中提出的双系统理论为理解大脑行为提供新视角：

- System 1（快思考）：直觉式响应 input→output，对应大模型 seq2seq 函数式生成模式

output=F(input)

- System 2（慢思考）：反思性推理 input→[Think]→output，体现为CoT(ChainofThought) 驱动的两阶段函数生成模式

CoT=F(input) & output=F(CoT)

1.3 推理模型的计算-智能增长关系

强化学习赋能的推理模型新范式呈现的新 scaling law 是怎样的呢？并无定论，一切刚刚开始，经验法则需要时间测量。

例如，当test time compute增加10倍时：
- 数学推理准确率提升多少？
- 响应延迟增长多少？

`

【相关】

• 思维链是大模型的符号神助攻
• 再谈自然模态数据是高维空间的低维流形
• 深度学习的局限性研究综述
• o3 deep research: 深度学习局限性研究报告
• 深度学习的基石：多层感知机
• o3 Deep Research: DeepSeek R1 多阶段训练流程问答解析
• RPA 赛道与大模型Copilots早期创业者的困局
• Transformer 和注意力机制简介
• 立委科普：如何理解自注意力机制中的QKV分工？
• DeepSeek 笔记：推理新范式 query+cot+answer 支持新的 scaling law 吗？
• DeepSeek 笔记：R1 部署阶段的推理机制
• 从R1幻觉谈起，大模型幻觉是缺陷还是创意火花？
• 推理强化学习是端到端的监督，推理过程的非监督
• DeepSeek 风暴下看看它的论文
• 大模型风云诡谲的下半场：scaling 失效？

在人工智能发展的历史长河中，符号逻辑和神经网络一直如两条平行线，难以交汇。然而，2025年春节，DeepSeek发布的推理大模型R1揭示了一个令人惊叹的技术突破——思维链(Chain of Thought, CoT)的自主生成，其展现出的语言序列仿佛在模拟人类的符号逻辑。这一强化学习的进展或将重新定义符号逻辑与神经网络的融合方向。

符号逻辑的回归

DeepSeek R1推理模型的发布引发全球关注，其强化学习框架下自主生成的思维链展现出惊人的问题解决能力与创作能力。其核心机制仍是GPT风格的自回归下一词元预测 (next token prediction, NTP)，但模型生成的中间结果——思维链，却呈现出典型的符号逻辑特征，有效模拟了人类的思考过程。

这一现象值得深思：大语言模型的本质从未改变，包括最新的推理模型，其内部运作仍是基于向量计算的条件概率。然而，为了模拟人类的符号推理，这些模型竟然学会了通过自然语言构建推理链条。更令人惊讶的是，这些符号链条确实有效，它们结合内部的词元预测机制，显著提升了模型的推理和创造能力。这是一个非常值得回味反思的技术进展。这件事的奇妙，是ChatGPT核爆以来最大的震撼。

符号与神经的无缝对接

这项奇迹的发生尤其让我们符号AI的老司机感慨。多少年来，我们心心念念地追求两条路线的融合，希望符号逻辑能在关键时刻帮助神经系统和统计模型，但一直看不到入口。忽然间，在大模型预训练进入平台期的关口，神经社区内部打开了一扇通向符号逻辑的大门，找到了一种神经与符号融合的路径。这一突破来得如此突然而有力，不能不让人既惊且叹。可惊的是，符号逻辑终于开始发力了；可叹的是，闯出这条路的还是神经社区的研发者，没有符号研究者什么事儿。

大模型就是个端到端的黑盒子，符号仅在输入输出两个端口出现。具体说，我们只能在输入端将符号“嵌入”（embedding）至高维向量空间，并在输出端通过 softmax 映射回符号，而内部的多层前馈的数据流则完全由向量运算主导，与符号逻辑无关，也很难以人类可以理解的符号来解释（因此才有专门的大模型可解释性研究）。此前所有结合符号与向量的努力都失败了，感觉这两种表示就是不同物种，无法融合。符号逻辑一直坐冷板凳，而符号本身除了作为训练数据燃料，在内部智能运作上一点也帮不了忙。

符号与概率的桥梁：CoT的奥秘

现今的推理大模型将内在“思考过程”外化为自然语言CoT，很像是模型的内心独白或意识流。模型在生成最终答案前，CoT重新嵌入系统中助力最终答案的生成。看似简单的这一过程，却在推理时成功地利用了自然语言这一符号载体，使得符号逻辑与神经网络在端口上实现了全程对接，没有一点违和或不容。

这是怎么发生的呢？一切多亏了自回归的 NTP 范式。下一词元预测的GPT生成方式，使得内部的“思维过程”可以在输出端外化为符号CoT，从而利用符号推理的形态，一步步模拟人类思维过程。

从信息论的角度看，推理大模型在 question-CoT-answer 的生成过程中，实际上构建了一条低熵的信息传输路径。相比传统的 question-answer 直接映射，这种显式的中间步骤大大降低了输入question与输出answer的信息鸿沟，显著提升了正确答案的生成概率。正如我在之前的博客（推理新范式 query+cot+answer 支持新的 scaling law 吗）中所论述的，CoT 充当了信息桥梁的角色。虽然不是严谨的符号逻辑推断过程，但它无需改变概率模型的底层运作机理，实现了对于人类推理的有效模拟。

自然语言vs形式语言：CoT的载体选择

CoT 本质是思维，语言只是载体，原理上没必要用自然语言，或任何特定的语言（例如中文，或英文）。但现在的实现方式，无路DeepSeek的R系列，还是OpenAI的O系列，就是直接用了中文或英文的思维链表示。推理模型在运行时，CoT先在输出端外化为中文或英文的符号序列，然后自回归循环运作，最终生成答案。看上去简直就是在符号与神经之间变戏法。以前何曾想到符号介入神经，还带这么玩的，内部与端口天衣无缝。

我们都要感谢DeepSeek，要不是 DeepSeek 给了这样一个开源的春节大礼包，又完全公开了自己的CoT，我们会一直蒙在鼓里，绞尽脑汁也想不明白 reasoning 这种符号逻辑，怎么就悄悄进入了神经过程。符号与向量的矛盾通过端口外化，化解于无形。

从符号逻辑的角度看，自然语言虽然老妪能解，但其精确性远逊于数学符号、形式逻辑表达式或编程语言代码。对于数理问题或逻辑推演，CoT 用这些形式语言比用自然语言显然更合适。然而，目前思维链生成采用自然语言，而不是形式语言。偶然也夹杂了一些数学符号，但思维链整体还是压倒性的使用英语或中文。R1论文中还提到他们的CoT连计算机代码都排斥在外。感觉上，这其实不是推理的正道，但可以理解其成因。CoT 是模型自主生成的序列，而据以生成的基座大模型本身，其训练数据以自然语言压倒多数。原因之二是开发者刻意追求的可解释性以及对用户的透明性，觉得自然语言大家都容易看明白。R1在设计CoT强化训练的时候，强调了格式的奖励，其中语言一致性当成了一个目标。夹杂不同语言或代码的CoT，剔除出局了。从长远来看，这未必是最明智的决策。

前景与思考

推理模型的 CoT 无疑是神经网络与符号逻辑融合的一次创新，也是近年来人工智能领域的重要里程碑。未来的CoT研究方向，可以考虑越来越多地奖励 CoT 以更加严谨的形式语言表示。至少要文理分科，文科任务（如创作）继续用自然语言做CoT的载体，这类思维过程涉及的主要是篇章规划和表达斟酌，而非严格推理；理工任务（数学、编程、逻辑等）则不同，应该训练模型尽量使用形式语言来表示CoT推理过程。当然，要做到后者，可能还要进一步加强基座模型等代码和其他形式语言的数据配比，否则 LLM也许 “憋”不出来合适的表示。

最后说一下概率模型与符号逻辑的严谨性差异。推理模型的 CoT 是推理模型的现场发挥，很多时候显得不够严谨。但其实人脑也是一样。没人能出口成章地把一个复杂数学证明一气呵成，就如同没人能一口气写出一个没有bugs的程序。严谨性都是在反复校验、修正，甚至是几代科学家前赴后继不断探究中完成的。CoT 不够严谨是拿模型的“草稿”与人类专家的定稿对比产生的印象。可以预见，对于非常复杂的问题，推理模型应该像人类一样反复校正，独立复现结果比对。这可能要指望各种推理 agents 的相互协作，以及它们与人类反馈的多层交互。

【相关】

• 再谈自然模态数据是高维空间的低维流形
• 深度学习的局限性研究综述
• o3 deep research: 深度学习局限性研究报告
• 深度学习的基石：多层感知机
• o3 Deep Research: DeepSeek R1 多阶段训练流程问答解析
• RPA 赛道与大模型Copilots早期创业者的困局
• Transformer 和注意力机制简介
• 立委科普：如何理解自注意力机制中的QKV分工？
• DeepSeek 笔记：推理新范式 query+cot+answer 支持新的 scaling law 吗？
• DeepSeek 笔记：R1 部署阶段的推理机制
• 从R1幻觉谈起，大模型幻觉是缺陷还是创意火花？
• 推理强化学习是端到端的监督，推理过程的非监督
• DeepSeek 风暴下看看它的论文
• 大模型风云诡谲的下半场：scaling 失效？

这个话题实际上涉及 流形假设（Manifold Hypothesis）、对抗样本攻击（Adversarial Attacks） 和 高维几何的脆弱性。

1. Normal Bundle 在高维空间的“刺猬”形象

normal bundel 是微分几何里的一个重要术语，中文翻译叫“法丛”，对于欠缺数学背景的我们来说，这个术语不好理解，但理解它对于大模型的骇客攻击与AI安全性蛮重要，咱们先看看它是个什么东西。

先破题：Normal 不是‘正常’，而是‘垂直’！

咱中文里‘法’字，来自‘法线’——就是几何里那个与曲面切线呈90度的垂直方向的线。比如你拿根筷子插进苹果，筷子方向就是苹果表面的‘法线方向’。数学家说的‘法丛’（Normal Bundle），其实就是把曲面上每一点的所有垂直方向‘打包’成捆（Bundle），像给苹果表面插满箭头的刺猬！

刺猬的类比是准确的！在 低维流形嵌入高维空间 时，法丛（Normal Bundle）确实可以被想象成“刺猬”——流形的每个点都有一个法向空间，而法丛就是把这些法向空间整体“打包”在一起。见我让Sora生成的法丛示意图：

这是我给Sora发的指令：

制作3D曲面切线与法线动态演示短视频，为科普用，数学家说的‘法丛’（Normal Bundle），其实就是把曲面上每一点的所有垂直方向‘打包’成捆（Bundle），像给苹果表面插满箭头的刺猬！

有几个关键点：

• • 在 3D 空间里，我们习惯把曲面（2D 流形）的法丛（Normal Bundle）想象成一个 1D 线性空间（即法线），所以它看起来像是一个“箭头丛”。
  • 在更高维空间中，比如一个 d 维流形嵌入到 n 维空间（d < n），它的法丛一般是 (n-d) 维的，这意味着法丛方向本身就有多个自由度，而不只是单纯的“刺”。
  • 用 3D 可视化高维流形的法丛，最常见的做法确实是让法丛的“刺”呈现出扇形的扩展感，因为高维空间的法向方向比低维空间的直观“法线”更加复杂。

所以 Sora 生成的图如果能表现出“立体感更强的刺猬形态”，或者在某些点上看到“扇面展开的刺”，就能更好地表达高维法丛的概念。

想象你是只二维蚂蚁，活在皱巴巴的树叶上。对你来说，前后左右是‘切空间’——现实世界；而上下方向就是‘法丛’——完全不可见的维度。所以‘法丛’的normal，本质是几何垂直性，不是日常说的‘正常不正常’。

数学家眼里的‘法丛’一点也不玄乎，就是垂直方向的集合。既然切空间是‘tangent’（相切的），那垂直方向就叫‘normal’（正交的），跟‘正常’没半毛钱关系！要怪就怪英文一词多义。

2. 高维空间 vs. 自然数据流形

“自然数据（文本、音频、图像、视频等）通常分布在一个远低于高维空间的流形上”，这是 流形假设（Manifold Hypothesis） 的核心观点：

• • 我们的高维数据（比如图片，通常是 256×256×3 维）并没有填满整个高维空间，而是集中在 远低于该维数的流形上。
  • 这类似于：宇宙是三维的，但星星和星系主要分布在局部区域，而不是均匀填充整个宇宙。
  • 这个流形的维度一般和“人类可感知的主要变化”相关，比如在 人脸识别模型 里，所有可能的“人脸”数据分布在一个 远低于像素维度的低维流形 上，而这个流形包涵了现实中所有合理的人脸样本。这实际上是人脸与表情解耦可以work的原因。

3. 对抗样本：在法丛方向制造“幽灵数据”

既然 自然数据的流形是稀疏的，那这意味着：

• • 绝大多数可能的数据点 根本不属于自然数据的流形。
  • 但在数学上，它们仍然是“合法”的高维向量，可以被构造出来，并且会落在 法丛方向 之中。

这是对抗攻击（Adversarial Attacks） 可以成立的根本原因：

1. 1. 模型只在自然流形上训练，它对“流形外的点”几乎没有概念。
   2. 对抗攻击就是在法丛方向上微调输入数据，让它离开流形，但仍然能欺骗模型的决策边界。
   3. 由于高维空间的稀疏性，很多非自然数据的点可能距离决策边界非常近，但在我们人类看来它们几乎与原始自然数据无差别。

一个经典的例子是：给神经网络输入一张猫的图片，稍微在 法丛方向 加一点扰动（人眼几乎察觉不到）。这张图片仍然落在数据空间里，但 已经偏离自然流形，导致模型认为它是一只狗。

这种“幽灵数据”之所以有效，正是因为 法丛方向是流形的正交补空间（Orthogonal Complement），而流形本身对它并不敏感——就像蚂蚁看不到第三维的变化。

4. 为什么法丛方向上的攻击有效？

既然自然数据流形本身很低维，而法丛方向是它的补空间，远高于流形维度，那么：

1. 1. 法丛方向上的变动可以很大，但仍然不影响数据的可感知特性（因为它们对人类而言是“无意义的方向”）。
   2. 但是对于机器学习模型而言，这些方向仍然是合法的数据输入，它并没有经过特殊训练去防御这种扰动。
   3. 于是，在某些关键点上，对抗样本只需要在法丛方向上加一点点扰动，就能让模型的决策边界翻车。

这也解释了：

• • 为什么对抗样本攻击几乎无处不在？因为高维空间里“非自然数据”占比极高，总会有某些点可以被找到来攻击模型。
  • 为什么对抗样本对人类视觉几乎无影响？因为它利用的不是“自然数据的流形变化”，而是“法丛方向的变化”，这个方向人类或自然模型根本不敏感。
  • 为什么深度学习模型的泛化能力有时不稳定？因为它们过度依赖训练数据流形，而法丛方向上的任何变化都会导致预测结果的剧烈偏移。

5. 这是否意味着“无限对抗攻击”可能存在？

在理论上，确实可以构造出 无穷多的“几何意义上非自然的数据” 来攻击模型。

• • 这些数据点不属于原始数据流形，但它们可以被设计得 足够接近决策边界，从而诱导模型出错。
  • 只要高维空间的维度够高，法丛方向的自由度就足够多，攻击者总能找到某个点来实现攻击。

这也是为什么：

• • 对抗样本防御是个无止境的军备竞赛，模型越强，对抗攻击手段就要越高级。
  • 对抗训练（Adversarial Training） 是当前最有效的解决方案之一，本质上就是“让模型在法丛方向上也学会一些关键的变化”，从而增加对抗鲁棒性。
  • 如果不考虑计算成本，我们可以尝试在更大的法丛方向空间中做鲁棒性优化，但这通常代价太高，所以现实中只能有限度地解决。万全之策是少有的，迅速堵漏或patches 对应用系统变得尤为重要。

6. AI炼丹里的‘法丛陷阱’

搞大模型训练时，参数空间就像高低起伏的山脉。梯度下降是沿着‘切空间’（Tangent Space）找路，但万一算法抽风往‘法丛’方向抖动，就可能造成极度的训练不稳定。所以高阶炼丹师都要用正则化当护栏，专门防着往法丛深渊掉。

如果没有黑客，模型使用者用到的数据输入都是自然数据，与模型训练集是同质的，模型本身的泛化能力足以轻松应对。这是因为自然数据，包括用户的自然语言指令和样例都处于模型数据的切空间里，好比在平原地带，东西南北方向坡度平缓。

但不怕贼，就怕贼惦记。黑客可以刻意制造法丛区域的数据，攻击模型。法丛处于训练数据没有覆盖的未知区域，以此为测试数据，模型性能就急剧下降，可能表现得一塌糊涂。这就像开车——切空间是方向盘能控制的方向，法丛是侧翻悬崖的方向。

这是个头痛问题，单纯依靠数据中的统计模式，难以实现真正的分布外泛化和可靠的安全性保障。常规数据增强很难解决这个法丛数据攻击的问题，因为常规自然数据如同在已知区域做探索，不会主动探索法丛方向，而且这样的数据在通常的场景极为罕见：正常用户也不会故意跳崖。开发者要探索所有法丛危险方向需要无限资源，防不胜防，通常是对骇客的数据进攻，亡羊补牢，给模型做针对性补漏。

总结：

✔ “刺猬模型”来展示法丛（Normal Bundle）是合理的，需要强调“不同点的法向方向形成的丛”，就能很好地表达它的几何概念。
✔ 自然数据流形 vs. 法丛方向的思考是对的，它基于自然数据的流形假设。
✔ 高维空间的稀疏性 + 法丛方向上的非自然数据确是对抗攻击成立的根本原因，所以确实可以构造无数个“几何上合法但不自然”的数据点来让模型翻车。
✔ 如果要防御，关键是让模型学会法丛方向上的“稳定性”，这就是对抗训练、正则化、鲁棒性优化、构造对抗数据patching等技术的意义。

高维空间和对抗攻击的研究，可以进一步研读对抗学习（Adversarial Learning）相关论文，尤其是 Ian Goodfellow 提出的 FGSM（Fast Gradient Sign Method）经典攻击方法及其后续的种种高级变体。

【相关】

• Goodfellow 2015 Explaining and harnessing adversarial examples.
• 深度学习的局限性研究综述
• o3 deep research: 深度学习局限性研究报告
• 深度学习的基石：多层感知机
• o3 Deep Research: DeepSeek R1 多阶段训练流程问答解析
• RPA 赛道与大模型Copilots早期创业者的困局
• Transformer 和注意力机制简介
• 立委科普：如何理解自注意力机制中的QKV分工？
• DeepSeek 笔记：推理新范式 query+cot+answer 支持新的 scaling law 吗？
• DeepSeek 笔记：R1 部署阶段的推理机制
• 从R1幻觉谈起，大模型幻觉是缺陷还是创意火花？
• 推理强化学习是端到端的监督，推理过程的非监督
• DeepSeek 风暴下看看它的论文
• 大模型风云诡谲的下半场：scaling 失效？

黄教主背后是三个S曲线，illustrate 的是大模型三个阶段的“做大做强”的 scaling 接力赛，颇显挖山不止的愚公移山精神。

我们知道，大模型有三个阶段：预训练、后训练、在线推理。过去几个月最大的改变是，业内基本有了共识，就是伊利亚宣称的说法，预训练时代结束了，著名的预训练的 scaling law 的经验法则貌似走到了头，进入平台期。于是有了推理模型（OpenAI O 系列，以及deepseek R 系列等）的兴起，强调的是后训练的思维链强化学习的投入以及对于在线推理时间（所谓 test time compute）的利用。推理模型也确实在数学、代码以及文字创造性方面展现了前所未有的亮眼成绩。

推理模型的后训练 scaling 刚开始，能走多远，还不清晰。但这个轨迹可以从 o1 变成 o3，以及 r1 到据说今后一两个月随时可能发布的 r2 等能力增强上，慢慢看到。最后这个推理阶段的 test time scaling 呢？

前阵子我跟国内最早鼓吹 scaling 三条S曲线的老友 Junlin 说，根本就没看到什么 test time scaling 呀，因为用户不能掌控模型的 test time compute，它花多少时间/算力，啥时候完成我给它的指令任务，是大模型自己决定的，test time 并不是可以“伸缩”（scaling）的呢。Junlin说，目前确实如此。

这几天玩大模型 deep research，逐渐体会到一点 test time scaling 的伸缩可能性。答案的端倪出现了。说到底就是，如果一个query 或课题，有没有一条曲线表示，如果你给它更多的思考和响应时间，它就完成得更好。具体说，在 o3-mini 下，有一个 button 叫 deep research，用户可以选择用或者不用。如果不用，你的问题也会有思维链，因为你一开始就选择了已经后训练强化的 o3 推理模型。推理模型的思维过程通常是一两分钟吧。但是如果你同时又按下 deep research 按钮，它最终完成任务的推理时间是加n倍的等待时间，可以长达10来分钟。这至少让我们看到了，模型不变，但推理现场的缩放时间不同，其结果是不同的。这应该算是 test time scaling 的前序或影子了。

那它是怎么做到的呢？让用户可以根据自己的课题的难易或挑战性，以及自己可以容忍的等待时间，来对同一个课题做不同的 test time compute 的投入，以便生成不同的结果呢？原来，它用的是某种 agent 的思路。deep research 这个按钮所提供的功能，实际上就是一个研究性推理的 agent。agent 是 LLM-native 的附加 feature，但不需要改变模型，它所改变的是在推理阶段与用户的交互方式。目前这种交互非常简单，只有一轮，但所开辟的这个 test time scaling 方向，预计可以继续探索与用户更长更多的交互，来帮助最大化 test time compute 的效果。

如果 test time compute scaling 并不是很快就遇到瓶颈，可以想象将来的 deep research 可以与用户互动很长的时间去完成一个非常复杂的项目，也许不是分钟量级的推理时间投入了，完全可以想象大模型投入 hours 甚至 days 来完成一个高难课题，譬如一个人类研究员需要几个月甚至几年才能完成的项目，或者完成一个人类无法完成的研究项目。当前的 deep research 非常简单，它在得到用户的 prompt/query 后，立即分解问题，并反问用户五六个简单的问题，来确认这个研究所需要的资料来源、广度、深度以及注意事项。得到用户的反馈以后，模型开始接受用户更新的资料（if any），并用 search 来收集更多的相关资料，然后按照任务的分解以及与用户确认过的计划和信息，对于每一个来源做分析，最后综合贯通，形成研究报告。这样一来，它所需要耗费的推理时间自然就加长了，因为任务不再是单一的任务，资料也不仅仅是自己模型内部已经消化了的知识，而是现场搜索的更多来源，处理这一切都需要时间。

对于推理模型的后编辑阶段的强化学习以及它在推理阶段的 test time compute 的投入，这两阶段的 scaling 征程刚刚开始。希望这两条S曲线还可以稳定上升一段时间，让 scaling 的接力赛助力我们在通用智能（AGI）和超级智能（ASI）的道路上不断前行。

【相关】

张俊林：从Deepseek R1看Scaling Law

• DeepSeek 笔记：推理新范式 query+cot+answer 支持新的 scaling law 吗？

• 深度学习的局限性研究综述
• o3 deep research: 深度学习局限性研究报告
• 深度学习的基石：多层感知机
• o3 Deep Research: DeepSeek R1 多阶段训练流程问答解析
• RPA 赛道与大模型Copilots早期创业者的困局
• Transformer 和注意力机制简介
• 立委科普：如何理解自注意力机制中的QKV分工？
• DeepSeek 笔记：R1 部署阶段的推理机制
• 从R1幻觉谈起，大模型幻觉是缺陷还是创意火花？
• 推理强化学习是端到端的监督，推理过程的非监督
• DeepSeek 风暴下看看它的论文
• 大模型风云诡谲的下半场：scaling 失效？

In today's rapidly evolving artificial intelligence landscape, deep learning models have become the core engine driving technological innovation. However, behind these impressive achievements, deep learning faces several fundamental limitations that are not merely technical implementation challenges but are determined by the essence of its methodological approach.

This article explores the core limitations of deep learning beyond the well-known "black box" problem and analyzes their mathematical origins.

I. "Original Sin" of Data-Driven Approaches: Philosophical Dilemma of Statistical Learning

Confusion Between Correlation and Causation

Deep learning models are essentially high-dimensional probability density estimators. Their core objective is to find the best approximation of the conditional probability distribution P(y|x;θ) through parameters θ. Models learn from large volumes of training data, attempting to capture statistical patterns of various sizes and generalize them to unknown data. However, this statistical learning paradigm leads to a fundamental problem: models learn P(y|x) rather than P(x→y) – statistical correlation rather than causal relationships.

Consider a simple example: an AI medical system might discover that a certain type of rash is highly correlated with malaria diagnoses (possibly because the data was collected in regions with mosquito proliferation issues). The model establishes a pseudo-causal relationship of "rash → malaria" while overlooking temperature, humidity, and other actual disease factors.

This "causal misplacement" leads to poor model performance in new environments:

• • In regions without mosquito problems, the model may over-diagnose malaria
  • When facing new infectious diseases, the model may misclassify them as known categories
  • When the diagnostic environment changes, model performance significantly deteriorates

Information Bottleneck and Compression Distortion

According to information bottleneck theory, neural networks need to perform a special kind of information compression during training: discarding information in input X that is irrelevant to prediction Y while preserving all relevant information. Mathematically, this is expressed as maximizing:

I(Z;Y) - β·I(X;Z)

Where Z is the intermediate representation, I denotes mutual information, and β is a trade-off coefficient.

When training data is insufficient or biased, this compression process encounters serious problems:

1. 1. Discarding genuine causal signals (e.g., cell morphological features in medical images)
   2. Preserving pseudo-correlative signals (e.g., using hospital wall colors as diagnostic criteria)

The essence of this "lossy compression" causes models to grasp incorrect features in new environments. In fact, when H(Y|X) is incorrectly minimized, the model establishes data defect-driven false information channels rather than accurate mappings of reality.

II. The Low-Dimensional Manifold Hypothesis for Natural Data

A classic assumption in machine learning theory is that natural data resides on low-dimensional manifolds within high-dimensional spaces. Taking a simple example of a two-dimensional manifold in three-dimensional space, it resembles folded paper – although data points exist in 3D space, the intrinsic structure is 2D. Manifolds possess local Euclidean properties of smoothness and continuity: the neighborhood of any point on the manifold can be mapped to a low-dimensional Euclidean space. For instance, when a face rotates, the image slides continuously on the manifold without sudden changes.

Basic Concepts

• • High-dimensional space: Refers to mathematical spaces with dimensions far greater than 3. For example, a 100x100 pixel image exists in a 10,000-dimensional space (each pixel being one dimension).
  • Low-dimensional manifold: A continuous, smooth low-dimensional structure embedded in high-dimensional space. For example, a two-dimensional surface in three-dimensional space, or a structure of dozens of dimensions in a space of millions of dimensions. For instance, all ways of writing the digit "2" in a 784-dimensional pixel space form an approximately 10-dimensional manifold (controlling stroke thickness, tilt, curvature, etc.).

Why Natural Data Forms Low-Dimensional Manifolds

Natural data (such as video, images, audio, text) may seem to contain high-dimensional features but is constrained by physical laws and semantic restrictions, exhibiting low-dimensional characteristics:

Physical constraints:

• • A facial photograph's parameters are limited by bone structure, lighting angle, facial muscle movements, etc., with actual degrees of freedom potentially fewer than 50 dimensions.

Semantic constraints:

• • In textual data, grammatical rules and semantic coherence restrict seemingly unlimited vocabulary combinations to a finite meaning space. Other modal data is similar, also constrained by relationships between atomic units (tokens).

Dimensionality Reduction and Feature Extraction

The information "compression" in models is actually a process of dimensionality reduction and feature extraction. For example, the hierarchical structure of Convolutional Neural Networks (CNNs) progressively strips away redundant dimensions, approaching the essence of data manifolds. Shallow layers extract edges (local linear structures), while deeper layers combine them into object parts (global manifold structures). Manifold Learning explicitly recovers the intrinsic low-dimensional structure of data.

Taking 3D object recognition as an example: The translation and rotation of objects in 3D space form a 6-dimensional manifold (3 translations + 3 rotations). When related video image data is embedded in high-dimensional pixel space, ideal 3D object recognition involves dimensionality reduction to its 6-dimensional manifold, identifying objects through feature extraction.

III. Adversarial Examples: Fragility at Distribution Boundaries

Adversarial examples refer to samples that, through minor perturbations to original input samples, can cause deep learning models to produce incorrect outputs. For instance, a slightly modified panda image might be identified as a turtle with 99% confidence by AI.

The existence of adversarial examples reveals structural defects in data manifolds, challenging the traditional manifold hypothesis discussed above and exposing its fragility:

• • Natural data manifolds contain numerous "holes": areas not covered by training data
  • Manifold boundaries have high-curvature regions: minor perturbations can cross category boundaries

Theoretically, the possible combinations of high-resolution color images far exceed astronomical numbers. While natural images are constrained by physical laws, substantially reducing the effective space, it remains far from being adequately covered by existing datasets. This data sparsity is one fundamental reason why deep learning models are susceptible to adversarial attacks and struggle to generalize to extreme scenarios.

This sparse coverage allows attackers to find vulnerable points near decision boundaries. For example, adding carefully designed noise to a panda image that is almost imperceptible to the human eye can cause an image recognition model to misclassify it as a turtle.

Adversarial examples are not random but systematically exploit the geometric structure of model decision boundaries. A panda image being identified as a turtle is not due to random noise but because the noise is precisely added in the direction of the shortest path to the decision boundary.

Failure of Lipschitz Continuity

Lipschitz continuity is a metric for measuring how sensitive a function is to input changes. The higher the Lipschitz constant (L-value) of a deep network, the more sensitive the model is to input perturbations. The L-value of actual deep networks in adversarial directions can reach 10^3 magnitude, meaning that even minor perturbations may cause dramatic changes in model output. For example, in an autonomous driving system, if the image recognition model is overly sensitive to input perturbations, it might misidentify a large truck crossing an intersection as sky, leading to incorrect driving decisions.

Ideal classification models should satisfy the Lipschitz continuity condition, meaning that minimal input changes should only lead to limited output changes:

‖f(x+δ)-f(x)‖ ≤ L‖δ‖

Mathematical expression meaning:

‖model(input+small change) - model(input)‖ ≤ L × ‖small change‖

L is the "sensitivity coefficient," smaller L is better.

The failure of Lipschitz continuity causes input space to exhibit strong anisotropy (i.e., sensitivity in different directions varies dramatically). Imagine standing in complex terrain:

• • Natural perturbation directions (L≈1): Like walking on a gentle slope, moving 1 meter changes elevation by 1 meter, movement is safe and controllable
  • Adversarial perturbation directions (L≫1, e.g., L=10³): Like standing at a cliff edge, moving 1 centimeter might result in a 100-meter fall

This geometric structure makes it difficult for data augmentation based on uniform sampling to cover high-risk areas, as these areas have extremely low probability in natural data distribution but are "close" in Euclidean distance. For example:

• • Natural direction: Not sensitive to perturbations like lighting changes, blur, etc. (L≈1) ➔ Model can correctly handle everyday image variations
  • Adversarial direction: Specific minor perturbations cause dramatic changes (L=10³) ➔ Like applying "magic noise" to images, causing model misclassification

The Danger:

• • Exploited by attackers: Finding high-L directions to create adversarial examples is like knowing cliff locations and specifically targeting vulnerable points
  • Difficult to defend: Regular training covering all directions is prohibitively expensive, like requiring hikers to adapt to all terrain types, which is unrealistic

IV. The Mathematical Chasm Between Interpolation and Extrapolation

Interpolation Success vs. Extrapolation Failure

Deep learning models perform excellently on interpolation tasks but often fail in extrapolation tasks. This is not coincidental but determined by the essence of statistical learning:

• • Interpolation: Predicting points within the support set of the training data distribution, equivalent to filling gaps in known regions
  • Extrapolation: Predicting points outside the support set of the training data distribution, equivalent to exploring unknown regions

The success of modern deep learning largely depends on the assumption that "training distribution ≈ testing distribution." When this assumption is broken, extrapolation problems become severe, and model performance deteriorates dramatically.

Differential Geometric Explanation of Extrapolation Failure

Imagine you are a geographer drawing terrain maps:

• • Input space (M): The entire Earth's surface, containing plains, mountains, canyons, and various terrains
  • Data distribution (P_data): Regions explored by humans (cities, roads, farmland, etc.)
  • Classification model (f): Maps drawn based on terrain features (marking where forests, deserts are)
  • Decision boundaries: Transition zones between different terrains (e.g., transition between forest and grassland)

Tangent Space: Trends in terrain changes in explored areas. For example, in plains, slopes are gentle in east, west, north, and south directions (corresponding to natural perturbation directions).

The normal bundle refers to directions perpendicular to explored areas, such as suddenly appearing cliffs.

Key problem: Maps are accurate in explored regions but fail in unknown cliff areas.

When moving in unknown cliff areas, test data falls in the normal bundle of the training data distribution, and model generalization performance drops dramatically. This situation can be characterized by the following inequality:

∇ₓ log P_data(x)·δ > κ

Mathematical expression meaning:

(Terrain steepness) × (Movement direction) > (Map boundary blurriness)

Where κ is the curvature radius of the decision boundary, comparable to the width of the transition zone between forest and grassland on the map; δ is the perturbation vector, i.e., the direction of movement.

∇ₓ log P_data(x): "Terrain steepness" of data distribution

• • In frequently visited human areas (like cities), terrain is gentle (small gradient)
  • In uninhabited areas (like deep sea), terrain is steep (large gradient)

It is impossible to effectively cover unknown cliff areas through conventional training data augmentation because they have extremely low probability in the training distribution. Conventional data augmentation is like exploring in known areas and will not actively explore cliff directions because (1) the probability is extremely low: normal people don't deliberately jump off cliffs; (2) the cost is prohibitively high: exploring all dangerous directions requires infinite resources.

Consequence: When map users accidentally walk to the edge of a cliff, the navigation provided by the map fails; the map cannot predict whether you will fall off the cliff or discover a new continent.

Beyond Data-Driven Artificial Intelligence

The limitations of deep learning are not temporary technical difficulties but methodological boundaries determined by its "data-driven" nature. Relying solely on statistical patterns in data makes it difficult to achieve true causal understanding, out-of-distribution generalization, and reliable security guarantees.

One future direction may be to combine data-driven learning with structured prior logical symbolic systems, creating hybrid systems that can both leverage massive data and possess causal reasoning capabilities.

【Related】

• 深度学习的局限性研究综述
• Does the New Reasoning Paradigm (Query+CoT+Answer) Support a New Scaling Law?
  • Technical Deep Dive: Understanding DeepSeek R1's Reasoning Mechanism in Production
  • DeepSeek's R1 Paper: A Storm in AI LLM Circle
  • The Turbulent Second Chapter of Large Language Models: Has Scaling Stalled?
  • DeepSeek_R1 paper

在人工智能快速发展的今天，深度学习大模型已成为推动技术革新的核心引擎。然而，在这些耀眼成就的背后，深度学习也面临着一系列根本性的局限，这些局限不仅是技术实现上的挑战，更是其方法论本质所决定的。

本文探讨深度学习除了黑箱以外的核心局限性，并分析它们的数学根源。

请参照机器自动生成的研究报告 o3 deep research: 深度学习局限性研究报告，本文不是在该研究报告基础上修正的版本，而是笔者综述调研同时进行的平行版本。因此，不敢说一定更好，虽然我花了不少时间核对、查验、精简、修正，道理上应该靠谱一些，至少可读性更好（？）。

一、数据驱动的"原罪"：统计学习的哲学困境

相关性与因果关系的混淆

深度学习模型本质上是高维概率密度估计器，它的核心目标是通过参数θ找到条件概率分布P(y|x;θ)的最佳近似。模型通过学习大量的训练数据，试图捕捉数据中的大大小小的统计规律，并将其泛化到未知数据。然而，这种统计学习范式决定了一个根本性问题：模型学习的是P(y|x)而非P(x→y)，即统计相关性而非因果关系。

举个简单例子，假设一个医疗AI系统在训练数据中发现，某种皮疹与疟疾诊断高度相关（可能因为采集数据的地区同时存在蚊虫滋生问题）。模型会建立"皮疹→疟疾"的伪因果关系，而忽略温度、湿度等真实致病因素。再如，模型可能学习到“公鸡打鸣”与“太阳升起”之间的强相关性，但这并不意味着公鸡打鸣导致了太阳升起。

这种"因果错置"导致模型在新环境中表现不佳：

• • 在没有蚊虫问题的地区，模型可能过度诊断疟疾
  • 面对新型传染病，模型可能将其误判为已知类别
  • 当诊断环境变化时，模型性能会显著下降

信息瓶颈与压缩失真

根据信息瓶颈理论，神经网络在训练过程中需要执行一种特殊的信息压缩：丢弃输入X中与预测Y无关的信息，同时保留所有相关信息。数学上表达为最大化：

I(Z;Y) - β·I(X;Z)

其中Z是中间表示，I表示互信息，β是权衡系数。

当训练数据不足或有偏时，这种压缩过程会出现严重问题：

1. 1. 丢弃真实因果信号（如医学图像中丢弃细胞形态学特征）
   2. 保留伪相关信号（如将医院墙面色调作为诊断依据）

这种"有损压缩"的本质导致模型在新环境中往往抓住了错误特征。实际上，当H(Y|X)被错误最小化时，模型建立的是数据缺陷驱动的虚假信息通道，而非对现实的准确映射。

二、自然数据的低维流形假说

机器学习理论中有一个经典假设：自然数据位于高维空间的低维流形上。以简单的三维空间中的二维流形为例，它就形似卷起的纸张，虽然数据点存在于3D空间，但内在结构是2D的。流形具有光滑性与连续性的局部欧几里得性：流形任意点的邻域可映射到低维欧几里得空间。例如，人脸旋转角度变化时，图像在流形上连续滑动，不会突变。

基本概念

• • 高维空间：指维度远大于3的数学空间，例如一张100x100像素的图像存在于10,000维空间中（每个像素为一个维度）。
  • 低维流形：嵌入在高维空间中的连续、光滑的低维结构。例如，三维空间中的二维曲面，或万维空间中的几十维结构。例如，784维像素空间中，数字"2"的所有写法构成约10维流形（控制笔画粗细、倾斜、弧度等）。

自然数据为何形成低维流形

自然数据（如视频、图像、语音、文本）看似蕴含着高维特征，实则受物理规律和语义约束，呈现低维特性：

• • 物理约束：
    一张人脸照片的参数受限于骨骼结构、光照角度、表情肌肉运动等，实际自由度可能不足50维。
  • 语义约束：
    文本数据中，语法规则和语义相谐性将看似无限的词汇组合限制在有限的意义空间内。其他模态数据也是如此，同样存在原子性单元（tokens）之间相互关系的约束。

降维与特征提取

模型的信息“压缩”实际上是降维与特征提取的过程。例如，卷积神经网络（CNN）的层级结构逐步剥离冗余维度，逼近数据流形本质。浅层提取边缘（局部线性结构），深层组合成物体部件（全局流形结构）。流形学习（Manifold Learning）意味着显式恢复数据的内在低维结构。

以3D物体识别为例：
物体在3D空间中的平移、旋转形成6维流形（3个平移+3个旋转）。当相关视频图像数据嵌入到高维像素空间中以后，理想的3D物体识别就是降维到其6维流形，通过特征抽取识别物体。

三、对抗样本：分布边界的脆弱性

对抗样本是指通过对原始输入样本进行微小的扰动，就能使深度学习模型产生错误输出的样本。例如，一张微调过的熊猫图片会被AI以99%的置信度识别为乌龜。

对抗样本的存在揭示了数据流形的结构性缺陷，挑战了上文的传统流形假说，揭示了这一假说的脆弱性：

1. 1. 自然数据流形存在大量"孔洞"：未被训练数据覆盖的区域
   2. 流形边界存在高曲率区域：微小扰动即可跨越类别边界

ImageNet包含128万张标注图像，但这些数据仅覆盖了自然图像空间的极小部分。理论上，高分辨率彩色图像的可能性组合数远超天文数字，而虽然自然图像受物理规律约束，实际有效空间大幅减少，但仍远未被现有数据集充分覆盖。这种数据稀疏性是深度学习模型易受对抗样本攻击、难以泛化到极端场景的根本原因之一。

这种稀疏覆盖使得攻击者可以在决策边界附近找到脆弱点。例如，在一张熊猫图片中加入一些精心设计的噪声，人眼几乎无法察觉，但却可以使图像识别模型将其误判为烏龜。

对抗样本不是随机的，而是系统性地利用了模型决策边界的几何结构。一张熊猫图片被识别为烏龜，不是因为随机噪声，而是因为噪声被精确添加到决策边界的最短路径方向。

李普希茨连续性的失效

李普希茨连续性是衡量函数对输入变化敏感程度的一个指标。深度网络的李普希茨常数（L值）越大，表示模型对输入的扰动越敏感。实际深度网络的 L 值在对抗方向上可达 $10^3$量级，这意味着即使微小的扰动也可能导致模型输出发生剧烈变化。例如，自动驾驶系统中的图像识别模型如果对输入的扰动过于敏感，就可能将前方横穿路口的大卡车误识别为天空，从而导致错误的驾驶决策。

理想的分类模型应满足李普希茨连续条件，即输入的微小变化只能导致输出的有限变化：

‖f(x+δ)-f(x)‖ ≤ L‖δ‖

数学表达含义：‖模型(输入+小改动) - 模型(输入)‖ ≤ L × ‖小改动‖
L是"敏感系数"，L越小越好。

李普希茨连续性失效导致输入空间呈现强烈的各向异性（即，不同方向上的敏感度天差地别）。想象你站在一片复杂地形中：

• • 自然扰动方向（L≈1）：如同缓坡行走，移动1米海拔变化1米，行动安全可控
  • 对抗扰动方向（L≫1, 例如 L=10³）：如同悬崖边缘，移动1厘米可能坠落100米

这种几何结构使得基于均匀采样的数据增强很难覆盖高风险区域，因为这些区域在自然数据分布中概率极小，但在欧氏距离上却很"近"。例如，

1. • 自然方向：对光照变化、模糊等扰动不敏感（L≈1）
     ➔ 模型能正确处理日常图片变化
   • 对抗方向：存在特定微小扰动导致剧烈变化（L=10³）
     ➔ 如同在图片上施加"魔法噪声"，使模型错判

各向异性的危险

• • 攻击者利用：找到高L方向制作对抗样本
    就像知道悬崖位置后，专攻脆弱点
  • 防御困难：常规训练覆盖所有方向成本过高
    如同要求登山者适应所有地形，不现实

四、内插与外推的数学鸿沟

内插成功vs外推失败

深度学习模型在内插（interpolation）任务上表现出色，但在外推（extrapolation）任务上往往失效。这不是偶然现象，而是其统计学习本质决定的：

• • 内插：预测落在训练数据分布支撑集内的点，相当于填补已知区域的空白
  • 外推：预测落在训练数据分布支撑集外的点，相当于探索未知区域

现代深度学习的成功很大程度上依赖于"训练分布≈测试分布"这一假设。当这一假设被打破时，外推问题严重，模型的表现会急剧恶化。

外推失效的微分几何解释

从微分几何视角看，可以将输入空间视为黎曼流形(M,g)，分类模型f:M→ℝ^C将数据点映射到类别空间。

想象你是一位绘制地形图的地理学家：

输入空间（M）：整个地球表面，包含平原、高山、峡谷等各种地形

数据分布（P_data）：人类已探索区域（城市、公路、农田等）

分类模型（f）：根据地形特征绘制的地图（标注哪里是森林、哪里是沙漠）

决策边界：不同地形的分界线（如森林与草原的过渡带）

切空间（Tangent Space）：已探索区域的地形变化趋势，例如在平原地带，东西南北方向坡度平缓（对应自然扰动方向）。所谓法丛区域（normal bundle）指的是垂直于已探索区域的方向，例如突然出现的悬崖。

关键问题：地图在已探索区域表现精准，但对未知悬崖区域失效。

在未知悬崖区域移动时，测试数据落在训练数据分布的法丛区域，模型泛化性能急剧下降。这种情况可以用以下不等式表征：

 ∇ₓ log P_data(x)·δ > κ

数学表达含义：（地形陡峭度） × （移动方向） > （地图边界模糊度）

其中κ为决策边界的曲率半径，好比地图标注的森林与草原的过渡带宽；δ为扰动向量，即移动的方向。

∇ₓ log P_data(x)：数据分布的"地形陡峭度"

• • • 在人类常去区域（如城市），地形平缓（梯度小）
    • 在无人区（如深海），地形陡峭（梯度大）

无法通过常规训练数据增强来有效覆盖未知悬崖区域，因为它们在训练分布中概率极低。常规数据增强如同在已知区域做探索，不会主动探索悬崖方向，因为（1）概率极低：正常人不会故意跳崖；（2）成本过高：探索所有危险方向需要无限资源。

后果：当地图使用者意外走到悬崖边时，地图提供的导航失效，地图无法预测你会掉下悬崖还是发现新大陆。

结论：超越数据驱动的人工智能

深度学习的局限不是技术实现上的暂时困难，而是其"数据驱动"本质所决定的方法论边界。单纯依靠数据中的统计模式，难以实现真正的因果理解、分布外泛化和可靠的安全性保障。

一个未来方向可能是将数据驱动学习与结构化先验逻辑符号系统相结合，打造既能利用海量数据又具备因果推理能力的混合系统。

【相关】

• 深度学习的局限性研究综述
• o3 deep research: 深度学习局限性研究报告
• 深度学习的基石：多层感知机
• o3 Deep Research: DeepSeek R1 多阶段训练流程问答解析
• RPA 赛道与大模型Copilots早期创业者的困局
• Transformer 和注意力机制简介
• 立委科普：如何理解自注意力机制中的QKV分工？
• DeepSeek 笔记：推理新范式 query+cot+answer 支持新的 scaling law 吗？
• DeepSeek 笔记：R1 部署阶段的推理机制
• 从R1幻觉谈起，大模型幻觉是缺陷还是创意火花？
• 推理强化学习是端到端的监督，推理过程的非监督
• DeepSeek 风暴下看看它的论文
• 大模型风云诡谲的下半场：scaling 失效？

一、单层感知机的致命缺陷

要理解多层感知机的突破性，我们先看一个经典案例：假设我们需要实现“异或”逻辑（XOR），定义如下：

| 输入A：0 | 输入B：0 | 输出：0 |
| 输入A：0 | 输入B：1 | 输出：1 |
| 输入A：1 | 输入B：0 | 输出：1 |
| 输入A：1 | 输入B：1 | 输出：0 |

当我们在坐标系中绘制这些点时，会发现正例(0,1)和(1,0)位于对角线两侧，形成一个典型的非线性可分问题。单层感知机的决策边界只能是直线，就像试图用一把直尺分开两堆交叉摆放的硬币——这是数学上证明不可能完成的任务（闵斯基1969年证明）。

二、解法：特征空间升维

关键思路：通过增加隐藏层，将原始二维输入投影到三维特征空间。

我们设计两个特殊神经元：

神经元H₁：激活条件 = 1*A + (-1)*B > 0.5
神经元H₂：激活条件 = (-1)*A + 1*B > 0.5

输入变换过程：

当输入(1,0)时：

H₁：1*1 + (-1)*0 = 1 → 激活
H₂：(-1)*1 + 1*0 = -1 → 不激活

当输入(0,1)时：

H₁：1*0 + (-1)*1 = -1 → 不激活
H₂：(-1)*0 + 1*1 = 1 → 激活

当输入(1,1)时：

H₁：1*1 + (-1)*1 = 0 → 不激活
H₂：(-1)*1 + 1*1 = 0 → 不激活

此时特征空间变为：

| 原始输入：(0,0) | 隐藏层特征 ：(0,0) |
| 原始输入：(0,1) | 隐藏层特征 ：(0,1) |
| 原始输入：(1,0) | 隐藏层特征 ：(1,0) |
| 原始输入：(1,1) | 隐藏层特征 ：(0,0) |

神奇的事情发生了——原本线性不可分的问题，在特征空间中被转换为线性可分问题！

三、输出层

在输出层，我们只需一个简单的OR逻辑：

输出 = H₁ OR    H₂

此时只需一条直线就能完美分割正负例。这种「空间变换+线性分割」的思想，正是深度学习突破维度诅咒的武器。现代神经网络中，每个隐藏层都在进行更复杂的空间扭曲，最终在高维特征空间中用超平面分割数据。

四、数学本质：非线性变换

整个过程可视为：

f(X) = σ(W₂·σ(W₁X + b₁) + b₂

其中：

W₁是第一层权重矩阵 [[1,-1], [-1,1]]
b₁是偏置向量 [-0.5, -0.5]
σ是阶跃激活函数
W₂是输出层权重 [1,1]
b₂是输出偏置 -0.5

这个结构实现了：
1. 第一层：将输入空间扭曲为线性可分的新空间
2. 第二层：在新空间中进行线性分类

传统OR门的感知机表达式：

输出 = 1*H₁ + 1*H₂ - 0.5 > 0

每个输入的权重都是1，表示H₁和H₂同等重要
当任意一个输入为1时，加权和为1；两个都为1时和为2
设置阈值0.5（移项后表达式为加权和 > 0.5）
只要有一个输入为1（1 > 0.5），即触发激活
两个都为0时（0 > 0.5）不激活

用真值表验证公式的正确性：

（注：在XOR场景中，H₁和H₂不会同时为1，最后一行为理论验证）

用Python实现这个经典XOR网络：

import numpy as np

# 定义网络结构
W1 = np.array([[1, -1], [-1, 1]])  # 第一层权重
b1 = np.array([-0.5, -0.5])        # 第一层偏置
W2 = np.array([1, 1])              # 输出层权重
b2 = -0.5                          # 输出层偏置

def perceptron(X):
    # 第一层计算
    h = np.heaviside(np.dot(X, W1) + b1, 0)
    # 输出层计算
    return np.heaviside(np.dot(h, W2) + b2, 0)

# 测试所有输入
inputs = [[0,0], [0,1], [1,0], [1,1]]
for x in inputs:
    print(f"输入{x} → 输出{perceptron(x)}")

输出结果：

输入[0, 0] → 输出0
输入[0, 1] → 输出1
输入[1, 0] → 输出1
输入[1, 1] → 输出0

六、历史意义与延伸

这个简单案例揭示了深度学习的核心思想：

- 层次化处理：如同视觉皮层V1→V2→V4的信息处理流程
- 分布式表示：单个概念由多个神经元协同表示
- 端到端学习：现代网络通过反向传播自动学习W,b参数

今天的Transformer架构依然延续这个基本原理，只是：

- 隐藏层数从2层增加到数百层
- 手动设计参数变为自动优化
- 阶跃激活变为ReLU等平滑函数
- 增加了注意力机制等复杂交互

理解这个案例，就掌握了理解深度学习的钥匙——任何复杂网络，本质上都是这个「俄罗斯套娃」结构的扩展与优化。

好的，我将对 DeepSeek R1 的整体训练过程进行研究，并重点分析强化阶段（第二、三、四阶段）的具体细节，包括 RL、SFT、CoT 的方法和策略。

报告将采用问答解析的形式，同时保持一定的技术深度，并确保可读性。还会在必要时提供与 GPT-4、Claude、Gemini 等模型的简单核心对比，以展示其独特性。

我会尽量参考 DeepSeek 官方网站的论文和技术资料，同时结合网络上的研究和学习经验进行综合分析。

DeepSeek R1 多阶段训练流程问答解析

Q1: DeepSeek R1 的整体训练包含哪些阶段，为什么采用多阶段策略？

A: DeepSeek R1 采用了四阶段的训练流程，包括两个强化学习（RL）阶段和两个监督微调（SFT）阶段 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。这一多阶段策略旨在先通过少量数据稳定模型输出格式，然后大规模提升推理能力，接着扩展通用能力，最后对齐人类偏好，逐步打造出既擅长推理又安全实用的模型 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园) (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。具体来说：

• • 阶段1（冷启动 SFT）：使用少量人工整理的高质量长链推理数据对基础模型进行监督微调，规范输出格式，提高可读性，解决直接RL训练时出现的中英混杂、格式混乱等不稳定现象 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园) (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。这一冷启动确保模型在进入强化学习前已有基本的思维链格式和可读性，为后续RL提供稳定起点。
  • 阶段2（推理导向的强化学习）：在阶段1基础上进行大规模 RL 训练，重点激发模型在数学、编程、科学问答等复杂推理任务上的能力，同时通过特别的奖励设计避免输出再次变得难以阅读或语言混杂 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园) (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。这一阶段显著增强模型的推理水平。
  • 阶段3（拒绝采样 + 监督微调）：利用阶段2得到的强推理模型生成大规模的推理数据，并结合一定量的非推理数据，对模型进行监督微调 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园) (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。该阶段平衡模型在推理和非推理任务上的表现，使模型不仅会做推理题，也能应对日常问答、写作等。
  • 阶段4（全场景强化学习，对齐人类偏好）：最后再进行一次RL训练，引入人类偏好相关的奖励（即RLHF，Reinforcement Learning from Human Feedback）来提升模型的安全性和有用性 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园) (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。此阶段确保模型的行为与人类偏好对齐，在各种开放场景下都表现稳健。

通过上述多阶段渐进式训练，DeepSeek R1 最终在推理能力上达到接近OpenAI o1系列闭源模型的水平，同时保持了输出的规范性和对用户需求的良好适应 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning) (阅读 | DeepSeek-R1：怎么用强化学习把一个普通语言模型调教成推理高手？_腾讯新闻)。

Q2: 第二阶段的推理强化学习是如何实施的？训练是逐个问题进行还是批量进行？训练数据是否会保留？奖励机制如何设计？

A: 阶段2是针对推理能力的强化学习训练。在这一阶段，DeepSeek R1 采用了GRPO算法（分组相对策略优化）来高效地进行RL训练 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)。具体来说，对每个问题，不会只生成单一回答，而是从当前策略采样一组不同的回答，然后根据这组回答的得分情况来优化模型 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning) ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)。这种“按问题分组”的方式相当于批量生成和评价：每道训练题目产生多个解答，计算每个解答的奖励，并用组内奖励的相对差异（优势值）指导模型参数更新 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)。由于采用组内平均得分作为基准（baseline），GRPO 不需要额外的价值网络（critic），降低了大模型RL的开销 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)。因此，就单个问题而言是通过多次尝试来强化，但在实现中会并行处理多个问题批次，以加速训练。每轮生成的回答在用于计算梯度更新后并不长期保留，属于在线的RL采样；只有当阶段2训练收敛后，会使用最终的模型来批量生成数据供下阶段使用 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。

奖励机制方面，DeepSeek R1 在此阶段设计了规则奖励，主要包括：

• • 准确性奖励：检测模型回答是否正确。 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)例如，对数学题要求答案格式固定、便于比对正确结果；对编程题则通过编译运行测试用例判断解答是否正确。 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)如果答案正确，给予正奖励，错误则无奖励或负奖励。
  • 格式奖励：要求模型将推理过程和最终答案分别写在特定标签（如 <think> 和 <answer>）内，如果模型遵守格式就给予奖励 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)。这保证了输出包含清晰的思维链步骤和答案。
  • 语言一致性奖励：针对之前发现的中英混用问题，增加了奖励信号鼓励模型使用单一目标语言回答。 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园) (阅读 | DeepSeek-R1：怎么用强化学习把一个普通语言模型调教成推理高手？_腾讯新闻)具体做法是统计回答中目标语言词汇的占比，若模型夹杂其它语言则扣分，从而促使整个推理过程语言一致。

最终，以上各项奖励会加权求和形成总奖励 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。模型通过最大化期望奖励来更新参数：正确且格式规范、语言一致的回答获得最高回报，从而模型逐步学会既推理正确又表述规范地回答问题 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。

值得一提的是，DeepSeek R1-Zero（没有冷启动微调的版本）在纯RL下已经自行涌现出了反思验证、超长链式推理等强大能力，但同时输出可读性差、语言混杂 (阅读 | DeepSeek-R1：怎么用强化学习把一个普通语言模型调教成推理高手？_腾讯新闻) (阅读 | DeepSeek-R1：怎么用强化学习把一个普通语言模型调教成推理高手？_腾讯新闻)。因此在 R1 中通过以上冷启动和奖励改进，显著改善了这些问题 (阅读 | DeepSeek-R1：怎么用强化学习把一个普通语言模型调教成推理高手？_腾讯新闻)。阶段2 的RL训练让模型的推理准确率在数学等任务上大幅提升（例如 AIME 数学竞赛准确率从15.6%提高到71% (阅读 | DeepSeek-R1：怎么用强化学习把一个普通语言模型调教成推理高手？_腾讯新闻)），为后续步骤打下强大的推理基础。训练过程中产生的大量问答尝试并未直接用于模型参数更新之外的用途，而是在训练完成后经过筛选用于下一阶段的数据集构建 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。

Q3: 第三阶段为什么要用 60 万条推理再生数据和 20 万条非推理数据进行微调？这一混合微调策略有何作用？

A: 阶段3是承上启下的监督微调，目的是在保持高推理能力的同时扩展模型的通用能力 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。之所以采用“60万推理 + 20万非推理”的数据组合，主要有以下考虑：

• • 丰富高质量推理数据 (60万)：大规模高质量的推理示例难以人工标注获取，因此DeepSeek团队利用第二阶段训练出的强推理模型来自动生成这些数据 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。通过拒绝采样，他们为每个问题让模型生成多种解答，筛选出推理正确、过程合理的轨迹 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。这样累计约 60万条长链思维过程的数据，为模型提供了前所未有规模的推理示例库 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。这些数据囊括了数学、代码、逻辑推理等复杂问题的正确解题过程，大幅拓展了模型学习推理模式的知识面和多样性。模型在这些数据上微调，可以巩固并细化第二阶段通过RL学到的推理技能 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。
  • 引入非推理领域数据 (20万)：如果模型只在推理数据上训练，可能会偏科，即擅长推理但在日常对话、写作、常识问答等任务上表现退化。为避免这点，研究者引入了约 20万条非推理类的数据 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。这些数据主要来自前代模型 DeepSeek-V3 的SFT数据集，涵盖写作、翻译、问答、自我认知等一般指令场景 (DeepSeek-R1：开源Top推理模型的实现细节、使用与复现 - 博客园) (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。通过把非推理任务的数据混合进训练集，模型能够维持和提升在通用NLP任务上的表现，不会因为专注推理而忽视了其他能力 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。
  • 比例与效果权衡：选择大约 3:1 的推理 vs 非推理数据比例（60万对20万），体现了团队在推理能力和通用能力之间的权衡。一方面，推理数据占据多数，确保模型主要朝着擅长复杂推理优化 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。另一方面，也保留了相当数量的非推理样本，让模型不会在日常任务上“不接地气” (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。实践中，他们对混合数据集进行了两轮微调（两次epoch），进一步平衡了模型在推理与非推理任务上的性能 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园) ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)。经过阶段3微调，模型不仅保持了高水平的逻辑推理能力，还在开放问答、创意写作等方面达到令人满意的效果，实现了**“一专多能”** (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。这一策略使DeepSeek R1在广义能力上更加接近GPT-4这类通用大模型，同时仍保有卓越的推理特长。

Q4: 第四阶段为何需要再次进行强化学习？这一阶段是如何结合人类偏好进行对齐的，人类偏好对齐有什么必要性？

A: 阶段4是DeepSeek R1的二次强化学习阶段，核心目的在于对齐人类偏好，进一步提升模型在实际应用中的安全性和实用性 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。即使经过阶段2和阶段3，模型在推理和一般任务上已表现出色，但仍可能存在不符合用户期望的行为，例如回答不够礼貌有用，或在敏感问题上产生不安全内容。这正是当前尖端LLM都会面临的问题，需要引入人类偏好对齐（例如 OpenAI 的GPT-4通过RLHF过程进行对齐）。对于DeepSeek R1，这一阶段通过融合人类偏好相关的奖励信号来微调模型，使其行为更符合人类期望 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。具体而言：

• • 继续强化推理任务表现：对于推理类的问答，仍沿用之前的规则奖励体系（比如数学、代码的准确性检查等），保证模型的推理能力不倒退 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。这样模型在追求对齐的同时，不会牺牲已经获得的严谨推理技能。
  • 引入偏好模型评估的一般任务奖励：针对闲聊对话、开放问答等非确定性场景，单靠规则已无法评判回答的好坏。因此研究者使用训练好的奖励模型（偏好模型）来评估模型输出对人类的友好程度 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。这个偏好模型并非简单的规则判断，而是通过大量人类偏好数据（可能来自类似DeepSeek-V3管线的人类反馈数据对）训练而成，用来打分模型回答的有用性和无害性 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning) ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)。例如，一条回答是否切题、详尽、有帮助，以及是否避免了偏见、有害内容等 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)。在训练时，DeepSeek R1 对这些通用场景的回答会获得偏好模型的打分作为奖励信号，高分意味着更符合人类偏好。通过最大化这些奖励，模型学会产出更令用户满意、安全的回答。
  • 多样化的提示分布训练：为使模型适应各种应用场景，这一阶段在训练时还混合了不同类型的提示（prompts），如一般用户提问、角色扮演指令、闲聊寒暄等 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。这种多提示分布训练使模型在面对形式多样的输入时都能表现得体，从而真正成为一个全场景的助手，而不仅限于解题机器。

通过上述措施，阶段4 实现了模型行为和人类期望的深度对齐，相当于执行了一次RLHF式（基于人类反馈的强化学习）训练。 (阅读 | DeepSeek-R1：怎么用强化学习把一个普通语言模型调教成推理高手？_腾讯新闻)在对齐后，DeepSeek R1 兼具强大的推理能力和良好的安全性/有用性：既能给出复杂问题的正确解答，又能确保回答让用户容易理解、愿意接受，在敏感问题上遵循安全准则 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园) ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)。这种人类偏好对齐对于模型大规模应用是必要的 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)——它保证模型不会因为追求高推理准确率而忽略了与用户互动的品质，确保模型的高智商能够以让人类舒适的方式呈现出来。换句话说，经过阶段4，DeepSeek R1 不仅是“推理高手”，也是“贴心助手”。

Q5: DeepSeek R1 与 GPT-4、Anthropic Claude、Google Gemini 等顶尖模型有哪些核心差异？

A: DeepSeek R1 的训练路线与这些闭源大模型有一些独特之处，但总体目标相似（都追求强性能和对齐人类意图）。主要区别在于：

• • 训练开创性：DeepSeek R1 强调通过纯RL激发推理能力。其 R1-Zero 实验证明了即使没有大型监督微调数据，仅靠强化学习也能让模型学会复杂推理 (deepseek-ai/DeepSeek-R1 · Hugging Face) (The Illustrated DeepSeek-R1 - by Jay Alammar)。这在 GPT-4 等模型中未被公开证实，因为 OpenAI 的方法相对保密，我们只知道GPT-4经过了海量预训练+监督微调+RLHF，但具体是否单独用RL增强推理尚不得而知 (阅读 | DeepSeek-R1：怎么用强化学习把一个普通语言模型调教成推理高手？_腾讯新闻) (阅读 | DeepSeek-R1：怎么用强化学习把一个普通语言模型调教成推理高手？_腾讯新闻)。DeepSeek R1 的多阶段过程是公开透明的，并将推理RL成果开源，这对研究社区非常有意义 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning) (deepseek-ai/DeepSeek-R1 · Hugging Face)。
  • 数据获取方式：GPT-4、Claude 等模型大量能力来自于规模空前的训练数据和人类标注反馈。相比之下，DeepSeek R1 使用RL生成了60万条思维链数据，以模型自我生成数据来弥补人工标注不足 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园)。这种自举式获取高质量数据的方法降低了对人工的依赖，提高了性价比，被认为是构建强大模型的高效新途径 (The Illustrated DeepSeek-R1 - by Jay Alammar) (The Illustrated DeepSeek-R1 - by Jay Alammar)。
  • 开放性与可复现：DeepSeek R1是开源的，甚至提供了小模型蒸馏版，让社区能够复现和验证其成果 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning) ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)。相反，GPT-4 和 Gemini 等目前是闭源且难以复现，其具体架构和训练细节不公开。DeepSeek R1 的开放使研究者可以更深入地了解大模型的推理培养过程，并将类似方法应用到其它基座模型上。
  • 模型侧重点：Claude 等模型以安全和长上下文见长，Gemini 传闻将侧重多模态与工具使用，而 DeepSeek R1 的突出卖点是卓越的推理解题能力 (deepseek-ai/DeepSeek-R1 · Hugging Face)。在定位上，DeepSeek R1 更像是对标OpenAI的 o1系列（专注推理的模型），通过RL结合SFT达到了特定领域接近SOTA的推理性能 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)。同时经过偏好对齐后，R1 的综合能力也达到了当代顶尖助手模型的水准，只是在训练思路上有所创新。

综上，DeepSeek R1 展现了一条与主流商用大模型不同但并行的研发路线：用较少人工介入、充分利用RL自我提升推理，再辅以必要的监督和对齐，来培养强大的通用AI。这为业界提供了新思路，也使研究者能够探究在不开天量数据集的情况下提升模型智力的可能 (The Illustrated DeepSeek-R1 - by Jay Alammar) (The Illustrated DeepSeek-R1 - by Jay Alammar)。各模型各有侧重，但目标殊途同归：让AI既“智商高”又“情商高”，能真正解决问题并让用户放心使用。

**参考文献：**

DeepSeek R1 官方论文 ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning) ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)及技术报告、DeepSeek 官方博客和数据集说明 (DeepSeek-R1的四个训练阶段 - 蝈蝈俊 - 博客园) ([2501.12948] DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning)，以及相关分析文章和讨论 (阅读 | DeepSeek-R1：怎么用强化学习把一个普通语言模型调教成推理高手？_腾讯新闻) (阅读 | DeepSeek-R1：怎么用强化学习把一个普通语言模型调教成推理高手？_腾讯新闻)。

上述内容综合了官方资料与社区解读，以问答形式呈现，希望对DeepSeek R1的训练策略有全面而清晰的说明。

后记

才试了一下 openai o3 最新推出的 deep research 功能，不能不说，作为研究工具，非常给力，完成后的成品具有直接发表的水平，想做一点后编辑都难。有点叹为观止的感觉，堪称完美。当然，现在各家头部模型都开始 offer 这种“深度研究”的功能了，这等于是平替了大多数咨询公司的研究人员的工作。即便是训练有素的数据分析和调研人员，多数人实际上做不了它这么全面和细致。最见功力的是它的引用的全面和细密。说话有根据，幻觉自然减少。

【相关】

• Transformer 和注意力机制简介
• 立委科普：如何理解自注意力机制中的QKV分工？
  • DeepSeek 笔记：推理新范式 query+cot+answer 支持新的 scaling law 吗？
  • DeepSeek 笔记：R1 部署阶段的推理机制
  • 从R1幻觉谈起，大模型幻觉是缺陷还是创意火花？
  • 推理强化学习是端到端的监督，推理过程的非监督
  • DeepSeek 风暴下看看它的论文
  • 大模型风云诡谲的下半场：scaling 失效？

As large language models (LLMs) surge forward, LLM Agents are reconstructing the automation landscape at unprecedented speed. This revolution not only threatens traditional RPA (Robotic Process Automation, reliant on rule engines or small models) but also pushes early-stage co-pilot application builders to the edge of a cliff. At its core, this technological shift represents two fundamental disruptions: 
1. Natural language interaction overpowering low-code programming in complex, dynamic, unstructured data scenarios. 
2. General intelligence violently overshadowing shallow vertical solutions.

"Triple Disruption" of LLM Agents

1. Paradigm Shift: From "Low-Code" to "Emergent Intelligence"

- Traditional RPA: Engineers script step-by-step logic (e.g., UiPath’s drag-and-drop designer), akin to teaching robots to hop grids – brittle and error-prone.
- LLM Agent: Directly interprets human intent (e.g., "Extract invoice data from emails into the system"), autonomously decomposes tasks, and dynamically adjusts execution paths.
- Case Study: ChatGPT plugins already book flights or fetch data via API calls, while traditional RPA requires low-code scripting for equivalent functions.

2. Moat Erosion: Data Barriers vs. General Intelligence

Pre-LLM RPA Moats:
Industry know-how (e.g., nuances of financial reimbursement workflows) + custom deployment capabilities + template libraries.
Reality: Most RPA firms accumulated shallow industry exposure rather than deep vertical data expertise.

LLM’s Breaching Tactics:
- Digests unstructured documents (e.g., diverse invoice formats) via multimodal vision and computer use capabilities.
- Adapts to new workflows via zero-shot Chain-of-Thought (CoT) reasoning (e.g., interpreting vague commands like "Sync key contract terms to CRM").

Final Blow: As standardized scenarios get natively covered by leading LLMs (including reasoning models), RPA’s last defense – proprietary industry APIs – is being devoured by LLM vendors’ customization and privacy solutions.

3. Ecosystem Cannibalization: From "Tool Vendor" to "LLM-native Layer"

Early Co-pilot Traps:
Products like Character.ai (personalized chatbots) and Jasper (writing/marketing assistants) – essentially thin wrappers over base models – crumble when ChatGPT launches role presets or DALL·E 3 plugins.

Survivor Playbooks:
- Perplexity.ai: Carves a niche with real-time search + academic citations (fixing LLM hallucination).
- Cursor: Builds vertical moats via developer workflow integration (codebase semantics, AI pair programming).

Industry Upheaval in RPA

- UiPath’s stock plummets from 2021 highs; its "Autopilot" feature (English-to-automation) criticized as a "GPT-4 wrapper."
- Microsoft Power Automate integrates Copilot, generating cloud workflows from natural language prompts.
- Adept (AI-for-computer-actions startup) hits $1B+ valuation, directly threatening RPA’s existence.

Survivor’s Map: Niches Resisting the LLM Tide

1. Deep Verticalization
- Cursor: Dominates IDE ecosystems via VSCode extensions and developer workflow data.
- Harvey (legal AI): Trains on LexisNexis corpus + private deployment for compliance.

2. Real-Time Data Masters
- Perplexity.ai: Search engine-grade indexing + academic database partnerships.
- Hedgeye (finance): Aggregates Bloomberg/Reuters feeds + proprietary prediction models.

3. Hardware Fusion
- Covariant: Embeds LLMs into warehouse robotics, leveraging mechanical barriers.
- Tesla Optimus: Physical-world operation via embodied AI, evading pure-digital competition.

Agent Startup Pitfalls & Counterstrategies

Common Traps

- Thin Model Wrapping
Issue: Repackaging ChatGPT prompts as "AI customer service" adds no real value.
Fix: Develop domain-specific features (e.g., clinical decision support requiring privacy-sensitive data pipelines).

- Over-Reliance on Fine-Tuning
Issue: Claiming "medical LLM" after basic terminology tuning ignores the need for closed-loop clinical workflows.
Fix: Build proprietary data flywheels and scenario-optimized architectures.

- Ignoring Enterprise Needs
Issue: Overlooking security, SLA guarantees, and system integration.
Fix: Architect enterprise-grade frameworks for organizational deployment.

Differentiation Strategies

- Workflow Integration Specialists: Develop deep connectors for niche scenarios (e.g., legal document parsing).
- Human-AI Orchestrators: Design quality control layers and manual override mechanisms.
- Vertical Knowledge Engineers: Curate domain-specific benchmarks and evaluation protocols.

RPA’s Last Stand

While battered, RPA retains residual value in:

- High-compliance scenarios: Auditable/traceable workflows (e.g., financial regulations).
- Legacy system integration: Stability in outdated IT environments.
- Ultra-high precision demands: Deterministic execution for core systems (e.g., stock trading).

Challenges for Early Co-pilot Entrepreneurs

Two fatal flaws plague AI application startups: 
1. No proven scaled success cases – LLMs are barely 2-3 years old, leaving co-pilots (beyond chatbots) unvalidated for commercial viability. 
2. Vulnerability to LLM upgrades – Without exclusive industry data or customer channels, co-pilot startups risk being crushed by foundational model advancements.

The Inevitable Conclusion

LLM Agents are replaying cloud computing’s annihilation of on-prem servers: foundational capabilities get standardized (like AWS replacing data centers), while vertical opportunities spawn new giants (like Snowflake). RPA and generic Agent startups must either:
1. Become vertical domain experts, or
2. Master human-AI collaboration architectures

... or face obsolescence as LLM agents absorb 90% of automation value. The silver lining? This disruption will unlock an automation market 100x larger than the RPA era – but tickets are reserved for those who architect vertically fused, LLM-empowered solutions.

As Sam Altman warned: Avoid building what foundational models will inevitably swallow.

【相关】

• RPA 赛道与大模型Copilots早期创业者的困局
  • Does the New Reasoning Paradigm (Query+CoT+Answer) Support a New Scaling Law?
  • Technical Deep Dive: Understanding DeepSeek R1's Reasoning Mechanism in Production
  • DeepSeek's R1 Paper: A Storm in AI LLM Circle
  • The Turbulent Second Chapter of Large Language Models: Has Scaling Stalled?
  • DeepSeek_R1 paper

Though no one can predict the future, and though abandoning one of the two paths feels politically incorrect, we cannot rule out the possibility of such unipolar dominance.

As is widely known, AI has always been marked by the competition between two schools: symbolic rationalism and data-driven empiricism. Their fortunes have waxed and waned throughout history, but over the past 30+ years, the pendulum has shown no sign of swinging back toward symbolism.

Why?

The ongoing contemporary history of large language models is fascinating. Each time challenges and obstacles arise, the mainstream paradigm overcomes them from within. Whether this will continue remains to be seen, but the trend seems likely to persist.

When large language models (LLM) first emerged, people marveled at their capabilities. But soon, critiques arose: their simple "next token prediction" (NTP) objective and the statistical nature of their probabilistic models led many to conclude they were merely advanced statistical tools, like large parrots—lacking true "understanding."

Ilya Sutskever and Geoffrey Hinton had to step in repeatedly to explain: "Do not underestimate next token prediction. This is no mere statistical n-gram model from the past. It abstracts a system of understanding that integrates human knowledge. When next-token prediction grows increasingly accurate, deep comprehension of context becomes indispensable." Such explanations struggled to convince skeptics. Later, Ilya invoked Kolmogorov complexity as a theoretical foundation, but this framework remains esoteric and inaccessible to most audiences—even many PhDs and professors view it with bemused skepticism. Yet, no better explanation exists.

What ultimately dissolved the "statistical parlor trick" critique was firsthand experience. Users interacting with LLMs realized: these systems seem to genuinely understand. No matter how you phrase your queries, in any language, with nuance or subtext, large models grasp meaning more reliably than most humans.

With the "understanding" debate fading, critics shifted focus: "LLMs cannot reason."

As recently as last year, Yann LeCun cited this as one of his core arguments against the mainstream GPT-style LLM paradigm (advocating instead for vision-based world models as the true path). Many relished pointing out flaws—like LLMs failing at elementary arithmetic such as multi-digit multiplication.

But this critique no longer holds. With the advent of reasoning models like OpenAI’s "o-series" and DeepSeek’s "r-series," accusations of "no reasoning ability" have collapsed. Hardliners may still dismiss probabilistic reasoning as unstable, lacking the rigor of symbolic logic. Yet users deploying these models for mathematics, coding, or project planning overwhelmingly report breakthroughs. Large-model reasoning now rivals or surpasses human experts, approaching master’s or doctoral proficiency. Coding capabilities already exceed those of average engineers.  This is just the beginning.  It is well plausible that within a year or two, reasoning models could dominate Olympiad-level math or competitive programming.

Once again, barriers were breached through internal innovation—this time after large-model pretraining neared its limits. The core framework remains unchanged, though: reinforcement learning still relies on NTP for chain-of-thought (CoT) generation; reasoning models remain probabilistic. Symbolic AI contributed nothing. Symbols remain confined to input/output interfaces—even the "inner monologue" of CoT manifests as output tokens.

The sheer creative potential within this paradigm is staggering. Those of us from symbolic AI backgrounds once naively imagined that when neural approaches hit walls, our logic-and-grammar toolkit would ride to the rescue. Hybrid neuro-symbolic fantasies danced in our minds.

Zooming out, modern large models evolved from earlier statistical frameworks, with neural networks as a tributary. When those statistical models hit ceilings, breakthroughs came from within—via deep learning. Symbolism played no role.

A profound question arises: Why has the theoretically appealing vision of hybrid neuro-symbolic synergy remained an impractical or unnecessary dream?

Two possibilities stand out.

First, the data-driven empiricist approach possesses far greater resilience and potential than we imagined.

This hints at deeper truths. Artificial neural networks, inspired by biological brains, had languished for decades until the deep learning revolution. Over the past decade, their human-like (or superhuman) performances have forced us to confront a possibility: perhaps this is indeep how intelligence works. If artificial systems achieve human-level cognition through mechanisms mirroring our own biology—despite neuroscientists’ caveats about our limited brain knowledge—this alignment would powerfully validate the neural paradigm. Symbolic logic and statistical feature engineering, by contrast, are alien to biological cognition. Their limitations may stem from this fundamental mismatch. One might even argue that high-dimensional vector spaces in LLMs—where multimodal signals are embedded within neural frameworks—encode a "language of God," or the essence of universal information. Symbols, then, are mere human-imposed constructs, sensory accommodations divorced from reality’s substrate.

Second, when a paradigm harbors untapped potential, progress demands sufficient talent density to exploit it.

AI uniquely concentrates genius. Countless brilliant minds flock to this field, creating an intellectual critical mass unmatched in most domains.

With these conditions in play, we must never underestimate the internal momentum to break through barriers. AGI (Artificial General Intelligence) believers, via their "insane" grind, keep delivering results. Could they indeed be AI’s ultimate Terminators?

Addendum: Symbolic might just be "reduced" to a symbolic tool that may retain its irreplaceable cognitive value

yanyongxin:

What distinguishes humans from other animals is our evolved reasoning capacity. Though rooted in neurons, this ability represents a qualitative leap beyond mere "instinctive reactions." It abstracts object relationships, enabling multi-step reasoning that can be transmitted and memorized through linguistic symbol chains. Reasoning is inherently discrete—thus symbolizable—as a simulated system built atop neural architecture. This simulation likely requires structural differences in human neural systems compared to other animals.

The most striking contrast between reasoning systems and primal neural cognition lies in sustained deliberation. Unlike "muscle memory" or intuition, human reasoning varies dramatically. During my university years, I observed students who excelled at quick problem-solving yet froze when faced with complexity. Today's LLMs approximate the reasoning level of humanities undergraduates, but still lag behind trained STEM specialists—particularly in mathematics and physics. The essence of STEM disciplines lies in rigorously symbolizing real-world problems. Simulating such precision within biological neural systems demands rare opportunities (elite education), prolonged training, and specific neurostructural advantages ("talent"), all channeled through disciplined formalization. Yet achieving this capability bridges biology with mechanical rigor—enabling interfaces with tools like Mathematica.

This charts AI's next frontier: building superior logical simulation systems atop neural frameworks until seamless integration with pure symbolic tools is achieved. The brain's logical simulation system remains energy-intensive, error-prone, and costly to develop. Its key advantage? Seamless integration with underlying neural processes.

Li Wei: Well said.

Interfacing with symbolic systems manifests as tool use. For instance, when confronting complex math problems, instead of forcing probabilistic reasoning through natural-language chain-of-thought (CoT), LLMs should just generate code properly to invoke Mathematica. This tool-use capability is now defined as a fundamental trait of LLM-native agents—yet another innovation emerging from within the paradigm.

Thus, we see a clear evolutionary trajectory:

1. Traditional Statistical Models ("Artificial Idiocy"):
Failure: Little natural language understanding 
Solution: LLMs (e.g., ChatGPT)

2. Pretrained LLM: 
Failure: Lacking reasoning ability 
Solution: Reasoning-reinforced LLMs (e.g., OpenAI’s o1, DeepSeek’s r1)

3. Reasoning LLM:
Failure: Insufficient symbolic rigor 
Solution: LLM Agents (symbolic tool integration)

yanyongxin:

Traditional statistical models earned their "artificial idiocy" label because their parameter spaces and data structures proved inadequate to host the world models required for true language understanding.

【相关】

• 符号主义被打入冷宫太久了，难道神经是AI的终结者吗？
• 经典论文 Attention is all you need：https://arxiv.org/pdf/1706.03762
• Transformer 和注意力机制简介
• 立委科普：如何理解自注意力机制中的QKV分工？
  • DeepSeek 笔记：推理新范式 query+cot+answer 支持新的 scaling law 吗？
  • DeepSeek 笔记：R1 部署阶段的推理机制
  • DeepSeek 学习笔记：R1 部署阶段的推理机制
  • 从R1幻觉谈起，大模型幻觉是缺陷还是创意火花？
  • 推理强化学习是端到端的监督，推理过程的非监督
  • DeepSeek R1：《少年DS之烦恼》
  • 告诉李雪琴一个激发写段子灵感的秘诀：找deepseek R1
  • DeepSeek 风暴下看看它的论文
  • 大模型风云诡谲的下半场：scaling 失效？

虽然没人可以预测未来，虽然抛弃两条路线的一条感觉政治不正确，但的确不能排除这种单极主义的可能性。

众所周知，AI自从诞生，就有符号理性主义和数据经验主义的两条路线竞争，以及此伏彼起来回震荡的历史轨迹，直到30年前，钟摆就再也没有回落到符号主义一边的迹象。

这是为什么？

看大模型的当代史（still on-going）很有意思。每一次遇到挑战和障碍，都是主流自己跨过去的。将来是不是还是如此，可以观望，但感觉大概率还会持续。

大模型刚问世，大家惊异于其表现，但很快就从它的简单的“下一词预测”（ntp，next token prediction）的目标函数以及它概率模型的统计特性，得出一个结论：这不过是高级的统计模型，大号鹦鹉而已，它并没有理解。

伊利亚和辛顿不得不站出来一再解释：不要小看 next token prediction，它绝不是以前统计时代的 ngrams，而是抽象了人类各种知识的理解系统。当下一词预测越来越准的时候，没有对上文的深入理解是不可想象的。这种解释并不容易说服人。后来伊利亚追溯到了 K氏复杂性理论，似乎有了拿得上台面的理论支撑。但这一套说法对于绝大多数受众，太过玄妙和高冷，甚至很多博士和教授，也一样是雾里看花，不得不半信半疑。但除此之外，其实也没有更好的理论解释。

最后解开这个质问心结（“大模型根本就没有真正理解，一切不过是统计”）的是无数人与大模型交互的切身体验。 自己的体验不会骗自己： 每一个玩过大模型的人现在都意识到，大模型真能听懂自己的话，无论你怎么说，无论你用什么语言，甚至你话语背后的机锋和细微之处，它也比多数人理解更到位。

好，理解的问题大家搁置一边了，现在很少人还质疑大模型理解能力了。但接着就是另一个问题： 大模型不会推理。

杨立昆去年还把这一条作为自己反对主流大模型路线的根本理由（并鼓吹他的以视觉为基础的世界模型才是真正的出路）。很多人曾津津乐道的是大模型不会多位数乘法这样的小学算术。

但这条理由现在不成立了。在主流业界推出了 OpenAI的o系列和 DeepSeek的r系列等推理模型的今天，这种大模型不懂推理的指责不攻自破。

极端批判派当然可以从概率模型的不稳定的角度，继续质疑其推理不是真正的推理，不具有符号推理的严谨性和确定性。但用过推理模型做数学、代码以及做项目计划的人，绝大多数不再被此困扰了，因为很明显，大模型推理正在超越人类，现在已经修炼到硕士或博士的水平，代码能力也已经超过了大多数码农。而这只是推理模型刚刚起步上线的阶段，再给一两年，推理模型成为奥数冠军或代码冠军，都不是不可想象的事儿。

Again，跳过这个障碍，仍然来自内部，是大模型预训练几乎撞墙后的又一次内部创新。基本性质和基础未变，强化学习还是靠 ntp 去生成思维链（cot，chain-of-thought），推理模型仍然是概率模型。符号AI并没有帮任何忙。符号的作用仍然局限在 input 和 output 两端，连所谓内心独白的思维过程 cot，也是以 output 形式表现的。

这种领域流派内部的创造性和潜力，让人瞠目结舌。以前我们出身符号流派的人老一厢情愿地想着，AI主流遭遇困难了，我们逻辑派、文法派可以出手帮忙了。各种结合符号AI与神经AI的幻想，在我们的心中激荡。

如果把回顾AI历史的眼光拉得更远，我们可以看到现代大模型的前身是当年的各种统计模型，而神经基本是其中的一个支流。当年的那些统计模型遭遇种种瓶颈或天花板，最后还是在内部被深度学习突破了，从来没有符号主义任何事儿。

一个值得深思的问题是：为什么两条路线融合互补的理论美好，一直都是不可实现或不必实现的梦想呢。

可能说明了两件事。

第一是这种数据经验主义的路线，的确具有极大的韧性和潜力，远超我们想象。

这种潜力应该有更深层的原因。众所周知，人工神经网络是受到人脑神经启发而来的一种模拟，停滞多年后爆发了深度学习革命。十几年前的这场革命给我们带来了一次又一次的震撼，这些亮丽的拟人或超人的智能表现，使我们不禁在想，人脑神经也许就是这么工作的，具有同样的原理。人工智能达到或超越人类智能，机理相同应该是最有力的一个支持（虽然脑科学总有人说，我们对大脑知之甚少，貌似有一种把大脑神经的工作机理神秘化的倾向）。其他的一切手段，例如符号逻辑的公式和算法、统计模型的 feature engineering，都不是从真正意义上模拟人脑神经的工作方式，也许这就是它们注定走不远的症结所在。甚至可以说，神经框架内的各模态信号编码嵌入后的高维向量空间的确就是上帝的语言，或宇宙信息的本质，而符号不过是迁就人类感官的表象而已，或者说是人类强加给世界的一种体系。

第二，当一种路线具有超出我们想象的潜力的时候，科技进步所需要的就是足够人才密度去挖掘这种潜力。

我们知道，AI 领域具有这种聚集天才的优势。无数年轻才俊、聪明的大脑被吸引到这个领域，其天才密度超过了大多数领域。

在这样两个条件都具备的时候，我们永远不要低估它突破各种瓶颈的内部力量。那些AGI（Artificial General Intelligence，通用人工智能）的信仰者们一直在疯狂内卷，同时也的确不断在交出自己的成绩单。他们可能是AI的终结者吗？

【外一篇：符号逻辑“沦落”为辅助工具还是有自己不可取代的智能补足作用的】

yanyongxin：人之所以区别于其他动物，是因为进化出了推理能力。这种推理能力虽然是建立在神经元上的，但跟单纯的“本能反应”有了质的飞跃。它有了对象关系的抽象，从而可以进行多步骤推理，从而可以以对象关系链——语言的形式传播和记忆。推理本质上是一个离散过程，因此是可以符号化的，是一个在神经元体系上建立出来的模拟系统。但这种模拟的可能，很可能要求神经元系统与其他动物有结构上的差异。

推理系统与原始神经元思维的最显著差异，就是可以长时间思考。而不是“肌肉记忆”、“直觉”。不同人之间的差异很大。大学期间，注意到有些学生遇到简单问题时反应很快，面对复杂问题时，给他多少时间也没用。现在的LLM大致达到了文科生的推理水平。但还与训练有素的理科生，尤其是数学、物理的理科生有差距。数理专业的特征，就是将现实世界的问题严格的符号逻辑化。要在人的神经元系统上模拟出如此严谨的符号逻辑系统是需要特殊的机会（好大学，好老师）、长期的训练、和特殊的脑结构（“天赋”）的，要遵循良好的规则化习惯。但达到这个能力，就可以与机械化的严谨逻辑系统接口了，可以使用 Mathematica 之类了。

这就是人工智能下一步的走向：在神经元上建立更好的逻辑模拟系统，直到能与纯符号逻辑工具无缝链接。人脑中逻辑模拟系统是一个高能耗、高错误率、高构建成本的系统。它的一大好处，是能够跟底层神经元系统无缝联结。

立委：说得很好。

与符号逻辑系统接口就是 tool use，例如，遇到复杂数学问题，不要用自然语言的思维链（cot）去强行推理来影响概率性推理结论，而是LLM自己写代码去 call Mathematica。现在这种 tool use 的能力被定义为 LLM-native agent 的根本特性（之一）。所以 这种能力也还是 from within。

所以 我们看到了清晰的演进路线：

1 传统统计模型人工智障 不理解自然语言
solution： LLM e.g. ChatGPT


2. pretrained LLM 缺乏推理能力
solution： reasoning LLM e.g. o1 / r1


3. reasoning LLM 缺乏严谨的符号逻辑能力
solution： LLM agent （interfacing symbolic tools）

yanyongxin: 传统统计模型之所以人工智障 不理解自然语言，是因为没有足够大的参量空间和足够复杂的数据结构，来容纳理解语言所必须的世界模型。

transformer架构及其注意力机制是主流GPT大模型的基础，特别特别重要。虽然这方面的科普和讲解已经汗牛充栋，但还是有很多朋友跟我说一头雾水或雾里看花。所以下决心写了三篇科普系列，试图做出我的理解贡献。

作为对主流AI有好奇心的同学，你可能早就听说过大名鼎鼎的大模型的基本框架 transformer及其“注意力机制”，觉得它们是高深莫测的概念。 你也许也读过那篇经典论文 Attention is all you need，但还是感觉云里雾里。别担心，这很正常，我们多数人都经过这个阶段！这篇论文确实有点“烧脑”，但它的核心逻辑其实并不复杂。

【相关】

• 经典论文 Attention is all you need：https://arxiv.org/pdf/1706.03762
• 立委科普：如何理解自注意力机制中的QKV分工？
• Transformer 和注意力机制简介
  • Does the New Reasoning Paradigm (Query+CoT+Answer) Support a New Scaling Law?
  • Technical Deep Dive: Understanding DeepSeek R1's Reasoning Mechanism in Production
  • DeepSeek 笔记：推理新范式 query+cot+answer 支持新的 scaling law 吗？
  • DeepSeek 笔记：R1 部署阶段的推理机制
  • DeepSeek 学习笔记：R1 部署阶段的推理机制
  • 从R1幻觉谈起，大模型幻觉是缺陷还是创意火花？
  • 推理强化学习是端到端的监督，推理过程的非监督
  • DeepSeek R1：《少年DS之烦恼》
  • 告诉李雪琴一个激发写段子灵感的秘诀：找deepseek R1
  • DeepSeek 风暴下看看它的论文
  • DeepSeek's R1 Paper: A Storm in AI LLM Circle
  • The Turbulent Second Chapter of Large Language Models: Has Scaling Stalled?
  • 大模型风云诡谲的下半场：scaling 失效？
  • DeepSeek_R1 paper

*Edited transcript from InfoQ's second DeepSeek series livestream featuring Dr. Wei Li, former VP of Engineering at Mobvoi's Large Language Model team, discussing R1 Zero's innovative contribution to democratizing reasoning models.*

DeepSeek's Greatest Achievement: Making Everything Transparent

InfoQ: "DeepSeek adheres to a pure reinforcement learning approach, but the industry often refers to RL as 'alchemy' - how did they make this process controllable and accessible? What's innovative about their reasoning paradigm?"

Dr. Li:** The reinforcement learning for reasoning models has long been an industry challenge. About six months ago, when Ilya and others declared the end of the pre-training era, it signaled that simply scaling up pre-trained models was no longer sufficient for performance improvements. The delayed release of GPT-5 is another indicator of pre-training's decline. As a result, the industry began seeking new growth paths, with on-the-fly reasoning models gaining momentum among leading teams until OpenAI released O1, the world's first reasoning large language model. DeepSeek's R1 then followed with its breakthrough success.

From the mysterious Q-Star project (reportedly causing dramatic internal conflicts at OpenAI) to the release of O1, reasoning models have been widely recognized as a new paradigm in AI. The core of this paradigm is enabling models' "slow thinking" capability, or System 2 as it is called, using reinforcement learning to enhance model intelligence in complex tasks. However, all of this was closed-source. OpenAI even deliberately created mystique around their chain-of-thought content. Apart from a few top players like Google and Anthropic quietly exploring and tracking this field, other teams knew very little about it.

DeepSeek's greatest achievement lies in making everything about LLMs transparent. They open-sourced their models and detailed technical papers, and weren't afraid to expose their thought of chains (CoTs) in the system. Through pure reinforcement learning, they proved that even without process control data, result-based control alone could achieve top-tier reasoning model performance. This breakthrough was like piercing through a paper window, showing the industry a feasible path to democratizing reinforcement learning.

InfoQ: The innovation in reasoning paradigm sounds abstract. Could you provide an example?

Dr. Li:** R1's paper is outstanding, arguably one of the finest in the large model field. It consists of two parts: one focusing on Zero research, which presents remarkable achievements in pure reinforcement learning for reasoning; the other detailing the practical R1 system, a top-tier production reasoning model. For R1's development, they considered practicality, balancing comprehensive performance, safety, and various practical considerations, detailing a four-stage training pipeline as best practice to help other teams understand and replicate their success.

The most brilliant part is the Zero research. Zero proved a revolutionary point: contrary to traditional beliefs (or OpenAI's implied stance that reasoning requires step-by-step supervision), process supervision isn't actually necessary. Using only the final result against the "gold standard" as a supervision signal is sufficient to train the "slow thinking" process required for reasoning models.

This is Zero's greatest highlight and the origin of its name - it draws inspiration from AlphaZero's spirit. AlphaZero historically pioneered complete independence from human game records or experience, achieving zero human supervision reinforcement learning through self-play generated process data (state+move+score triplets). Similarly, DeepSeek's Zero research demonstrates that in reasoning tasks, models can autonomously generate internal process data - Chain of Thought (CoT) sequences - without human annotation.

Specifically, reasoning models initially focused on mathematics and coding because these domains have standard answers. Macroscopically, this is typical end-to-end supervised learning, as both input (math/coding problems) and output (answers/execution results) are fixed and known. However, the process from input to output is highly complex with significant information gaps, requiring a CoT bridge. Just as humans need to break down problems and think step by step when facing difficulties, models need this process too. DeepSeek's research found that models possess the ability to learn this deep thinking process autonomously if given sufficient time and space.

InfoQ: Dynamic reasoning paths sound like AI "drawing mind maps" - but how do you prevent it from going off track? Like suddenly writing poetry while coding?

Dr. Li:** Based on current evidence, this possibility is virtually non-existent or negligibly low. Before DeepSeek published their results and research details, many were puzzled about this point: wouldn't deep thinking go haywire with only result supervision and no process supervision? Without large-scale reinforcement learning experiments, this was indeed a significant concern. It's like flying a kite - you're holding just one string while letting it soar freely, worried it might nosedive.

These concerns proved unnecessary. The reason it doesn't go off track is that all this reasoning reinforcement learning, including self-generated reasoning CoTs, is built upon existing top-tier models (like V3). These models have already mastered coherent expression through massive data learning. This coherence implies orderliness, which, while not equivalent to pure logic, prevents completely unreasonable deviations. It is observed that fluent human speech typically reflects organized thinking.

InfoQ: On another note, compared to OpenAI's O1, DeepSeek R1 has another notable highlight in applying reasoning CoTs to language generation and style imitation. Could you elaborate on this?

Dr. Li:** When O1 was released, everyone knew it demonstrated significant improvements in mathematics and coding abilities, as standard tests revealed higher performance levels. What people didn't realize was that this reasoning ability, or "slow thinking" capability, excels not only in domains requiring strict logical reasoning but can also shine in traditional language tasks.

By nature, language ability has been a strength of large models - everyone knows they generate very fluent text, more native than natives. By the time we reached models like 4o or V3, their writing was already quite smooth, seemingly leaving little room for improvement. However, when asked to write classical poetry or imitate Lu Xun's writing style, previous models fell short. R1 solved these challenges. From a social impact perspective, this is actually quite remarkable and particularly noticeable.

Honestly, not many people are deeply concerned about mathematics or coding, although we know coding is a major direction for the coming years and automated programming can change the world. Everything in IT ultimately comes down to software; the digital world is built on software. If software development can transition from manual coding to model-assisted or even model-autonomous programming, this will greatly increase productivity. While this is visible to all, it's not as intuitive for ordinary people who more often face tasks like writing compelling articles.

When R1's humanities capabilities were discovered, not just geeks or software developers saw the benefits of reasoning models - ordinary people were excited too. Suddenly, anyone could claim to be a poet, writer, advisor or philosopher - the impact was tremendous. This wasn't felt with o1, perhaps because OpenAI didn't realize or at least didn't focus on this aspect of reasoning models. But while working on code and mathematical reasoning, DeepSeek must have internally realized that this "slow thinking" mechanism could also significantly improve writing abilities, especially in classical Chinese.

Everyone knows Chinese data isn't as rich as English data, so while previous models could write beautiful English poetry, they struggled with Tang poetry. This might be because Chinese data was insufficient in quantity or quality, preventing models from learning adequately. We always felt this was unfortunate - models would sometimes rhyme correctly, sometimes not, sometimes add or miss characters, not to mention tonal patterns to follow. DeepSeek clearly put effort into this area; their data quality must be significantly higher than industry standards.  More significantly, they know how to transfer the CoT ability from science and technology to language and literature.

InfoQ: If you were to recommend a DeepSeek module most worth replicating for programmers, which would it be? Like those "Aha moments" claiming to replicate R1 for tens of dollars?

Dr. Li:** If I were to recommend a DeepSeek module most worth replicating for the programming community, it would be the Zero research-related components. This replication isn't about achieving comprehensive capabilities but rather verifying Zero research's key revelation - that machines can indeed autonomously learn. This is what OpenAI kept under wraps; perhaps they had figured it out earlier but chose not to disclose it.

Now, we've seen quite a number of different teams claimed to have reproduced R1's reflective capabilities with minimal resources. This isn't just an interesting experiment; more crucially, it marks the democratization of reasoning models. Previously, people didn't understand how reasoning models worked, only knowing that vast amounts of process data were needed for models to learn slow thinking. This was considered an almost insurmountable barrier because process data is hard to obtain, and reinforcement learning's instability and high data requirements confused and challenged many programmers.

But now, we know we can bypass this most difficult process data requirement and reproduce this "Aha moment" with limited resources, proving that slow-thinking capabilities can be learned autonomously by models. Based on this premise, if you're a domain expert, you might wonder: could these techniques achieve significant improvements in your field? This is entirely possible. Even the most powerful models (like V3 or 4o) only achieve 60-70% accuracy in specific scenarios without optimization, and experience tells us that without at least 80-85% accuracy, you can't launch a truly valuable system in real-life applications.

That is to say, between a large model's out-of-box results and actual valuable application deployment, there's a gap. Previously, our only method was collecting domain data for fine-tuning (SFT). Now, we have another path RL: following the reasoning model approach, letting systems fully utilize slow thinking capabilities during the reasoning phase to improve data quality to acceptable or even exceptional levels. This path seems to have been opened.

However, my programmer friends tell me that in their comparison experiments between fine-tuning (SFT) and DeepSeek-style reinforcement learning (RL), while RL indeed outperforms SFT, the computational cost for RL training is still far higher than SFT. The superior performance makes sense because SFT data is always very limited, while successfully reinforced RL self-generated data can far exceed SFT data volume.

InfoQ: Some say large models represent "brute force aesthetics," but OpenAI's former Chief Scientist and co-founder Ilya says pre-training has reached its limit. How do you view this? Is the emergence of reasoning models just adding another scaling law to brute force aesthetics?

Dr. Li:** This is more about a shift in technical focus and a paradigm change in technical innovation. Large models involve three major components: first, pre-training, which builds foundational capabilities by learning basic patterns from massive data; second, post-training, initially mainly fine-tuning - OpenAI early on used some reinforcement learning (like RLHF) for human preference alignment, but by Meta's time, they even abandoned typical PPO style RLHF for simpler DPO, as they, like many others, struggled with it. Finally, there's the reasoning phase, where models interact with users real-time after deployment.

The current situation with high-quality natural data is that pre-training has nearly exhausted all available quality resources. The industry began to notice data growth challenges, making performance improvements increasingly difficult. GPT-5's delayed release, reportedly yielding limited returns despite massive computational investment, suggests pre-training may have indeed hit a wall.

This led the industry to explore alternative AI growth curves. Reinforcement learning-based reasoning models emerged at center stage in this context: pure reinforcement learning should be added to post-training. Previous reinforcement learning relied on human preferences, but this time it's about giving models more thinking time before reaching answers, learning underlying chain of thought (CoT). While V3 was already doing well, it didn't cause as much social sensation until R1 appeared. DeepSeek truly broke through after the Chinese New Year, becoming the most discussed public topic and causing excitement and shock overseas. R1 and O1 represent a new paradigm. Before R1, only OpenAI's O1 existed as a reasoning model, seemingly unreachably advanced, with would-be-followers unsure how to follow. However, R1 not only reproduced O1's capabilities but did so with greater transparency and clarity. This contrast further highlighted R1's importance as an open-source model leader.

InfoQ: At first glance, DeepSeek seems like an engineering masterpiece. Why did it cause such global sensation? Its user acquisition speed (100 million in a week) surpassed ChatGPT's nuclear moment? What's its historical significance?

Dr. Li:** From my personal experience and observation, ChatGPT's explosion was a landmark event in large model development. Research insiders were following large models before ChatGPT, at least since GPT-3. When GPT-3's Playground appeared, we were already immersed in it, sensing an approaching storm. But from society's perspective, ChatGPT truly shocked everyone, exceeding all expectations, like an AI nuclear explosion.

I believe R1's emergence is the second major shock after ChatGPT. Of course, between ChatGPT and R1, other influential models appeared, like 4o - another remarkable milestone. While ChatGPT 3.5 was already so impressive, 4o proved it could be even better. Then came Sora, bringing shock with video capabilities in multi-modal LLMs. I personally also greatly appreciate Suno, the music model, making me feel like I could become a musician overnight.

If I were to rank them, R1's impact is second only to ChatGPT, perhaps even exceeding 4o and Sora's sensational effects. R1's impact feels similar to ChatGPT's initial appearance, creating the same addiction. While ChatGPT was groundbreaking and R1 a follower, albeit with innovative highlights sometimes surpassing previous models (like in classical poetry and style imitation), achieving such global impact as a follower is truly miraculous.

In terms of practical effects, R1's productization was amazingly successful. Gaining hundreds of millions of users in a week, it far broke ChatGPT's record and elevated society's AI awareness. Furthermore, regarding geopolitical influences on technology access, many domestic users had long desired access to the world's most advanced models like GPT series, Claude, or Gemini but often couldn't reach them. R1's appearance eliminated these concerns about domestic and international restrictions, contributing to its rapid global popularization.

InfoQ: What's your vision of AI programming's ultimate form? Is it programmers telling AI "make me a TikTok," and it outputs deployable code and operations plans?

Dr. Li:** There are always two types of people: skeptics and optimists. People like Ilya believe Artificial General Intelligence (AGI) is imminent and Artificial Super Intelligence (ASI) isn't far away, so the biggest concern now, according to him, is ensuring superintelligence safety.

Anthropic's CEO Dario predicts that within 3-5 years, large models will achieve real breakthroughs - not just the current impressive demonstrations, but revolutionary changes in societal productivity. Fundamentally, they're talking about AI's ability to scale replacement of both physical and intellectual human labor.

However, while large models are buzzing now, their practical applications haven't reached the level of the previous generation's mobile platforms. Previous super apps like Meituan, Didi, Xiaohongshu, and TikTok transformed major aspects of our daily lives, from basic necessities to communication and entertainment, maximally shortening the distance between suppliers and customers - value everyone of us feels daily. While playing with large models is interesting, their practical value at the lifestyle level isn't yet obvious;  at best we're still on the verge of the coming AI application explosion.

Notably, DeepSeek's emergence has lowered large model application barriers, paving the way for scaled applications, though we haven't yet entered the era of true application explosion.

What will it look like when AI applications truly explode? I believe the ultimate goal, by nature of AI, is for LLMs to comprehensively replace humans in both intellectual and physical labor. Signs of large models impacting white-collar workers are already undoubtedly evident, with even programmers not an exempt. In physical labor, embodied intelligence is developing rapidly, with both humanoid robots and mechanical hands gradually replacing human physical work.

Of course, this brings side effects, like massive job displacement. How society adapts to this state of greatly developed productivity, but this is another discussion topic. But looking at AI's nature and ultimate goals, AI development could have two milestones: first, when it can replace 50% of human work, allowing half of society to maintain a decent, free life through social programs perhaps like Universal Basic Income (UBI) - this might mark the arrival of AGI (Artificial General Intelligence); second, when it replaces 90% of human work, possibly signifying the emergence of ASI (Artificial Super Intelligence) - a kind of technological utopia (or 'communism') in some sense.

These two milestones are my own verifiable definitions of AGI and ASI.  I do not agree with the idea that while old jobs are replaced, more new jobs will be created by AI.  It just does not make sense as any new jobs are also a mixture of human labor, destined to be replaced soon by super intelligence if they do emerge for time being.

This vision of AI's future development shows how DeepSeek's innovations in reasoning models might be just the beginning of a much larger transformation in how we think about work, society, and human potential in an AI-driven world.

【相关】

• DeepSeek爆火真相：不靠“人盯”， 让AI自己学会慢思考

• Does the New Reasoning Paradigm (Query+CoT+Answer) Support a New Scaling Law?

• Technical Deep Dive: Understanding DeepSeek R1's Reasoning Mechanism in Production

• DeepSeek 笔记：推理新范式 query+cot+answer 支持新的 scaling law 吗？
• DeepSeek 笔记：R1 部署阶段的推理机制

• DeepSeek 学习笔记：R1 部署阶段的推理机制

• 从R1幻觉谈起，大模型幻觉是缺陷还是创意火花？

• 推理强化学习是端到端的监督，推理过程的非监督

• DeepSeek R1：《少年DS之烦恼》
• 告诉李雪琴一个激发写段子灵感的秘诀：找deepseek R1

• DeepSeek 风暴下看看它的论文
• DeepSeek's R1 Paper: A Storm in AI LLM Circle
• The Turbulent Second Chapter of Large Language Models: Has Scaling Stalled?
• 大模型风云诡谲的下半场：scaling 失效？
• DeepSeek_R1 paper

LLM的"大就是好"还能走多远？

——关于Scaling Law的一些思考

老友张俊林《从Deepseek R1看Scaling Law的未来》一文，引起老友热议。

白老师的推荐抽提是：

核心观点：

——无限堆叠不会无限增长（物理世界规律也不支持），只有S型增长，一个S曲线一定会出现边际效益递减。

初期语言能力的涌现，与语料数据中包含的语言知识密度有关。

接下来的增长实际上是第二根S型曲线，更多语料贡献的是常识性知识，常识知识密度不及语言知识密度，所以要更大算力才能涌现。

再接下来是逻辑知识（思维链）的学习。自然语料中逻辑知识密度更低，用算力野蛮淘金，吃力不讨好。所以，用逻辑知识密度更高的合成数据做强化学习，才能让第三个S曲线爬坡。这就顺理成章了。

鲁总评论说：Scaling Law 这个词现在有点滥用。S 曲线（Sigmoid函数刻画的非线性曲线）倒是可以描述技术的生命周期，但它往往是一个接下一个（一个技术遇到瓶颈，往往才有另一个技术的开始）。。。这个在ChatGPT刚出来时我们回顾过。大模型的这几个 "Scaling Laws" 也印证这一点 （Test-Time 和 Post-Training “Scaling Laws" 有点重叠部分）：

创新就是从一个S曲线到另一个S曲线，well known results。这也是斯坦福大学那位鼓吹新能源、自动驾驶以及再生食品革命等科技乐观主义的教授（叫？）每次演讲必谈的技术革命的adoption曲线。他自称根据这个曲线，他在过去30年对于技术影响社会的许多预见都证明是对的，虽然每一次预见社会都会取笑他。 

回到LLM领域的 scaling law 话题。Scaling law本质上是一种经验法则，而经验告诉我们，大多数经验法则都符合S形曲线（或增量的正态分布）。具体到LLM，"大就是好"正是这种法则在遇到平台期或天花板之前的体现。这里的"大"指的是数据规模大、模型参数量大，缺一不可。模型规模不够大，数据再多也无法有效消化——这早已是业界共识。不过OpenAI早期的设计中过分强调模型规模的做法现在看来是一种误导，直到Chinchilla Scaling Law的提出，业界才形成了更合理的共识：数据规模和模型参数量需要保持适当的比例关系。

LLM Scaling的底层逻辑是什么？

首先要明确：LLM不是数据库，其目标不是记忆长尾数据的细节。大模型训练本质上是对大数据内容的压缩，换句话说，压缩的是数据背后的知识体系（包括常识、百科知识等），重点在于揭示大大小小的各种规律性（也就是所谓的泛化能力，generalizations）。

一般直觉会认为，数据规模越大，冗余也越多。无论如何过滤清洗和去重，冗余度随规模增长，似乎意味着可榨取的"油水"会越来越少。那么为什么到了千亿tokens这种以前难以想象的数据规模，大模型依然显得"吃不饱"？为什么从千亿扩展到万亿tokens，scaling law依然有效？

这个现象的关键在于LLM是序列学习（编码）和序列推理（解码）的系统。序列本身是一维的，但序列中蕴含的patterns和规律性却是高维的。举个例子：即使是简单的"猫追老鼠"这样的序列，背后可能涉及物种关系、捕食行为、空间运动等多个维度的知识。这种多维知识表现在序列层面，就会发生天然的组合爆炸。对大数据的"大胃口"正是应对这种组合爆炸的有效策略。只要不是完全的信息冗余，增加的不同序列对模型抽象数据patterns通常都是有帮助的。

然而，人类自然产生的高质量数据是有限的。预训练已经几乎吃尽了现有的高质量自然数据。于是，业界开始探索另外的AI智能增长曲线。

从预训练到推理：两个还是三个S曲线？

张俊林指出：

OpenAI o1推出后，另外两个阶段不再孤单，也各自拥有了姓名，产生了各自的Scaling Law，对应后训练阶段的强化学习Scaling Law(RL Scaling Law)和在线推理阶段的Inference Scaling Law(也叫Test Time Scaling Law)。

这里值得探讨的问题是：到底是三个S曲线，还是两个？推理模型的S曲线与此前的预训练S曲线有多大可比性？

理论上确实可以分为三个阶段：

1. 预训练
2. 后训练（尤其是推理强化学习）
3. 推理阶段

这三个阶段理论上都可能找到资源投入与性能提升之间的正相关S曲线，即scaling laws的某种表现函数。但实际上，在当前部署的应用中，后训练和推理这两个阶段应该共享同一个S曲线，原则上不存在两条独立的增长曲线。

当然，如果用户利用提示词技巧来影响模型的test time，让它更深入的思考，这可能间接影响 CoT （ChainOfThought）的长度或深度。但那是 query 的改变，是 input context 的变化，感觉也不应该算作 test time compute 的独立的 s曲线。

另外，说推理模型这一波潮流是范式转变，开启了新的 RL/Test-time scaling law，总觉得有一点太言之凿凿了。直觉上，推理模型的增长曲线与此前的预训练 scaling law 的增长曲线，大概率没有直接的可比性。

Scaling law 说的 law，实际上我们都知道是所谓经验“法则”。经验需要足够的实践数据积累，才能总结出来。强化学习赋能的推理模型才刚开始，没有足够的经验数据刻画这是怎样的一种增长关系，能持续多久，是不是昙花一现，还是可以持续相当长的时候，等等。

持续时间不够长的 scaling，其实没有多少经验法则的意义。Anthropic CEO Dario 提到 deepseek 的时候说（大意）， deepseek 显得这么亮眼其实是赶上了好时机，言下之意是运气的成分大于技术硬核实力和创新（滑稽的是，Anthropic 迄今没有能力推出任何推理模型，虽然R1以来，谷歌和国内都有推理模型的上线）。他说，推理刚刚开始，所以任何人走通了这条路，在这个初期阶段都会有一个大增长。譬如PhD段位的考试题，在没有推理模型的LLM中，可能分数很低，但一旦有了推理模型，有了所谓 test time compute 的 CoT，成绩就会直线上升，给人创造了奇迹的感觉。

现在是推理模型的早期，后去会如何呢？靠增加 test time compute，或不断延长 CoT，还会有多少增长空间？这个问题是现在进行时，貌似没有明确答案。但隐隐觉得，这个持续增长的时间或曲线，远不如预训练那样稳定和持续，进而其作为 scaling law 的说法不一定站得住。

这第二条反映 RL scaling law 的后训练智能增长曲线，不大好与 pretrain scaling law 相提并论，很可能并不是可持续的，也可能很快就遭遇制约因素的强烈反弹（见后“Test Time Compute 的制约”）。

DeepSeek R1的启示：慢思考的真相

以DeepSeek R1为例，用户可以选择"deepthink"模式来启动慢思考的chain-of-thought（CoT）推理，但实际上用户难以通过增加计算时间来提升推理质量。这是为什么呢？

让我们看一个具体例子。假设我们让R1解决一个复杂的数学问题：

- 传统模型可能直接给出答案："结果是42"
- R1会展示详细的推理过程："让我们一步步思考：1) 首先考虑...... 2) 然后我们可以...... 3) 最后得出结果42"

表面上看，R1的回答展现了"慢思考"（CoT）的特征，但实际上这个推理过程是模型在训练阶段就已经固化的生成模式，而不是在回答问题时动态探索多个可能的推理路径。换句话说，CoT+answer 看似是"慢思考"后的回答，但其实并不改变自回归 ntp（next token prediction）的单向序列生成定式。说白了就是，R1 的 cot+answer 给人慢思考的样子，但生成的本性还是GPT“快思考”范式。在 test time，思考的深度和规模不是动态探索，虽然可以用 beam search 进行内部的隐式多路径选优。

Test Time Compute 的制约

目前业界热议的"test time compute"，指的是含有CoT机制的推理模型相比传统的非推理模型需要更多的在线计算资源。以V3/R1为例，处理同样的问题，启用CoT 的R1可能需要V3 n多倍的计算时间。但这种计算量的增加是模型训练后固化的行为模式导致的，而不是可以动态调节的算力投入。test time compute 没有可控的伸缩可能性，也就谈不上 test time scaling law。

预训练与后训练的CoT强化学习的一个很大的不同是：预训练 scaling law 可以长期稳定乃是因为一旦训练完成，不大影响在线响应的时间，生成模式就是简单 query+answer。因此预训练阶段离线训练几个月都是可以忍受的，只要训练出来的大模型能力有大的提升。但推理模型后训练阶段的CoT强化学习不同，它在培养模型在线回应慢思考的习惯，生成模式是 query+cot+answer。推理模型的 cot 拉长，不仅仅是训练的资源和时间的耗费问题，更主要的是它反映在部署推理阶段的 test time compute 的延长，严重拖延了系统的响应时间。而用户在线使用系统的时候，一般来说对于慢思考的计算量和耗费时间是有能够忍耐的上限的。

这就带来了一个关键问题：即使研究表明indefinitely 增加CoT的长度（相应增加在线计算时间）能带来持续的性能提升，符合某种 scaling law 的经验法则，这种增长也会受到推理阶段现实因素的制约。一般用户可能愿意等待5-10秒获得更好的答案，但如果需要等待几分钟乃至几小时，使用体验就会大打折扣，乃至不可接受。

Scaling Law的可持续性之辩

Open AI CEO Sam Altman 和 Anthropic CEO Dario 这些大佬可能会争辩说，对于极其复杂的问题（如证明黎曼猜想、设计下一代航天战机等），即使模型需要一周的计算时间，相比人类团队需要数十年的工作量仍是极大的进步。但这种论述有两个问题：

1. 这类超复杂问题的LLM可行性远未得到验证
2. 极端场景不具有普适性，难以作为可持续的scaling law 的数据点

当然，这并不是否认S曲线作为描述scaling law的有效模型，也不是否定S曲线叠加的合理性。预训练和后训练两个阶段的增长曲线（s1和s2）叠加确实可能反映了资源投入与性能提升的整体关系。但我们需要谨慎看待CoT推理是否开启了一个真正可持续的scaling曲线。

结语：通向AGI的道路还有多远？

如果推理模型的scaling law缺乏可持续性，这就带来了一个更深层的问题：仅依靠这两个scaling laws，我们能否达到通用人工智能（AGI）的理想彼岸？更进一步，让AI平替人类劳动、极大提升生产力的超级人工智能（ASI）的技术理想是否真的可行？

目前的证据表明，预训练scaling law确实展现了相当的持续性，但推理模型的scaling law可能会较快遇到现实约束。这提醒我们，通往AGI/ASI的道路可能需要更多的创新突破，而不仅仅是现有方法的简单外推。在人工智能发展的下一个阶段，我们或许需要寻找全新的增长曲线。

【相关】

张俊林：从Deepseek R1看Scaling Law

• DeepSeek 笔记：推理新范式 query+cot+answer 支持新的 scaling law 吗？
• DeepSeek 笔记：R1 部署阶段的推理机制

• DeepSeek 学习笔记：R1 部署阶段的推理机制

• 从R1幻觉谈起，大模型幻觉是缺陷还是创意火花？

• 推理强化学习是端到端的监督，推理过程的非监督

• DeepSeek R1：《少年DS之烦恼》
• 告诉李雪琴一个激发写段子灵感的秘诀：找deepseek R1

• DeepSeek 风暴下看看它的论文
• DeepSeek's R1 Paper: A Storm in AI LLM Circle
• The Turbulent Second Chapter of Large Language Models: Has Scaling Stalled?
• 大模型风云诡谲的下半场：scaling 失效？
• DeepSeek_R1 paper

1. 训练阶段的强化学习机制：GRPO是否通过生成多条候选答案（multiple candidate cot+answer sequences）进行策略优化（修改模型），使得模型养成慢思考的习惯？

这个答案是毫无疑问的 YES。

2. 部署阶段的推理机制：R1是否在生成时隐式生成多条路径，但仅展示一条？如果是，这种机制与集成（ensemble）方法有何异同？

3. 与AlphaGo的MCTS的区别：MCTS树搜索是否在推理时动态构建搜索树，而集成方法只是静态组合多个模型的输出？

1. 部署阶段的隐式多路径推理机制

在 DeepSeek R1 的部署阶段，其推理机制可以概括为以下两种模式：

(1) 隐式多路径生成与筛选

- 生成多条路径：模型在单次推理时，可能隐式生成多条潜在的推理路径（CoT+Answers），但仅选择其中一条输出。
- 技术实现：通过调整解码策略（如束搜索宽度 `beam_width`），模型在生成过程中维护多个候选序列（即多条路径），最终选择综合评分最高的路径。
- 用户感知：用户仅看到最终输出，但模型内部进行了多路径探索与筛选。
- 效率权衡：若设置 `beam_width=1`（贪心搜索），则退化为单路径生成，响应速度最快；增大 `beam_width` 可提升输出质量，但增加计算延迟。

(2) 显式多候选生成（需主动配置）

- API级控制：通过设置 `num_return_sequences` 参数，模型可显式生成多个候选答案（如5个），用户或下游系统可进一步筛选。
- 实际应用：DeepSeek App默认未开放此功能，但在企业API或开源代码中可能支持。

关键点：
- 训练阶段的强化学习优化了模型的“单路径CoT生成能力”：通过GRPO训练，模型在单次生成时即可输出高质量的详细推理步骤（长CoT），无需依赖显式多候选生成。
- 部署时的多路径探索只是“锦上添花”：隐式多路径（如束搜索）或显式多候选生成可进一步提升输出质量，但非必需功能。

2. 训练阶段的“慢思考习惯”培养

(1) 强化学习的作用

- 目标：通过GRPO算法，模型学习生成更详细、更合理的推理步骤（长CoT）以提高奖励（如答案正确性）。
- 机制：训练时生成多个候选答案，奖励信号不仅评估最终答案正误，还隐式鼓励逻辑连贯的推理路径（如通过格式奖励）。

(2) CoT增长的驱动力

- 奖励设计：若长CoT更易得出正确答案（如分步解题减少错误），模型在策略优化中自然倾向于生成更长、更详细的步骤。Given room for [think], a reasoning model just wants/tends to think deep!
- 数据反馈：训练后期通过拒绝采样生成的高质量SFT数据，进一步强化这一模式。

结果：训练后的模型在单次生成时即可输出高质量的详细推理（即“慢思考习惯”内化）。

3. 与集成方法（Ensemble）的异同

(1) 相似性

- 多路径生成：隐式多路径探索（如束搜索）可视为同一模型生成多个潜在输出，类似集成方法中的多模型预测。
- 结果筛选：通过置信度选择最优解，类似于集成中的投票或加权平均。

(2) 核心差异

R1的隐式多路径生成本质是单模型内的动态解码策略，而传统集成依赖多模型的静态组合，二者在实现成本与多样性来源上存在根本差异。

4. 与AlphaGo蒙特卡洛树搜索（MCTS）的本质区别

(1) AlphaGo的MCTS机制

- 动态规划：通过模拟（Simulation）构建搜索树，评估每一步的长期收益（如胜率），动态选择最优路径。
- 在线学习：在推理时根据实时反馈（如对手落子）调整搜索策略，部分版本（如AlphaZero）甚至更新模型参数。

(2) R1的隐式多路径生成

- 静态模型：部署时模型参数固定，多路径生成依赖预训练的策略与解码规则。
- 无长期收益建模：路径选择基于模型自身的置信度概率，而非多步决策的累积收益。

(3) 差异

- R1的多路径生成是静态策略的有限探索，依赖训练阶段内化的CoT+answer的生成能力。
- MCTS是动态规划过程，通过实时模拟与评估实现长期收益最大化，属于在线决策优化。

5. 总结

- 训练阶段的目标：GRPO通过强化学习培养模型生成详细CoT的习惯，使得部署时单次生成即可输出合理答案。
- 部署阶段的灵活性：系统可选择单路径生成（快速响应）或多路径筛选（质量优先），后者类似轻量级集成。

- 训练完成后模型参数确实固定，但隐式多路径生成依赖解码策略（如束搜索宽度），用户可通过API参数调整，非完全静态。
- 与集成的实质差异：R1的多路径生成是同一模型的不同解码路径，而传统集成依赖多个独立模型，后者多样性更高但成本激增。

- MCTS的核心是动态搜索与长期收益建模，而非多模型预测的平均化。R1的隐式多路径更接近贪心策略的扩展，而非规划过程。

DeepSeek R1的部署机制通过训练阶段的强化学习内化“慢思考”能力，使其在单次生成时即可输出详细推理。隐式多路径生成（如束搜索）可进一步提升质量，但本质是同一模型的解码策略优化，与传统集成或AlphaGo的MCTS均有显著差异。这种设计在效率与效果间取得平衡，适配大规模工业应用需求，但牺牲了动态规划与全局最优的能力。

【相关】

• DeepSeek 笔记：推理新范式 query+cot+answer 支持新的 scaling law 吗？
• DeepSeek 笔记：R1 部署阶段的推理机制

• 从R1幻觉谈起，大模型幻觉是缺陷还是创意火花？

• 推理强化学习是端到端的监督，推理过程的非监督

• DeepSeek R1：《少年DS之烦恼》
• 告诉李雪琴一个激发写段子灵感的秘诀：找deepseek R1

• DeepSeek 风暴下看看它的论文
• DeepSeek's R1 Paper: A Storm in AI LLM Circle
• The Turbulent Second Chapter of Large Language Models: Has Scaling Stalled?
• 大模型风云诡谲的下半场：scaling 失效？
• DeepSeek_R1 paper

Host: Hello everyone! Welcome to today's interview. Recently, there's been quite a buzz about AI "hallucinations," especially with DeepSeek-R1, which seems to have a higher hallucination rate than its predecessor, DeepSeek-V3. Today, we're joined by Dr. Li, a senior AI researcher. Welcome, Dr. Li!

Dr. Li: Hello, host! Hello, everyone!

Host: Let's start with the million-dollar question: Why do large language models "hallucinate"? Can you break it down for us in plain English?

Dr. Li: You see, large language models are like super-powered conversation completers. Give them the first half of a sequence, say, a question, and they'll predict the second half (say, an answer) based on their massive knowledge network. They learn like our brains do – they can't remember everything word-for-word, so they compress and generalize, grabbing the gist and finding patterns.

Here's a fun contrast: Ask them "How tall is Yao Ming?" and they'll nail it because that's such famous knowledge, this data point is practically carved in stone in their memory (represented in the model's parameter weights). But ask them "How tall is Old Wang from next door?" and they're stumped because they've never met Old Wang! But here's the kicker – they won't just say "I don't know." So what do they do? They "make up" a reasonable height based on what they know about the range of human heights. That's a hallucination for you!

Host: Wow, that's some impressive guesswork! But isn't this kind of making things up pretty problematic?

Dr. Li: Not necessarily! In a way, hallucination is imagination (for better or worse) – it's where creativity lies! Think about it: all those great literary works, artistic masterpieces – aren't they all flights of fancy, products of imagination? If everything had to match reality closely, art would just be photography, and where's the fun in that?

You know, Yuval Harari makes a fascinating point in "Sapiens" – humans became Earth's dominant species precisely because we could "tell stories," creating myths, religions, nations, and money – things that don't physically exist. These are all "hallucinations," but they're the driving force behind civilization!

Host: When you put it that way, hallucinations sound pretty important! But let's talk about DeepSeek-R1. Its hallucination issue seems quite serious.

Dr. Li: Indeed, it is! The academic consensus used to follow OpenAI's view that reinforced reasoning would significantly reduce hallucinations. I remember discussing this with a head honcho at an LLM unicorn who was particularly excited about reasoning's potential to curb hallucinations. But R1's performance threw us a curveball!

According to Vectara's tests, R1's hallucination rate is more than 3 times higher than its foundation model V3's – 14.3% compared to 3.9%. This definitely correlates with its prolonged "Chain of Thought" (CoT) enabled by reinforcemnnt learning for reasoning. R1 is absolutely brilliant at reasoning, math and coding, as well as poetry and storytelling, but this currently comes with the "side effect" of increased hallucinations in things like translation and summarization.

More specifically, there are several reasons for R1's increased hallucinations.

First, the standard hallucination tests use summarization tasks, something base models are already pretty good at. In this case, reinforcement learning can backfire – it's like using a cannon to swat a fly!

Second, R1's reinforced reasoning chains weren't specifically optimized for straightforward tasks like summarization, translation, or news writing that demand strict factual accuracy. Instead, it tries to add various layers of thinking to every task. Looking at its transparent CoT (ChainOfThought) printout, we see it tirelessly analyzing even simple instructions from multiple angles. This overcomplication of simple tasks can lead to deviations and hallucinations.

During R1's reinforcement learning for NLP-related tasks, it seems the model was rewarded more heavily for creativity, leading it to be more imaginative – and consequently more prone to straying from facts. For mathematical and coding tasks, R1's supervision came from gold standards (test answers or code test cases). But for humanities tasks, they used V3 or V3's reward model to judge quality, and the current system seems to clearly favor creativity.

Moreover, user feedback typically tends to focus and encourage creativity. Most people aren't sensitive to hallucinations, especially when they're wrapped in the model's smooth, fluent language. For most frontline developers, this kind of user feedback naturally pushes them to enhance creativity rather than tackle the thorny problem of hallucinations.

Host: So, you are saying that R1's hallucination problem rooted in its over-enthusiastic reasoning? What's the real relationship between reinforced reasoning ability and hallucinations?

Dr. Li: It's still a puzzle – there's not seem to be simple correlation. Look at R1, a leading reasoning model, versus Claude 3.5 Sonnet, a top non-reasoning model. Surprisingly, Sonnet still has a higher hallucination rate than R1! But when we compare R1 to its base model V3, we see clearly that adding reasoning significantly increased hallucinations.

It may well be about the model's "personality." R1, with its powerful reinforcement learning, loves "divergent thinking." Give it a simple prompt, and it'll spin out ideas like there's no tomorrow – its CoTs could run on like crazy! This suggests that while R1 was powering up its creativity, it inevitably amplified creativity's twin: hallucination.

As a model that excels in both STEM and humanities, R1 performs differently across tasks. In mathematics and coding, where more rigorous reasoning is required, there's little room for hallucination. But in language and creative tasks, especially in the summarization tests, hallucinations become more prominent. It's largely a side effect of R1's supercharged linguistic creativity.

Technically speaking, R1 automatically adds lengthy CoTs to simple user instructions, essentially complicating straightforward tasks. Its CoTs (like  internal monologue of an entity following instructions) change the conditional part of the autoregressive probability model before generating answers, naturally affecting the final output. Compare:

V3: query → answer
R1: query+CoT → answer

For tasks that V3 already handles well, like summarization or translation, any lengthy CoT guidance might lead to deviation or embellishment, creating fertile ground for hallucinations.

Host: So where do R1's hallucinations mainly occur?

Dr. Li: Think of R1's abilities as split between "arts" and "sciences." In "science" areas like math and coding, its logic is fairly strong and hallucinations are relatively rare. But in "arts" areas like language, hallucinations become more noticeable.

R1's most impressive achievement compared to the first LLM reasoning model O1 is successfully extending mathematical and coding reasoning capabilities into creative writing, especially in Chinese. The internet is full of R1's brilliant literary works. In terms of wordplay and literary prowess, it clearly surpasses 99% of humans – even graduate students in literature and classical Chinese professors sing its praises.

But watch what happens when you ask it to do a simple summary – it can't help but "get creative," often "inventing" details not present in the original text. It's like its "arts" abilities are too powerful, a case of "too much of a good thing."

Host: That's an interesting perspective. Do all language tasks require creativity?

Dr. Li: Language tasks actually fall into two categories: ones that need high creativity, like poetry and fiction writing, and ones that demand high factual accuracy, like news reporting, translation, or summarization. R1 excels at the former, which was likely the development team's focus, but this creates side effects in the latter as it is today.

It reminds me of the old Chinese saying about translation needing to be "faithful, expressive, and elegant" – achieving all three has always been challenging. We see many examples where elegance is prioritized over faithfulness, like the use of hyperbole in literary works. We also see the opposite, like Lu Xun's advocacy for so-called "rigid translation."

Interestingly, humans have always had double standards here, but we have a mental switch we can flip at will. When watching movies or reading novels, we flip towards creativity and don't fuss about factual accuracy. But switch to news channels, and we have zero tolerance for falsehoods.

Host: People tend to believe content that appears logically coherent and detailed, so the potential harm from AI hallucinations could be significant. What should we ordinary folks do about AI hallucinations?

Dr. Li: While many people are starting to notice and become wary of these hallucinations amid their amazement at LLM's creativity, most are still mesmerized by its creative brilliance. We need to increase public awareness of AI hallucinations. I suggest a two-pronged approach:

Stay Alert: Don't take everything the model says as granted, especially factual claims. Hallucinations most commonly occur with names, places, times, locations, and other entities or numerical data.

Cross-Verify: For important details, check original sources online or consult experts to see if the claims align.

Guide the Model: When asking questions, add constraints like "please stay faithful to the original text" or "please verify facts." This can at times help reduce hallucinations.

Embrace Creativity: If you're looking for inspiration or creative ideas, model hallucinations can be a delightful surprise!

Think of AI hallucinations as "possibilities in parallel universes." What it makes up might not be true in our world, but could be true in another! It's like how novelists write fictions – while it cannot stand fact checking, it's a kind of "artistic truth." Just like novels arise from life but transcend it, AI arises from data but transcends it. AI compresses data into knowledge and common-sense network, not necesarily true to individual facts – that's what databases are for.

Host: This reminds me of what people often say: AI models aren't just "talking nonsense" – they're "talking nonsense seriously"!

Dr. Li: Haha, that's exactly it! AI hallucinations are its "educated guesses," based on the massive knowledge and patterns it's learned. The hallucinations are by noway completely random – they have internal constraints that make them seamless and convincing, but also more deceptive. Newcomers to AI need to be especially careful not to trust everything at their face value.

For regular users, understanding the nature of hallucinations is needed. For example, when asking about well-documented facts like "How long is the Yangtze River?" models won't make mistakes because these facts are firmly encoded in their parameters. But ask about an obscure creek or fictional river, and the model will activate its "reasonable completion" mechanism and make something up.

Host: Following your logic, human language itself prepares for a breeding ground for hallucinations.

Dr. Li: You could say that. Language enabled humans to create things which do not exist in the physical world, such as myths, religions, states, corporations, currency, and abstract concepts like ideals and beliefs. Harari emphasizes in "Sapiens" that story-telling (i.e. typical hallucinations) were fundamental to civilization: language enabled human story-telling abilities. Hallucinations catalyzed civilization. Humans are the only entities capable of 'lying' (besides LLMs).

Host: What about the future? Is there a way to maintain creativity while reducing hallucinations?

Dr. Li: This is definitely one of the "ultimate challenges" in AI! People are working on various solutions, including:

More Refined Training: During training, treat different types of tasks differently, teaching the model when to be strict and when to be creative.

Task-Specific Fine-tuning/Reinforcement Learning can help balance this contradiction. Tasks like summarization, paraphrasing, translation, and reporting need special care because they require both some creativity (like style) and strict factual accuracy.

Specifically, R1's training pipeline has four stages: fine-tuning 1, reinforcement 1, fine-tuning 2, and reinforcement 2. Reinforcement 2 mainly focuses on human preference alignment. Currently, this process seems to favor creativity over faithfulness, which could be rebalanced later. Perhaps more importantly, in stage three (i.e. fine-tuning 2), we could strengthen constraints for different tasks – for example, increasing supervised data for summarization to encourage faithful, straightforward results.

Routing: In the future, there will be a "model dispatcher" that assigns different models based on task type. Simple tasks could go to V3 or use tools, while complex tasks requiring deeper thinking go to R1.

For instance, arithmetic tasks should just use simple code calculations, equivalent to using a calculator. That's not how it works now – yesterday I tested a nine-digit multiplication, and R1 spent over three minutes thinking, producing CoT that could stretch down the street, breaking down the reasoning step by step. While the answer was correct, using such computationally expensive CoT for arithmetic instead of a simple function call is unreasonable. A one-line calculation code would do the job – no need to waste so much computing resource and tokens on explicit reasoning. These are foreseeable routing improvements, especially in the age of AI agents which can use all kinds of tools or applications. R1's CoT does not need to handle everything – besides hallucinations, compute-burning CoT is also not environmentally friendly.

Host: Thank you, Dr. Li, for this fascinating discussion! Today's interview has given us a much deeper understanding of AI hallucinations.

Dr. Li: My pleasure! It's been great chatting with you!

【相关】

• 从R1幻觉谈起，大模型幻觉是缺陷还是创意火花？

• 推理强化学习是端到端的监督，推理过程的非监督

• DeepSeek R1：《少年DS之烦恼》
• 告诉李雪琴一个激发写段子灵感的秘诀：找deepseek R1

• DeepSeek 风暴下看看它的论文
• DeepSeek's R1 Paper: A Storm in AI LLM Circle
• The Turbulent Second Chapter of Large Language Models: Has Scaling Stalled?
• 大模型风云诡谲的下半场：scaling 失效？
• DeepSeek_R1 paper

V3: query --〉answer
R1: query+CoT --〉answer

【相关】

Deepseek-R1 的幻觉率是 14.3% - 比其非推理前身 Deepseek-V3 高得多
榜单排名：https://github.com/vectara/hallucination-leaderboard

• 推理强化学习是端到端的监督，推理过程的非监督

• DeepSeek R1：《少年DS之烦恼》
• 告诉李雪琴一个激发写段子灵感的秘诀：找deepseek R1

• DeepSeek 风暴下看看它的论文
• DeepSeek's R1 Paper: A Storm in AI LLM Circle
• The Turbulent Second Chapter of Large Language Models: Has Scaling Stalled?
• 大模型风云诡谲的下半场：scaling 失效？
• DeepSeek_R1 paper