{
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 "nbformat_minor": 5,
 "cells": [
  {
   "id": "b94a88a25a974c3e95bb22d89421a340",
   "metadata": {
    "deepnote_block_id": "b94a88a25a974c3e95bb22d89421a340",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "8098f8817fa2aed47cbbef30792187a97da68adcf3a6c9189029d73c4143ec4c"
   },
   "source": "# 自回归：每一步最可能，整句就最可能吗？\n\n本册用一个可以完全枚举的两步模型回答三个问题：联合概率怎样由条件概率组成；贪心为何可能错过最高概率序列；温度究竟改变了什么。\n\n**先预测，再运行。** 第一步 `P(A)=0.6, P(B)=0.4`；接着 `P(0|A)=0.51, P(1|A)=0.49`，`P(0|B)=0.99, P(1|B)=0.01`。你会选哪个完整序列？先写出逐步贪心的答案，再算四个联合概率。\n\n你的产出是一张四行概率表，以及一句区分“概率最高”“从分布采样”“提高温度”的解释。\n\n**本轮入口：先看下面的保存图，再只改一个参数。** 原有可手算代码与推导完整保留在后面。",
   "cell_type": "markdown"
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deepnote_block_id": "459cd54da2664cbc8da31cae0412730b"
   },
   "source": "## 先看问题与保存结果\n\n这是一张给定概率表的解析实验。先比较整条路径与局部最优，再改变温度；代码没有训练语言模型。保存图显示温度改变的是每个前缀后的条件分布，完整路径还要把沿途概率相乘。\n\n![这是一张给定概率表的解析实验。先比较整条路径与局部最优，再改变温度；代码没有训练语言模型。保存图显示温度改变的是每个前缀后的条件分布，完整路径还要把沿途概率相乘。](https://codingai-lec04.pages.dev/assets/labs-v13/lab01-temperature.png)\n\n[连续概念解释](https://codingai-lec04.pages.dev/lecture.html#ch02)。读完后留下一个结果：固定量、改变项、实际观察，以及它支持的机制。"
  },
  {
   "id": "3f5f23b769b34b2db84a673efb6a82c0",
   "metadata": {
    "deepnote_block_id": "3f5f23b769b34b2db84a673efb6a82c0",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "70f0fe335d367f64ea440e09fa567b8db443a8f999a9e2559d8984ff1c870fe2",
    "cloud_original_source": "## 先看保存结果：同一概率表的树、完整序列与温度\n\n![同一概率表的树、完整序列与温度：图1](https://codingai-lec04.pages.dev/assets/labs-v13/lab01-tree.png)\n\n![同一概率表的树、完整序列与温度：图2](https://codingai-lec04.pages.dev/assets/labs-v13/lab01-temperature.png)\n\n先沿树相乘：局部贪心走 A0（0.306），完整序列 MAP 是 B0（0.396）。采样保留四个结果，并不强制选 MAP。三温度图对每个温度重复5枚种子，点的波动与整组柱子的变化是不同现象。每个前缀各自归一化，因此逐 token 调温与整句概率调温通常不同。\n\n**结果身份：** 2026-09-28由下方同源Python代码在本地CPU实际生成并核对。手工指定两步概率模型，没有训练或调用语言模型。 图不是模型训练输出。\n\n[无需GPU的即时探索](https://codingai-lec04.pages.dev/course/experiments/lab01.html)\n\n保存数据、图片与代码随下载材料提供；静态图无需GPU。学生重算需要Python、NumPy、matplotlib，不发起网络请求、不打印密钥，只在当前目录写入本册输出文件夹。"
   },
   "source": "## 先看保存结果：同一概率表的树、完整序列与温度\n\n![同一概率表的树、完整序列与温度：图1](attachment:lab01-tree.png)\n\n![同一概率表的树、完整序列与温度：图2](attachment:lab01-temperature.png)\n\n先沿树相乘：局部贪心走 A0（0.306），完整序列 MAP 是 B0（0.396）。采样保留四个结果，并不强制选 MAP。三温度图对每个温度重复5枚种子，点的波动与整组柱子的变化是不同现象。每个前缀各自归一化，因此逐 token 调温与整句概率调温通常不同。\n\n**结果身份：** 2026-09-28由下方同源Python代码在本地CPU实际生成并核对。手工指定两步概率模型，没有训练或调用语言模型。 图不是模型训练输出。\n\n[无需GPU的即时探索](https://codingai-lec04.pages.dev/course/experiments/lab01.html)\n\n保存数据、图片与代码随下载材料提供；静态图无需GPU。学生重算需要Python、NumPy、matplotlib，不发起网络请求、不打印密钥，只在当前目录写入本册输出文件夹。",
   "cell_type": "markdown",
   "attachments": {
    "lab01-tree.png": {
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    "lab01-temperature.png": {
     "image/png": 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    }
   }
  },
  {
   "id": "112c8a75b37e41b79c4ebe56d34bab0c",
   "metadata": {
    "deepnote_block_id": "112c8a75b37e41b79c4ebe56d34bab0c",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "ff4abe10f13b6025d10dc87b0ec4dcfd00003da212429bb945aad41f6af1079d"
   },
   "source": "## 只改一个变量：TRY_T\n\n把 TRY_T 从 1 改成 0.35 或 2。模型表、种子与每次6000个样本保持固定；精确概率与重复抽样同时变化。\n\n在下面参数区改值后运行本格；重算图会显示在输出中，并保存在 `lab01-visual-output`。接着用图中的具体变化解释，不从一次样本判断整个分布。",
   "cell_type": "markdown"
  },
  {
   "id": "224f93b820ae476897d0ae7f68bfe5a3",
   "metadata": {
    "deepnote_block_id": "224f93b820ae476897d0ae7f68bfe5a3",
    "deepnote_block_type": "code",
    "cloud_source_sha256": "9de95687d03daba48a5113ca4760ce2bd87c08f104829f026b06b89c983b5e32",
    "execution_provenance": {
     "provider": "Deepnote",
     "run_id": "584c0796-4d82-4548-aed1-ff4bea509572",
     "completed_at": "2026-09-28T15:27:40.388Z"
    }
   },
   "source": "import math, json, time, platform\nfrom pathlib import Path\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n# Change only this temperature, keeping the model table and sample count fixed.\nTRY_T = 1.0\nVISUAL_SEED = 20260928\nVISUAL_N = 6000\nOUT = Path('lab01-visual-output'); OUT.mkdir(exist_ok=True)\n\nFIRST_VIS = np.array([.6,.4])\nNEXT_VIS = np.array([[.51,.49],[.99,.01]])\nSEQUENCES_VIS = ['A0','A1','B0','B1']\n\ndef vis_softmax_temperature(p, temperature):\n    assert temperature > 0\n    logp=np.log(p)/temperature; weights=np.exp(logp-logp.max())\n    return weights/weights.sum()\n\ndef vis_joint(temperature):\n    first=vis_softmax_temperature(FIRST_VIS,temperature)\n    second=np.stack([vis_softmax_temperature(row,temperature) for row in NEXT_VIS])\n    return (first[:,None]*second).flatten()\n\ndef vis_uniforms(seed,n):\n    # Portable 32-bit LCG; the browser uses exactly this stream, not a second dataset.\n    state=int(seed)&0xffffffff; values=[]\n    for _ in range(2*n):\n        state=(1664525*state+1013904223)&0xffffffff\n        values.append(state/4294967296)\n    return np.asarray(values).reshape(n,2)\n\ndef vis_counts(temperature,seed=VISUAL_SEED,n=VISUAL_N):\n    u=vis_uniforms(seed,n); first=vis_softmax_temperature(FIRST_VIS,temperature)\n    a=(u[:,0]>=first[0]).astype(int)\n    p0=np.array([vis_softmax_temperature(row,temperature)[0] for row in NEXT_VIS])\n    b=(u[:,1]>=p0[a]).astype(int)\n    return np.bincount(2*a+b,minlength=4)\n\nfig,axes=plt.subplots(1,2,figsize=(12,4.6),gridspec_kw={'width_ratios':[1.1,1]})\nax=axes[0]; pos={'start':(0,.5),'A':(1,.77),'B':(1,.23),'A0':(2,.92),'A1':(2,.63),'B0':(2,.37),'B1':(2,.08)}\nfor a,b,label in [('start','A','.60'),('start','B','.40'),('A','A0','.51'),('A','A1','.49'),('B','B0','.99'),('B','B1','.01')]:\n    x,y=pos[a]; xx,yy=pos[b]; ax.annotate('',(xx,yy),(x,y),arrowprops={'arrowstyle':'->','color':'#687484'})\n    ax.text((x+xx)/2,(y+yy)/2+.035,label,ha='center',fontsize=11)\nbase=vis_joint(1)\nfor key,(x,y) in pos.items():\n    label=key if key not in SEQUENCES_VIS else f'{key}   {base[SEQUENCES_VIS.index(key)]:.3f}'\n    ax.text(x,y,label,ha='center',va='center',bbox={'boxstyle':'round,pad=.4','fc':'#fff4cf' if key=='A0' else '#cde6ed' if key=='B0' else 'white','ec':'#36546b'},fontsize=11)\nax.set(xlim=(-.35,2.55),ylim=(-.02,1.08),title='Same model: greedy A0; whole-sequence MAP B0');ax.axis('off')\naxes[1].bar(SEQUENCES_VIS,base,color=['#e2aa37','#b7c6cf','#26799b','#b7c6cf'])\naxes[1].set(ylim=(0,.5),ylabel='Exact joint probability',title='Sampling keeps all four outcomes')\nfig.tight_layout();fig.savefig(OUT/'lab01-tree.png',dpi=160);plt.show();plt.close(fig)\n\ntemperatures=[.35,1.,2.]\nfig,axes=plt.subplots(1,3,figsize=(12,3.8),sharey=True); result=[]\nfor ax,T in zip(axes,temperatures):\n    exact=vis_joint(T); empirical=vis_counts(T)/VISUAL_N; reps=np.stack([vis_counts(T,VISUAL_SEED+i)/VISUAL_N for i in range(5)])\n    positions=np.arange(4)\n    ax.bar(positions-.17,exact,.34,label='exact',color='#003262');ax.bar(positions+.17,empirical,.34,label='sample',color='#fdb515')\n    ax.scatter(np.repeat(positions,5),reps.T.flatten(),s=12,c='#967318',alpha=.6,label='5 repeat seeds')\n    ax.set(xticks=positions,xticklabels=SEQUENCES_VIS,title=f'T={T:g}',ylim=(0,.55),xlabel='Complete sequence'); ax.legend(fontsize=8)\n    result.append({'T':T,'exact':exact.tolist(),'empirical':empirical.tolist(),'repeats':reps.tolist()})\naxes[0].set_ylabel('Probability / relative frequency');fig.suptitle(f'Only temperature changes; N={VISUAL_N} per seed',fontsize=13)\nfig.tight_layout();fig.savefig(OUT/'lab01-temperature.png',dpi=160);plt.show();plt.close(fig)\n\nfig,ax=plt.subplots(figsize=(7,3.5)); exact=vis_joint(TRY_T); observed=vis_counts(TRY_T)/VISUAL_N\nax.bar(np.arange(4)-.17,exact,.34,label='exact',color='#003262');ax.bar(np.arange(4)+.17,observed,.34,label='sample',color='#fdb515')\nax.set(xticks=range(4),xticklabels=SEQUENCES_VIS,ylim=(0,1),ylabel='Probability',title=f'Your controlled change: T={TRY_T:g}');ax.legend();fig.tight_layout();fig.savefig(OUT/'lab01-your-temperature.png',dpi=160);plt.show();plt.close(fig)\npayload={'kind':'finite constructed probability model; not an LLM','seed':VISUAL_SEED,'n':VISUAL_N,'table':{'first':FIRST_VIS.tolist(),'next':NEXT_VIS.tolist()},'comparisons':result,'changed':{'T':TRY_T,'exact':exact.tolist(),'observed':observed.tolist()},'python':platform.python_version(),'numpy':np.__version__}\n(OUT/'lab01-results.json').write_text(json.dumps(payload,indent=2))\nprint(json.dumps(payload['changed'],indent=2))\nassert abs(sum(base)-1)<1e-12 and SEQUENCES_VIS[int(base.argmax())]=='B0'\n",
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1200x460 with 2 Axes>",
      "image/png": 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"
     },
     "metadata": {
      "image/png": {
       "width": 1189,
       "height": 449
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 1200x380 with 3 Axes>",
      "image/png": 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     },
     "metadata": {
      "image/png": {
       "width": 1190,
       "height": 377
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 700x350 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {
      "image/png": {
       "width": 690,
       "height": 340
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "text": "{\n  \"T\": 1.0,\n  \"exact\": [\n    0.306,\n    0.294,\n    0.396,\n    0.004\n  ],\n  \"observed\": [\n    0.2995,\n    0.29383333333333334,\n    0.4035,\n    0.0031666666666666666\n  ]\n}\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "id": "986a9e03ac034b77a81dd1eb2e0c8529",
   "metadata": {
    "deepnote_block_id": "986a9e03ac034b77a81dd1eb2e0c8529",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "91056e13cd3921eef89f1f52b2f7cf9c096644b3cd35f91ce85df0d3ebee214f"
   },
   "source": "## 本轮运行与后续阅读\n\n**本地执行与云端复核均已完成。** 2026-09-28，本册全部代码在本地CPU从空命名空间顺序执行；另通过Deepnote全本运行，状态为success，运行ID为 `584c0796-4d82-4548-aed1-ff4bea509572`，完成时间 2026-09-28T15:27:40.388Z（UTC）。运行快照检查到本册图形输出且无失败代码块。原模型逐步贪心A0、完整序列MAP B0；三温度精确概率和6000样本对照已输出。\n\n云端运行使用Python 3.13数据科学环境。平台总用时包含启动、Notebook执行与输出保存，不作为算法速度基准；五本均为小规模CPU计算，不调用外部模型或付费API。上方静态图仍明确保留其本地生成来源，云端输出是另一次实际复核。学生修改参数后得到的是自己的新结果。\n\n下面保留此前逐步计算与推导。历史本地数字保留原身份，可把图中一个关系追到对应公式。",
   "cell_type": "markdown"
  },
  {
   "id": "7653c5a67b224da4a432b6b9416e7edc",
   "metadata": {
    "deepnote_block_id": "7653c5a67b224da4a432b6b9416e7edc",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "e37a426c56a7e2d47754c2faa62b8e01715065b433c2f2c78de93e6dbd2579b7"
   },
   "source": "## 固定对象：两个位置、四条序列\n\n所有序列都恰好长 2，没有 EOS、长度惩罚或词表截断。模型参数是下面手工指定的概率，不是训练出的语言模型。\n\n链式法则给出 $p(x_1,x_2)=p(x_1)p(x_2\\mid x_1)$。条件表的每一行都归一化，因此乘积也会成为一个归一化的联合分布。这里“第 2 步预测”可以使用第 1 个 token；若把两步都当作独立边际采样，就已经换了模型。",
   "cell_type": "markdown"
  },
  {
   "id": "e239e22a62db4243b1d50f5cbc5565f2",
   "metadata": {
    "deepnote_block_id": "e239e22a62db4243b1d50f5cbc5565f2",
    "deepnote_block_type": "code",
    "cloud_source_sha256": "7045ead2bb900d15b45a4f447a699c4d3fa7ea7d9ffb4289b4698b0944429b5e",
    "execution_provenance": {
     "provider": "Deepnote",
     "run_id": "584c0796-4d82-4548-aed1-ff4bea509572",
     "completed_at": "2026-09-28T15:27:40.388Z"
    }
   },
   "source": "import math\nimport random\nfrom collections import Counter\n\nFIRST = {\"A\": 0.6, \"B\": 0.4}\nNEXT = {\"A\": {\"0\": 0.51, \"1\": 0.49},\n        \"B\": {\"0\": 0.99, \"1\": 0.01}}\n\ndef joint(first, nxt):\n    return {a + b: pa * pb\n            for a, pa in first.items()\n            for b, pb in nxt[a].items()}\n\nBASE = joint(FIRST, NEXT)\nfirst_choice = max(FIRST, key=FIRST.get)\ngreedy = first_choice + max(NEXT[first_choice], key=NEXT[first_choice].get)\nmap_sequence = max(BASE, key=BASE.get)\nprint(\"sequence | exact joint probability\")\nfor seq, prob in BASE.items():\n    print(f\"{seq:8s} | {prob:.6f}\")\nprint(\"greedy =\", greedy, \"probability =\", BASE[greedy])\nprint(\"global MAP =\", map_sequence, \"probability =\", BASE[map_sequence])\nassert abs(sum(BASE.values()) - 1) < 1e-12\nassert greedy == \"A0\" and map_sequence == \"B0\"\n",
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [
    {
     "name": "stdout",
     "text": "sequence | exact joint probability\nA0       | 0.306000\nA1       | 0.294000\nB0       | 0.396000\nB1       | 0.004000\ngreedy = A0 probability = 0.306\nglobal MAP = B0 probability = 0.396\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "id": "033b4b5f8a1447bcb46124c202192b12",
   "metadata": {
    "deepnote_block_id": "033b4b5f8a1447bcb46124c202192b12",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "46acc20a1ce7947ffef18ab63deda5c22251ead2315f4f22f632a499c92239f7"
   },
   "source": "### 历史本地保存输出（2026-09-26；本轮执行记录见开篇）\n\n```text\nsequence | exact joint probability\nA0       | 0.306000\nA1       | 0.294000\nB0       | 0.396000\nB1       | 0.004000\ngreedy = A0 probability = 0.306\nglobal MAP = B0 probability = 0.396\n```\n\n## 解释一次失败，而不是给解码器排榜\n\n贪心在第 1 步只比较 0.6 与 0.4，看不到分支后面概率怎样分散。`A` 分支把质量近乎对半分给两条路，`B` 分支几乎集中到 `B0`，于是完整序列的排序翻转。\n\n这个反例证明逐步局部最大不保证全局最大，并不证明真实语言任务应总取 MAP：最高概率句子与有用、正确、多样的回答也是不同目标。序列很长时，像本册一样穷举通常不可行。",
   "cell_type": "markdown"
  },
  {
   "id": "50d22d9f484044e49086020292284f47",
   "metadata": {
    "deepnote_block_id": "50d22d9f484044e49086020292284f47",
    "deepnote_block_type": "code",
    "cloud_source_sha256": "5e55d10a8afbc4e94ac5a30a7c97a178af6f85e0bcbf3d576a441c2d31f5d7cf",
    "execution_provenance": {
     "provider": "Deepnote",
     "run_id": "584c0796-4d82-4548-aed1-ff4bea509572",
     "completed_at": "2026-09-28T15:27:40.388Z"
    }
   },
   "source": "def temperature_distribution(distribution, temperature):\n    assert temperature > 0\n    # 对 log 概率缩放，减最大值避免数值溢出。\n    logits = {k: math.log(v) / temperature\n              for k, v in distribution.items()}\n    offset = max(logits.values())\n    weights = {k: math.exp(v - offset) for k, v in logits.items()}\n    total = sum(weights.values())\n    return {k: v / total for k, v in weights.items()}\n\ndef local_temperature(temperature):\n    first = temperature_distribution(FIRST, temperature)\n    nxt = {a: temperature_distribution(row, temperature)\n           for a, row in NEXT.items()}\n    return joint(first, nxt)\n\ndef entropy(distribution):\n    return -sum(p * math.log2(p) for p in distribution.values() if p)\n\ndef tv(p, q):\n    return 0.5 * sum(abs(p[k] - q[k]) for k in p)\n\nprint(\"T    | local A0 A1 B0 B1              | H(bits) | local/global TV\")\nfor temperature in (0.35, 1.0, 2.0):\n    local = local_temperature(temperature)\n    global_scaled = temperature_distribution(BASE, temperature)\n    numbers = \" \".join(f\"{local[k]:.4f}\" for k in BASE)\n    print(f\"{temperature:4.2f} | {numbers} | {entropy(local):.4f} | {tv(local, global_scaled):.6f}\")\n    assert abs(sum(local.values()) - 1) < 1e-12\nassert tv(local_temperature(1.0), BASE) < 1e-12\nassert tv(local_temperature(0.35), temperature_distribution(BASE, 0.35)) > 0.05\n",
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
    {
     "name": "stdout",
     "text": "T    | local A0 A1 B0 B1              | H(bits) | local/global TV\n0.35 | 0.4023 0.3588 0.2389 0.0000 | 1.5526 | 0.285792\n1.00 | 0.3060 0.2940 0.3960 0.0040 | 1.6031 | 0.000000\n2.00 | 0.2780 0.2725 0.4084 0.0410 | 1.7413 | 0.062151\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "id": "f9f05916ebf1430391c76b12bc81a2ec",
   "metadata": {
    "deepnote_block_id": "f9f05916ebf1430391c76b12bc81a2ec",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "a42b8c691f816a9c9fec6cb21e9a362ed4e08e335a20a405e8cfae95897c0ad5"
   },
   "source": "### 历史本地保存输出（2026-09-26；本轮执行记录见开篇）\n\n```text\nT    | local A0 A1 B0 B1              | H(bits) | local/global TV\n0.35 | 0.4023 0.3588 0.2389 0.0000 | 1.5526 | 0.285792\n1.00 | 0.3060 0.2940 0.3960 0.0040 | 1.6031 | 0.000000\n2.00 | 0.2780 0.2725 0.4084 0.0410 | 1.7413 | 0.062151\n```\n\n## 为什么整句温度与逐 token 温度不同？\n\n局部温度在每个前缀下分别计算 $q_T(x_t\\mid x_{<t})\\propto p(x_t\\mid x_{<t})^{1/T}$。这些归一化常数依赖前缀，乘起来后并不通常等于对整个联合分布一次性做 $q_T(x)\\propto p(x)^{1/T}$。\n\n`T=1` 恢复原分布；温度调整没有更新 FIRST 或 NEXT 的学习参数。表中熵描述本例完整序列的随机性，不是回答正确率。尤其不要把“每个给定前缀下的分布变平”直接推广为“任意自回归模型的完整序列熵必然单调增加”：温度也改变了访问不同前缀的频率。",
   "cell_type": "markdown"
  },
  {
   "id": "3634e300adf64553887866f99034beb6",
   "metadata": {
    "deepnote_block_id": "3634e300adf64553887866f99034beb6",
    "deepnote_block_type": "code",
    "cloud_source_sha256": "18c55ed35399570ebda31c1e038b2ef9bf19b96b93f1f8be2070733288ecf42e",
    "execution_provenance": {
     "provider": "Deepnote",
     "run_id": "584c0796-4d82-4548-aed1-ff4bea509572",
     "completed_at": "2026-09-28T15:27:40.388Z"
    }
   },
   "source": "def draw(distribution, rng):\n    keys = list(distribution)\n    return rng.choices(keys, weights=[distribution[k] for k in keys], k=1)[0]\n\ndef sample_ar(temperature, rng):\n    a = draw(temperature_distribution(FIRST, temperature), rng)\n    b = draw(temperature_distribution(NEXT[a], temperature), rng)\n    return a + b\n\nSEED, N, T = 20260926, 30000, 1.0\nrng = random.Random(SEED)\nobserved = Counter(sample_ar(T, rng) for _ in range(N))\nexact = local_temperature(T)\nprint(f\"seed={SEED}, n={N}, T={T}\")\nprint(\"sequence | expected | observed | absolute error\")\nfor seq in BASE:\n    empirical = observed[seq] / N\n    print(f\"{seq:8s} | {exact[seq]:.5f}  | {empirical:.5f}  | {abs(empirical-exact[seq]):.5f}\")\nmax_error = max(abs(observed[s] / N - exact[s]) for s in BASE)\nassert max_error < 0.015\nprint(\"sampling max absolute frequency error =\", round(max_error, 6))\n",
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [
    {
     "name": "stdout",
     "text": "seed=20260926, n=30000, T=1.0\nsequence | expected | observed | absolute error\nA0       | 0.30600  | 0.30530  | 0.00070\nA1       | 0.29400  | 0.29113  | 0.00287\nB0       | 0.39600  | 0.39933  | 0.00333\nB1       | 0.00400  | 0.00423  | 0.00023\nsampling max absolute frequency error = 0.003333\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "id": "e7faae84d81a43be920c073b25a380a2",
   "metadata": {
    "deepnote_block_id": "e7faae84d81a43be920c073b25a380a2",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "e2245427563f204e412d90d338ab1a0a517302f4b21449c43327e2aaeb92ea5d"
   },
   "source": "### 历史本地保存输出（2026-09-26；本轮执行记录见开篇）\n\n```text\nseed=20260926, n=30000, T=1.0\nsequence | expected | observed | absolute error\nA0       | 0.30600  | 0.30530  | 0.00070\nA1       | 0.29400  | 0.29113  | 0.00287\nB0       | 0.39600  | 0.39933  | 0.00333\nB1       | 0.00400  | 0.00423  | 0.00023\nsampling max absolute frequency error = 0.003333\n```\n\n## 只改一个条件：温度\n\n保持 FIRST、NEXT、样本量和种子固定，把下一格的 `TRY_T` 从 1 改为 0.35 或 2。先预测 `A0`、`B0` 和极少发生的 `B1` 哪一个增加，再看枚举与抽样。\n\n先前一格展示的是采样频率是否符合指定分布；下一格的交叉熵则是另一个问题：如果未来数据仍由原始 BASE 产生，修改采样温度后的分布给这些数据多少概率？不能把这两个判断混为一谈。",
   "cell_type": "markdown"
  },
  {
   "id": "5b35ff2b202b4a8486609c4701f49724",
   "metadata": {
    "deepnote_block_id": "5b35ff2b202b4a8486609c4701f49724",
    "deepnote_block_type": "code",
    "cloud_source_sha256": "76f66a4e79782fc337ede91761954866ec360e4fdaf1d42847c54b95d0832c4c",
    "execution_provenance": {
     "provider": "Deepnote",
     "run_id": "584c0796-4d82-4548-aed1-ff4bea509572",
     "completed_at": "2026-09-28T15:27:40.388Z"
    }
   },
   "source": "TRY_T = 2.0\nchanged = local_temperature(TRY_T)\nrng_changed = random.Random(SEED)\nchanged_counts = Counter(sample_ar(TRY_T, rng_changed) for _ in range(N))\ncross_entropy = -sum(BASE[s] * math.log2(changed[s]) for s in BASE)\nforward_kl = sum(BASE[s] * math.log2(BASE[s] / changed[s]) for s in BASE)\nprint(\"changed temperature:\", TRY_T)\nfor seq in BASE:\n    print(seq, \"exact=\", round(changed[seq], 5),\n          \"observed=\", round(changed_counts[seq] / N, 5))\nprint(\"H(BASE):\", round(entropy(BASE), 6), \"bits/sequence\")\nprint(\"cross entropy H(BASE, changed):\", round(cross_entropy, 6))\nprint(\"KL(BASE || changed):\", round(forward_kl, 6))\nassert abs(cross_entropy - entropy(BASE) - forward_kl) < 1e-12\nassert forward_kl >= -1e-12\n",
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "name": "stdout",
     "text": "changed temperature: 2.0\nA0 exact= 0.27801 observed= 0.2774\nA1 exact= 0.2725 observed= 0.27057\nB0 exact= 0.40844 observed= 0.4116\nB1 exact= 0.04105 observed= 0.04043\nH(BASE): 1.603095 bits/sequence\ncross entropy H(BASE, changed): 1.646546\nKL(BASE || changed): 0.043451\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "id": "5c3ea6dd5c61409ca2af211e3f3dccfd",
   "metadata": {
    "deepnote_block_id": "5c3ea6dd5c61409ca2af211e3f3dccfd",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "f098bc11fc730ccb63e47a1357bfca0c9c66f4e8446fe056f7582035d7516826"
   },
   "source": "### 历史本地保存输出（2026-09-26；本轮执行记录见开篇）\n\n```text\nchanged temperature: 2.0\nA0 exact= 0.27801 observed= 0.2774\nA1 exact= 0.2725 observed= 0.27057\nB0 exact= 0.40844 observed= 0.4116\nB1 exact= 0.04105 observed= 0.04043\nH(BASE): 1.603095 bits/sequence\ncross entropy H(BASE, changed): 1.646546\nKL(BASE || changed): 0.043451\n```\n\n## 带着数据回答\n\n1. 用四个联合概率说明，为什么 `A0` 是逐步贪心答案，`B0` 才是 MAP？\n2. 选择一行 `T != 1`，解释局部温度与整体温度的 TV 为什么非零。\n3. 分别报告 `B1` 的概率、完整序列熵和相对 BASE 的交叉熵。哪些指标增加了？这能说明语义质量吗？\n\n可请 AI 用你实际运行的四行表解释；先让它核对模型表没有随温度一起变化，再讨论观察。",
   "cell_type": "markdown"
  },
  {
   "id": "aeb2d98ce9af46f98e833751c44b8667",
   "metadata": {
    "deepnote_block_id": "aeb2d98ce9af46f98e833751c44b8667",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "209720cfb454d4fe0e8111c9520cdcba756958047ecd4f62b66cd5ff98bd2e92"
   },
   "source": "## 本册证据的边界\n\n这是手工概率模型的精确枚举与伪随机抽样，没有数据训练、神经网络、长上下文或语义评价。本地保存输出来自执行这些代码；Deepnote 是否重跑应以平台运行记录为准。抽样误差会随样本量变化，精确概率不受种子影响。\n\n链式法则与信息量的背景可读 [Deep Learning：Probability and Information Theory](https://www.deeplearningbook.org/contents/prob.html)。本册反例和数值为教学构造，不是该书报告的实验结果。",
   "cell_type": "markdown"
  },
  {
   "id": "7aecc644adaf455e9a833597754725b3",
   "metadata": {
    "deepnote_block_id": "7aecc644adaf455e9a833597754725b3",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "71432270f50067136f908a1d1b8e43c96b78639c09620db323d1894fd1fd6a36"
   },
   "source": "## 接回主讲\n\n回到“把联合概率拆成下一步”“训练与生成的前缀不同”“温度改变采样分布”三处。下一步若研究真实语言模型，应固定模型、提示、长度和解码配置，再分别评价质量与多样性；本册不替这些实验预判结果。",
   "cell_type": "markdown"
  },
  {
   "id": "e0777fc492b248218984af651b4c15d6",
   "metadata": {
    "deepnote_block_id": "e0777fc492b248218984af651b4c15d6",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "bf16f08f51d9a2de220dd3470c6af3cb7ee28cb8117d0417d5eb6d106f8d6463"
   },
   "source": "## 从课堂展开：推导、反例与变量实验\n\n先完成上面的有限例子，再按自己尚未弄清的问题选择推导。已有代码只覆盖本册明确列出的计算；后面的研究练习是可继续提出的实验，不是已经运行的结果。\n\n\n\n\n- [从当前课堂回到这套概率表](https://deepnote.com/project/6f83a923-d155-47be-be58-680db701ff7f/notebook/39071d41f84d4621ad69c6140a6dccc9?utm_source=openai&utm_medium=mcp&utm_campaign=openaimcp&utm_content=39071d41f84d4621ad69c6140a6dccc9&utm_term=get_notebook#f8bca478ae9148978d09113d71f6ee06)\n- [输入和标签为什么错开一个位置](https://deepnote.com/project/6f83a923-d155-47be-be58-680db701ff7f/notebook/39071d41f84d4621ad69c6140a6dccc9?utm_source=openai&utm_medium=mcp&utm_campaign=openaimcp&utm_content=39071d41f84d4621ad69c6140a6dccc9&utm_term=get_notebook#4a770ec239d14b6a9691935d71b7766a)\n- [真实前缀与自身前缀，为何可能带来不同表现](https://deepnote.com/project/6f83a923-d155-47be-be58-680db701ff7f/notebook/39071d41f84d4621ad69c6140a6dccc9?utm_source=openai&utm_medium=mcp&utm_campaign=openaimcp&utm_content=39071d41f84d4621ad69c6140a6dccc9&utm_term=get_notebook#a411c825c6514134bb2bccbb2263250e)\n\n原有解释按连续主题拆到下方；本入口继续保留。",
   "cell_type": "markdown"
  },
  {
   "id": "f8bca478ae9148978d09113d71f6ee06",
   "metadata": {
    "deepnote_block_id": "f8bca478ae9148978d09113d71f6ee06",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "73a8dde77ced915e33cd2522e9860ed6ea7c247e5bdee8dc6cdeb43385f07d30"
   },
   "source": "### 从当前课堂回到这套概率表\n\nN09 的依赖关系在此变为四个可枚举结果；N11 的训练/生成差别是前缀来源。对真实序列 A0，训练第二项读取 A 并给真实 0 评分；自由生成若先抽到 B，下一项必须用 NEXT[B]，不能继续查 A 行。teacher forcing 允许真实过去，不允许当前目标提前进入输入。\n\nN10 的木球问题可做纯手算状态表：起点3颗，取出1颗后2颗，再放入2颗后4颗。把最后事件从放入2颗改成取出2颗，答案应为0颗。这与 N56 回访的是同一事件序列。该对照检验目标需要哪些信息，不是本册四格代码已经测得语言模型状态能力。\n\n外部条件 c 与生成前缀来自不同位置。固定前缀“桌上有一只”，分别给猫照片和狗照片，正确的条件分布应响应输入对象。可用两份手写条件表验证 p(x|c)=∏p(x_i|x_<i,c)，但这里只提出检查方式，未新增或运行模型实验。\n\n下列进一步阅读分成“联合关系与上下文”“似然与信息边界”“解码与采样检查”三组，数值实验继续使用 A0、A1、B0、B1 四种序列。\n\n\n### 两个各自正确的边缘分布，仍能拼出错误世界\n\n分别学会每个变量，为什么还不够？\n\n考虑本课程的两盏灯算例：真实数据只有同时关闭和同时打开，各占一半。单看第一盏或第二盏，亮灯概率都是二分之一。如果独立地从两个边缘分布采样，四种组合会各占四分之一，于是得到真实数据从未出现的一亮一灭。两个边缘分布都被精确拟合，联合分布却错了。这不是网络规模不足造成的，而是独立生成时丢掉了变量关系。自回归通过条件分布保留这种依赖，也说明“每个局部看起来合理”不足以保证整体合理。\n\n**追问：**两个单灯预测都百分之百符合统计，为什么整幅图仍然错？\n\n因为每个变量的边缘概率没有记录它与另一个变量一起出现的方式。原数据要求两盏灯一致，独立采样没有执行这个限制。联合概率可以有相同的行和列总和，却在四个格子里分配不同质量。你需要检查成对事件的频率，或者显式学习给定第一盏灯以后第二盏灯的条件概率。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N09.html?view=notes)\n\n相关阅读：[Autoregressive Models](https://mit-6s978.github.io/assets/pdfs/lec3_ar.pdf)\n\n### 条件概率是在一条已知分支上重新归一化\n\n知道第一盏灯亮了，第二盏灯的分布怎样改变？\n\n延续两灯例子，当第一盏灯亮时，第二盏灯亮的条件概率为一；第一盏灯灭时，第二盏灯亮的条件概率为零。计算条件概率时，先只保留与已知条件相容的联合事件，再除以该条件事件的总概率。边缘概率二分之一与条件概率零或一并不矛盾，因为它们回答不同问题。概率树中每个节点的出边应加和为一，但整条路径的概率需要相乘。条件事件概率为零时，不能直接用通常的比值定义该条件分布。\n\n**追问：**条件概率变成一，是不是模型突然对整个世界都没有不确定性了？\n\n它只是在这个精确算例、这个给定条件下对第二盏灯没有不确定性。第一盏灯本身仍然随机，因此整个二变量样本仍有两种可能。不要把一个条件节点的确定性扩展为整个联合分布的确定性。实际任务还要检查条件是否可靠、是否见过，以及数据关系是否真的像本例这样完全一致。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N09.html?view=notes)\n\n相关阅读：[Autoregressive Models](https://mit-6s978.github.io/assets/pdfs/lec3_ar.pdf)\n\n### 只看最近一个 token，是新的模型假设\n\np(xᵢ|x<ᵢ) 什么时候能简化为 p(xᵢ|xᵢ₋₁)？\n\n完整链式分解允许当前位置依赖全部前缀。若把条件只保留为最近一个变量，就变成一阶 Markov 假设；在某些过程上合理，在另一些过程上会丢失长期信息。构造序列：第一个符号决定最后一个符号，中间全是相同占位符。只看最后一个占位符无法知道首符号，而完整前缀可以。这个例子为课程补充，用来定位上下文截断的代价。实际语言模型的有限窗口也是一种可用信息边界，不能与无条件独立或完整历史建模混称。\n\n**追问：**名字叫自回归，是不是天然只使用上一步输出？\n\n不是。“把已有输出作为条件”没有限定只能保留一个输出。完整自回归因子可以使用整个前缀，也可以通过隐藏状态压缩过去。只看一个位置是另外施加的假设。评估模型时需要问清上下文窗口和状态表示，不能仅从“自回归”这个名称推断它能记住多少历史。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N09.html?view=notes)\n\n相关阅读：[Autoregressive Models](https://mit-6s978.github.io/assets/pdfs/lec3_ar.pdf)\n\n### 乘积变求和：负对数似然落到每个位置\n\n为什么训练代码经常只有一个交叉熵？\n\n对数把序列概率的乘积变成条件对数概率之和，所以负对数似然是每个真实下一 token 的负对数概率相加。离散输出配合 one-hot 标签时，这就是常用交叉熵。若两个位置分别给真实 token 概率0.8和0.5，整段概率为0.4，总负对数似然为−log0.8−log0.5。该数值例为课程补充。按 token 求平均与按序列求平均会改变不同长度样本的权重；需要在实现和报告中明确归一化方式。条件概率过低的那个位置会贡献较大损失，可据此定位具体预测问题。\n\n**追问：**每个 token 都做分类，为什么整件事还能叫生成模型？\n\n局部分类器预测的是给定前缀时下一变量的分布。将这些条件分布按链式法则组合，就定义了整个序列的联合分布；再逐步从中采样，就得到完整序列。局部计算形式像分类，不妨碍整体用于生成。关键是条件如何变化、各局部分布怎样组合，以及生成时怎样接回前一步结果。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N10.html?view=notes)\n\n相关阅读：[Autoregressive Models](https://mit-6s978.github.io/assets/pdfs/lec3_ar.pdf) · [Generative Models (part 1)](https://cs231n.stanford.edu/slides/2026/lecture_13.pdf)",
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   "source": "### 输入和标签为什么错开一个位置\n\n模型正在预测输入位置，还是下一个位置？\n\n对序列“红、杯、结束”，可用“开始、红、杯”作为输入，对应标签是“红、杯、结束”。每个位置的表示据此预测下一个符号。开始和结束标记是常见实现约定；具体分词器可有不同处理，但输入目标错位必须一致。若把输入与标签原样对齐，再允许当前位置读取自身，就可能训练成复制器。这个短序列为课程构造，服务于原课的目标右移一格图。检查损失时还应排除填充位置，避免模型从大量无意义标签获得看似很好的平均分数。\n\n**追问：**我把完整句子输入网络，再让它输出同一句子，损失也下降了，哪里错？\n\n这可能是在做重构或复制，而不是下一步预测。若当前位置能够直接读取真实目标，它不必利用前缀建立预测能力。需要检查输入标签是否错开、因果遮罩定义与损失位置是否一致。训练损失下降只能说明当前代码中的目标变容易了，不能证明实现了想要的自回归概率分解。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N11.html?view=notes)\n\n相关阅读：[Autoregressive Models](https://mit-6s978.github.io/assets/pdfs/lec3_ar.pdf)\n\n### 一条路径的概率，与一个节点的概率\n\n选到“新深色轿车”究竟有多大概率？\n\n使用原课车辆树结构，另设本课程数值：轿车概率0.6，给定轿车时深色概率0.25，给定深色轿车时新车概率0.8。那么抽到新深色轿车的联合概率为0.12，而不是0.8。后一个数只在已经走到深色轿车节点后成立。若问所有新车的概率，则要把不同车型、颜色路径中属于新车的概率加起来。这个算例让采样轨迹和概率运算一一对应，也可以用于验证自编采样器的长期频率。把所有叶节点概率相加，还应重新得到总概率一。\n\n**追问：**最后一步模型很有把握，为什么完整结果还是很罕见？\n\n因为走到这个条件可能本来就很罕见。条件概率评价已知前提下的相对可能性，联合概率还需要把前提发生的概率算进去。一个完整长序列的概率常常很小，并不必然意味着每个局部预测都很差。比较时应说明长度和归一化方式，避免把低联合概率直接解释成低质量。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N12.html?view=notes)\n\n相关阅读：[Autoregressive Models](https://mit-6s978.github.io/assets/pdfs/lec3_ar.pdf)\n\n### 温度改变输出分布，不改变已训练权重\n\n降低温度以后，模型真的学到了更多吗？\n\n本页为课程补充算例，原课页码只提供条件分布背景。给定logits [0,1,2]，温度T通过softmax(z/T)改变归一化概率。T降低时最大项更集中，T增大时更平缓；只有T为正才使用这个公式。参数θ并未改变，改变的是从模型分数到抽样概率的映射。更平缓可能带来更多变化，也可能增加错误；更集中可能提高某些一致性却降低覆盖。词表有并列最大值时，零温极限仍需说明如何处理并列。比较时同时记录概率表与实际抽样结果，避免用几次偶然输出判断趋势。\n\n**追问：**温度高生成得更奇怪，是不是等于模型更有创造力？\n\n这里只能证明概率变平、较低分候选更可能出现，不能单凭奇怪程度定义创造力。是否有价值、是否满足条件、是否保持事实与结构，都需要任务标准。你应在相同模型、提示和样本预算下比较，并同时记录成功与失败。采样分布更宽是机制事实，创造力更好是另一个尚需证据的评价。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N12.html?view=notes)\n\n相关阅读：[Autoregressive Models](https://mit-6s978.github.io/assets/pdfs/lec3_ar.pdf)\n\n### 每一步选最大，并不保证整条序列最大\n\n局部最优为什么可能拼不出全局最优？\n\n课程自编两步树：第一步P(A)=0.6、P(B)=0.4；A后P(0)=0.51，B后P(0)=0.99，其余概率由补数给出。贪心先选A再选0，得到A0，路径概率0.306；但B0概率0.396更大。两步局部选择无法预先比较全部后续分支，因此贪心结果未必是联合概率最大者。这个反例也不说明最高概率句子必然最符合人的任务要求；搜索目标、采样目标和语义质量仍要分别定义。原课提供链式结构，数值与反例由课程补充。即使穷举这个小树没有困难，长序列的分支数量仍会随长度迅速增加。\n\n**追问：**既然最高概率完整序列更好，我们是否应该永远搜索它？\n\n最高联合概率只是一个明确定义的优化目标，不自动等于对用户最有用或最多样的输出。搜索还有计算成本与长度偏置等问题。若任务要求从模型分布抽样，永远返回同一最高概率序列反而改变了目标。先确认要的是随机样本、最可能路径还是满足外部约束的结果，再选择解码规则。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N12.html?view=notes)\n\n相关阅读：[Autoregressive Models](https://mit-6s978.github.io/assets/pdfs/lec3_ar.pdf)\n\n### 检验采样器，不能只看一条顺眼的序列\n\n概率实现正确，怎样留下可检查的证据？\n\n课程实验可先使用完整已知的小联合表，通过条件树生成大量样本，再比较每条路径的理论概率与经验频率。实验中固定概率表、随机数算法和样本预算，并保留种子，便于定位实现错误。有限样本与理论概率不必完全一致，因此应观察不同样本量下偏差的变化，而不是要求每一批都精确命中比例。随后故意让采样器忽略条件，检查它何时仍能匹配部分边缘统计。这个对照能揭示只看边缘或精选样本的盲点。\n\n**追问：**固定种子每次都得到一样结果，能否证明代码正确？\n\n只能证明在当前环境和设置下执行可复现。一个错误的条件索引也可以非常稳定地复现。正确性需要把输出与目标分布的可计算统计比较，并进行能区分正确与错误实现的对照。种子、统计检验和代码检查分别解决不同问题；三者都重要，但不能互相替代。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N12.html?view=notes)\n\n相关阅读：[Autoregressive Models](https://mit-6s978.github.io/assets/pdfs/lec3_ar.pdf)",
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   "source": "### 真实前缀与自身前缀，为何可能带来不同表现\n\n一个早期选择会怎样改变后面的任务？\n\n训练常在真实数据前缀上评价下一步概率；自由生成时前缀由模型先前的选择构成。某些罕见或错误选择可能把后续计算带到训练较少覆盖的条件区域，进而出现连锁变化。这个现象不等于每次偏离参考文本都是错误，因为多解任务本来允许其他合理续写。需要区分不一样、违反条件和结构失效，再设计对照。可以固定模型与后续随机数，在某个位置替换一个token，观察后面哪些变化来自前缀而非重新训练。\n\n**追问：**只要输出与参考答案不一样，就说明出现了 exposure bias 吗？\n\n不能。参考可能只是条件分布中的一个样本，另一个续写也可能合理。要先定义失败标准，再检查失败是否与自身前缀引起的分布变化相关。即便观察到相关，也需要排除目标不匹配、模型能力不足等解释。不要用一个术语把所有生成差异打包，否则既无法验证，也难以改进。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N14.html?view=notes)\n\n相关阅读：[Autoregressive Models](https://mit-6s978.github.io/assets/pdfs/lec3_ar.pdf)",
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