{
 "nbformat": 4,
 "nbformat_minor": 5,
 "cells": [
  {
   "id": "cf11c54b59c2417181d4bb373a78ff6f",
   "metadata": {
    "deepnote_block_id": "cf11c54b59c2417181d4bb373a78ff6f",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "425ed421909c92e7281ca0cba833b915b722e7fd1ec626f7a85c7c7d92bb42b8"
   },
   "source": "# 遮挡文本：多个位置各自合理，整句就相容吗？\n\n本册的文本世界只有两句：“猫 会 喵 ， 猫 喵”和“狗 会 汪 ， 狗 汪”，各占一半。**先预测**：全句遮住时，若每个位置独立按其边际概率填入 token，得到合法句子的概率是多少？\n\n然后比较三条采样轨迹：一次并行填充、使用已揭示内容重新预测、从左到右自回归。这里的预测器是手工分布的精确条件计算，**不是训练过的扩散语言模型，也不是 LLaDA 复现**。\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": "531d0767346542d6b92768a9955a5c8f"
   },
   "source": "## 先看问题与保存结果\n\n本实验比较同一小语法任务：逐个提交、多位置独立候选、迭代相容。先看保存的 token 状态和合法率，再改变提交策略。规则轮数并不是大语言模型的端到端延迟。\n\n![本实验比较同一小语法任务：逐个提交、多位置独立候选、迭代相容。先看保存的 token 状态和合法率，再改变提交策略。规则轮数并不是大语言模型的端到端延迟。](https://codingai-lec04.pages.dev/assets/labs-v13/lab04-token-traces.png)\n\n[连续概念解释](https://codingai-lec04.pages.dev/lecture.html#ch07)。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": "e9ca7e98b48741d4b1bb900cc6ab1ba8",
   "metadata": {
    "deepnote_block_id": "e9ca7e98b48741d4b1bb900cc6ab1ba8",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "0cc7093d2188618c32182e1c738e2eb2b7fbdcd9b935b57cec7db46e2ba0c855",
    "cloud_original_source": "## 先看保存结果：相同遮罩输入，三种填词次序\n\n![相同遮罩输入，三种填词次序：图1](https://codingai-lec04.pages.dev/assets/labs-v13/lab04-token-traces.png)\n\n![相同遮罩输入，三种填词次序：图2](https://codingai-lec04.pages.dev/assets/labs-v13/lab04-validity-rounds.png)\n\n图中 cat/can/meow 对应“猫/会/喵”，dog/woof 对应“狗/汪”；问号是未知，金色是本轮新提交，蓝色是此前保留。三种方法均从相同全遮罩输入出发。默认一次并行的精确合法率1/8，4000种子的实测为0.1325；迭代与AR在此构造语法中均为1，分别用3与6个依赖轮次。本调度器只提交，不重遮罩或修正已知token；看见“修订”需求时应把相应位置明确重新设为未知，不能把保留图色误读为已实现自动纠错。\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。解析两句语法，不调用真实语言模型。轮数是依赖关系，不代表GPU延迟；此结果不为扩散LLM和AR排名。 图不是模型训练输出。\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：相同遮罩输入，三种填词次序\n\n![相同遮罩输入，三种填词次序：图1](attachment:lab04-token-traces.png)\n\n![相同遮罩输入，三种填词次序：图2](attachment:lab04-validity-rounds.png)\n\n图中 cat/can/meow 对应“猫/会/喵”，dog/woof 对应“狗/汪”；问号是未知，金色是本轮新提交，蓝色是此前保留。三种方法均从相同全遮罩输入出发。默认一次并行的精确合法率1/8，4000种子的实测为0.1325；迭代与AR在此构造语法中均为1，分别用3与6个依赖轮次。本调度器只提交，不重遮罩或修正已知token；看见“修订”需求时应把相应位置明确重新设为未知，不能把保留图色误读为已实现自动纠错。\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。解析两句语法，不调用真实语言模型。轮数是依赖关系，不代表GPU延迟；此结果不为扩散LLM和AR排名。 图不是模型训练输出。\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": {
    "lab04-token-traces.png": {
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    "lab04-validity-rounds.png": {
     "image/png": 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    }
   }
  },
  {
   "id": "c6258df90db940cc969d24bc6a6ff1d0",
   "metadata": {
    "deepnote_block_id": "c6258df90db940cc969d24bc6a6ff1d0",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "98023a3968f9dba3c43bb204c246b43d7d8a494b8eadbae501d74cb3b1bf8581"
   },
   "source": "## 只改一个变量：COMMIT_THRESHOLD\n\n把 COMMIT_THRESHOLD 从0.99改为0.5，保持语法、输入与4000枚种子固定。较低门槛使不确定位置同时提交，迭代法在这个特例退化为一次并行。\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 `lab04-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": "cc45955957bc40f7bc405c20794a2b43",
   "metadata": {
    "deepnote_block_id": "cc45955957bc40f7bc405c20794a2b43",
    "deepnote_block_type": "code",
    "cloud_source_sha256": "6d01b2b8d775d465d5ad03b5a288694a9c89d9e57b1c54a85e6cccc82dbd8d6f",
    "execution_provenance": {
     "provider": "Deepnote",
     "run_id": "31d43ed5-a356-481c-9e72-9a48e0a078ab",
     "completed_at": "2026-09-28T15:30:48.794Z"
    }
   },
   "source": "import random, json, platform\nfrom collections import Counter\nfrom pathlib import Path\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom matplotlib.patches import Rectangle\n\n# Change one variable: threshold. At <=0.5 uncertain positions commit together.\nCOMMIT_THRESHOLD=.99\nVISUAL_SEED=20260928\nVISUAL_N=4000\nOUT=Path('lab04-visual-output');OUT.mkdir(exist_ok=True)\nGRAMMAR_VIS={('cat','can','meow',',','cat','meow'):.5,('dog','can','woof',',','dog','woof'):.5}\n\ndef vis_conditionals(state):\n    compatible={s:p for s,p in GRAMMAR_VIS.items() if all(v is None or v==s[i] for i,v in enumerate(state))}\n    total=sum(compatible.values())\n    if not total:raise ValueError('Visible tokens conflict with the fixed grammar')\n    out={}\n    for i,v in enumerate(state):\n        if v is None:\n            d=Counter()\n            for s,p in compatible.items():d[s[i]]+=p/total\n            out[i]=dict(d)\n    return out\n\ndef vis_draw(d,rng):return rng.choices(list(d),weights=list(d.values()),k=1)[0]\ndef vis_sampler(mode,seed,threshold=COMMIT_THRESHOLD,initial=None):\n    rng=random.Random(seed);state=list(initial) if initial else [None]*6;trace=[state.copy()];new=[]\n    while None in state:\n        dist=vis_conditionals(state)\n        if mode=='parallel':selected=list(dist)\n        elif mode=='AR':selected=[min(dist)]\n        else:\n            selected=[i for i,p in dist.items() if max(p.values())>=threshold]\n            if not selected:selected=[rng.choice(list(dist))]\n        updates={i:vis_draw(dist[i],rng) for i in selected}\n        for i,value in updates.items():state[i]=value\n        trace.append(state.copy());new.append(selected)\n    return {'tokens':state,'rounds':len(new),'valid':tuple(state) in GRAMMAR_VIS,'trace':trace,'new':new}\n\nfig,axes=plt.subplots(1,3,figsize=(13,5.2));traces={}\nfor ax,mode in zip(axes,['parallel','iterative','AR']):\n    r=vis_sampler(mode,2);traces[mode]=r\n    for row,state in enumerate(r['trace']):\n        changed=[] if row==0 else r['new'][row-1]\n        for col,value in enumerate(state):\n            color='#edf0f2' if value is None else '#f8dc8b' if col in changed else '#cbdde8'\n            ax.add_patch(Rectangle((col,-row),.94,.8,facecolor=color,edgecolor='white'))\n            ax.text(col+.47,-row+.4,'?' if value is None else value,ha='center',va='center',fontsize=9)\n        ax.text(-.15,-row+.4,str(row),ha='right',va='center',fontsize=9)\n    ax.set(xlim=(-.5,6),ylim=(-6.5,1),title=f'{mode}: {r[\"rounds\"]} rounds; valid={r[\"valid\"]}');ax.axis('off')\nfig.suptitle('Same fully masked input: gray unknown, gold newly committed, blue retained',fontsize=12)\nfig.tight_layout();fig.savefig(OUT/'lab04-token-traces.png',dpi=160);plt.show();plt.close(fig)\n\nrecords=[]\nfor mode in ['parallel','iterative','AR']:\n    outputs=[vis_sampler(mode,VISUAL_SEED+i) for i in range(VISUAL_N)]\n    records.append({'mode':mode,'valid_rate':sum(r['valid'] for r in outputs)/VISUAL_N,'mean_rounds':float(np.mean([r['rounds'] for r in outputs])),'cat_mass':sum(tuple(r['tokens'])==next(iter(GRAMMAR_VIS)) for r in outputs)/VISUAL_N})\nfig,axes=plt.subplots(1,2,figsize=(10,3.6))\naxes[0].bar([r['mode'] for r in records],[r['valid_rate'] for r in records],color=['#a3b4c2','#003262','#c18f16']);axes[0].axhline(.125,color='#a5563c',ls='--',label='one-shot exact 1/8');axes[0].set(ylim=(0,1.08),ylabel='Joint validity');axes[0].legend(fontsize=8)\naxes[1].bar([r['mode'] for r in records],[r['mean_rounds'] for r in records],color=['#a3b4c2','#003262','#c18f16']);axes[1].set(ylabel='Dependency rounds (not wall-clock time)',ylim=(0,7))\nfig.suptitle(f'{VISUAL_N} seeds; iterative threshold={COMMIT_THRESHOLD:g}',fontsize=12);fig.tight_layout();fig.savefig(OUT/'lab04-validity-rounds.png',dpi=160);plt.show();plt.close(fig)\nassert abs(records[0]['valid_rate']-.125)<.03\nif COMMIT_THRESHOLD>.5:assert records[1]['valid_rate']==1\nassert records[2]['valid_rate']==1\npayload={'kind':'exact two-sentence grammar, no language-model inference','seed':VISUAL_SEED,'n':VISUAL_N,'threshold':COMMIT_THRESHOLD,'traces':traces,'results':records,'legend':{'gray':'unknown','gold':'newly committed this round','blue':'retained; no remasking/revision in this scheduler'},'python':platform.python_version()}\n(OUT/'lab04-results.json').write_text(json.dumps(payload,indent=2));print(json.dumps(records,indent=2))\n",
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1300x520 with 3 Axes>",
      "image/png": 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     },
     "metadata": {
      "image/png": {
       "width": 1289,
       "height": 514
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 1000x360 with 2 Axes>",
      "image/png": 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"
     },
     "metadata": {
      "image/png": {
       "width": 989,
       "height": 357
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "text": "[\n  {\n    \"mode\": \"parallel\",\n    \"valid_rate\": 0.1325,\n    \"mean_rounds\": 1.0,\n    \"cat_mass\": 0.06825\n  },\n  {\n    \"mode\": \"iterative\",\n    \"valid_rate\": 1.0,\n    \"mean_rounds\": 3.0,\n    \"cat_mass\": 0.49375\n  },\n  {\n    \"mode\": \"AR\",\n    \"valid_rate\": 1.0,\n    \"mean_rounds\": 6.0,\n    \"cat_mass\": 0.51\n  }\n]\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "id": "3c738568ffb0460792fd17f04dee9bad",
   "metadata": {
    "deepnote_block_id": "3c738568ffb0460792fd17f04dee9bad",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "8352daa0c51ad9c855e0c5be433ed11f462f01801043a8b558dd1446d623bc7b"
   },
   "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 `31d43ed5-a356-481c-9e72-9a48e0a078ab`，完成时间 2026-09-28T15:30:48.794Z（UTC）。运行快照检查到本册图形输出且无失败代码块。token轨迹与合法率图已输出；4000种子一次并行0.1325、迭代1、AR1；轮数分别1/3/6。\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": "3aa3a0975d8e438392edc8a5450dc5b1",
   "metadata": {
    "deepnote_block_id": "3aa3a0975d8e438392edc8a5450dc5b1",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "fd81d410fef1b634fe39427a3312920b4860b1d80c6323be7215bd54ca258d46"
   },
   "source": "## 什么是已知，什么还未知\n\n`None` 表示遮挡位置；已有 token 必须保持不变。我们先找出与所有可见 token 相容的完整句子，再计算每个遮挡位置的条件边际。这是一个小型精确 oracle，可以排除学习误差，把注意力放在采样组织上。\n\n随机遮挡是离散 token 的破坏方式，与对 token ID 加高斯噪声不同。下一格只展示一次前向遮挡和条件预测，不执行任何训练。",
   "cell_type": "markdown"
  },
  {
   "id": "03f2b18076374fec97ef93aa4b37d1b3",
   "metadata": {
    "deepnote_block_id": "03f2b18076374fec97ef93aa4b37d1b3",
    "deepnote_block_type": "code",
    "cloud_source_sha256": "c8a17b0048188d3de6a49710b8d81e32c9fed7cc9e1267aea910833a491dbcb3",
    "execution_provenance": {
     "provider": "Deepnote",
     "run_id": "31d43ed5-a356-481c-9e72-9a48e0a078ab",
     "completed_at": "2026-09-28T15:30:48.794Z"
    }
   },
   "source": "import itertools\nimport random\nfrom collections import Counter\n\nSENTENCES = {\n    (\"猫\", \"会\", \"喵\", \"，\", \"猫\", \"喵\"): 0.5,\n    (\"狗\", \"会\", \"汪\", \"，\", \"狗\", \"汪\"): 0.5,\n}\nLENGTH = 6\ndef show(state):\n    return \" \".join(token if token is not None else \"[MASK]\" for token in state)\n\ndef conditionals(state):\n    compatible = {seq: p for seq,p in SENTENCES.items()\n                  if all(token is None or token == seq[i] for i,token in enumerate(state))}\n    total = sum(compatible.values())\n    if total == 0:\n        raise ValueError(\"Visible tokens contradict every sentence in this fixed model.\")\n    output = {}\n    for i, token in enumerate(state):\n        if token is None:\n            dist = Counter()\n            for seq,p in compatible.items():\n                dist[seq[i]] += p/total\n            output[i] = dict(dist)\n    return output\n\nsource = next(iter(SENTENCES))\nrng_corrupt = random.Random(10)\nmask_rate = 0.7\ncorrupted = [None if rng_corrupt.random() < mask_rate else t for t in source]\nprint(\"clean:\", show(source))\nprint(\"masked:\", show(corrupted))\nprint(\"conditional predictions:\", conditionals(corrupted))\nprint(\"fully masked predictions:\", conditionals([None]*LENGTH))\n",
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [
    {
     "name": "stdout",
     "text": "clean: 猫 会 喵 ， 猫 喵\nmasked: [MASK] [MASK] [MASK] [MASK] 猫 喵\nconditional predictions: {0: {'猫': 1.0}, 1: {'会': 1.0}, 2: {'喵': 1.0}, 3: {'，': 1.0}}\nfully masked predictions: {0: {'猫': 0.5, '狗': 0.5}, 1: {'会': 1.0}, 2: {'喵': 0.5, '汪': 0.5}, 3: {'，': 1.0}, 4: {'猫': 0.5, '狗': 0.5}, 5: {'喵': 0.5, '汪': 0.5}}\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "id": "b8be1fff01414d82a1bb3af3a4dca76d",
   "metadata": {
    "deepnote_block_id": "b8be1fff01414d82a1bb3af3a4dca76d",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "16f5adcad846bcc5b8c60e0ac0773a88219e9c03474b0f0be5098fd7f5c7b5bb"
   },
   "source": "### 历史本地保存输出（2026-09-26；本轮执行记录见开篇）\n\n```text\nclean: 猫 会 喵 ， 猫 喵\nmasked: [MASK] [MASK] [MASK] [MASK] 猫 喵\nconditional predictions: {0: {'猫': 1.0}, 1: {'会': 1.0}, 2: {'喵': 1.0}, 3: {'，': 1.0}}\nfully masked predictions: {0: {'猫': 0.5, '狗': 0.5}, 1: {'会': 1.0}, 2: {'喵': 0.5, '汪': 0.5}, 3: {'，': 1.0}, 4: {'猫': 0.5, '狗': 0.5}, 5: {'喵': 0.5, '汪': 0.5}}\n```\n\n## 一次并行独立采样丢了什么？\n\n四个内容位置都各自有两个等概率 token；“会”和逗号则确定。一次性独立采样因此产生 16 种等概率组合，只有 2 种属于原分布，合法率为 $2/16=1/8$。\n\n问题不在每个位置的边际概率算错，而在把相依位置当成相互独立。下一格穷举这一步产生的完整分布，不能把“各位置概率准确”误写成“联合分布准确”。",
   "cell_type": "markdown"
  },
  {
   "id": "3a950b8cec334079b5f21b2658777077",
   "metadata": {
    "deepnote_block_id": "3a950b8cec334079b5f21b2658777077",
    "deepnote_block_type": "code",
    "cloud_source_sha256": "ad2f6c494cb493717ea817cb1fd563b906d11a3e36f97aebeaa995f825ca3219",
    "execution_provenance": {
     "provider": "Deepnote",
     "run_id": "31d43ed5-a356-481c-9e72-9a48e0a078ab",
     "completed_at": "2026-09-28T15:30:48.794Z"
    }
   },
   "source": "marginals = conditionals([None]*LENGTH)\nparallel_joint = {}\nfor candidate in itertools.product(*(list(marginals[i]) for i in range(LENGTH))):\n    probability = 1.0\n    for i, token in enumerate(candidate):\n        probability *= marginals[i][token]\n    parallel_joint[candidate] = probability\nvalid_mass = sum(p for seq,p in parallel_joint.items() if seq in SENTENCES)\nprint(\"parallel support size:\", len(parallel_joint))\nprint(\"exact valid probability:\", valid_mass)\nprint(\"one incompatible candidate:\", next(show(s) for s in parallel_joint if s not in SENTENCES))\nassert abs(sum(parallel_joint.values()) - 1) < 1e-12\nassert valid_mass == 0.125\n",
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
    {
     "name": "stdout",
     "text": "parallel support size: 16\nexact valid probability: 0.125\none incompatible candidate: 猫 会 喵 ， 猫 汪\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "id": "1cc5dacc42534be7a07656800c576a9c",
   "metadata": {
    "deepnote_block_id": "1cc5dacc42534be7a07656800c576a9c",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "7d8eaaa6509b851d28ae889ac3f1728bb79af6b0265d2aeb34a69b078dd9a20c"
   },
   "source": "### 历史本地保存输出（2026-09-26；本轮执行记录见开篇）\n\n```text\nparallel support size: 16\nexact valid probability: 0.125\none incompatible candidate: 猫 会 喵 ， 猫 汪\n```\n\n## 一个可逐步检查的迭代规则\n\n每轮预测所有仍被遮挡的位置。如果有至少 0.99 置信度的位置，先同时提交这些位置；否则只随机提交一个不确定位置，再重新计算条件分布。当前例子中，“会、逗号”先确定，随后选定一个内容 token，最后其他内容 token 都由相容性确定。\n\n这是教学调度规则，**不是从扩散方程推导的通用采样器**。对于本册精确 oracle，阈值 0.99 只选中概率 1 的确定项。真实模型的高置信度可能错；换一个存在多种相关模式的分布，同样规则也不保证正确联合采样。",
   "cell_type": "markdown"
  },
  {
   "id": "afca8bc160a440ef870fbd3a6375ac0f",
   "metadata": {
    "deepnote_block_id": "afca8bc160a440ef870fbd3a6375ac0f",
    "deepnote_block_type": "code",
    "cloud_source_sha256": "300a9ac94c53b340db1f2ffb6eb92fd2822e03be0c22f5d90580d555fc15db1f",
    "execution_provenance": {
     "provider": "Deepnote",
     "run_id": "31d43ed5-a356-481c-9e72-9a48e0a078ab",
     "completed_at": "2026-09-28T15:30:48.794Z"
    }
   },
   "source": "def draw(dist, rng):\n    tokens = list(dist)\n    return rng.choices(tokens, weights=[dist[t] for t in tokens], k=1)[0]\n\ndef parallel_once(rng, initial=None):\n    state = list(initial) if initial is not None else [None]*LENGTH\n    prediction = conditionals(state)\n    for i, dist in prediction.items():\n        state[i] = draw(dist, rng)\n    return tuple(state), 1, [show(state)]\n\ndef iterative(rng, initial=None, threshold=0.99):\n    state = list(initial) if initial is not None else [None]*LENGTH\n    trace = [show(state)]\n    rounds = 0\n    while None in state:\n        prediction = conditionals(state)\n        confident = [i for i,dist in prediction.items() if max(dist.values()) >= threshold]\n        selected = confident if confident else [rng.choice(list(prediction))]\n        # 所有 selected 都使用本轮旧状态；不会在同一轮内偷偷传递刚生成的 token。\n        updates = {i: draw(prediction[i], rng) for i in selected}\n        for i, token in updates.items():\n            state[i] = token\n        rounds += 1\n        trace.append(show(state))\n    return tuple(state), rounds, trace\n\ndef autoregressive(rng, initial=None):\n    state = list(initial) if initial is not None else [None]*LENGTH\n    trace = [show(state)]\n    rounds = 0\n    for i in range(LENGTH):\n        if state[i] is None:\n            state[i] = draw(conditionals(state)[i], rng)\n            rounds += 1\n            trace.append(show(state))\n    return tuple(state), rounds, trace\n\nfor name, sampler in [(\"parallel once\", parallel_once), (\"iterative\", iterative), (\"AR\", autoregressive)]:\n    result, rounds, trace = sampler(random.Random(4))\n    print(\"\\n\", name, \"rounds=\", rounds, \"valid=\", result in SENTENCES)\n    for step, state in enumerate(trace):\n        print(step, state)\n",
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [
    {
     "name": "stdout",
     "text": "\n parallel once rounds= 1 valid= True\n0 猫 会 喵 ， 猫 喵\n\n iterative rounds= 3 valid= True\n0 [MASK] [MASK] [MASK] [MASK] [MASK] [MASK]\n1 [MASK] 会 [MASK] ， [MASK] [MASK]\n2 [MASK] 会 [MASK] ， [MASK] 喵\n3 猫 会 喵 ， 猫 喵\n\n AR rounds= 6 valid= True\n0 [MASK] [MASK] [MASK] [MASK] [MASK] [MASK]\n1 猫 [MASK] [MASK] [MASK] [MASK] [MASK]\n2 猫 会 [MASK] [MASK] [MASK] [MASK]\n3 猫 会 喵 [MASK] [MASK] [MASK]\n4 猫 会 喵 ， [MASK] [MASK]\n5 猫 会 喵 ， 猫 [MASK]\n6 猫 会 喵 ， 猫 喵\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "id": "81288fe429614fb2a07f1a542b2f748a",
   "metadata": {
    "deepnote_block_id": "81288fe429614fb2a07f1a542b2f748a",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "8a8a838f67873c5ed3b4edac5228d6f6d0674bee3cd87c011f894f78db0b1a79"
   },
   "source": "### 历史本地保存输出（2026-09-26；本轮执行记录见开篇）\n\n```text\n\n parallel once rounds= 1 valid= True\n0 猫 会 喵 ， 猫 喵\n\n iterative rounds= 3 valid= True\n0 [MASK] [MASK] [MASK] [MASK] [MASK] [MASK]\n1 [MASK] 会 [MASK] ， [MASK] [MASK]\n2 [MASK] 会 [MASK] ， [MASK] 喵\n3 猫 会 喵 ， 猫 喵\n\n AR rounds= 6 valid= True\n0 [MASK] [MASK] [MASK] [MASK] [MASK] [MASK]\n1 猫 [MASK] [MASK] [MASK] [MASK] [MASK]\n2 猫 会 [MASK] [MASK] [MASK] [MASK]\n3 猫 会 喵 [MASK] [MASK] [MASK]\n4 猫 会 喵 ， [MASK] [MASK]\n5 猫 会 喵 ， 猫 [MASK]\n6 猫 会 喵 ， 猫 喵\n```\n\n## 重复采样：合法率与轮次是两个量\n\n下一格使用各自独立、固定的随机流生成 4,000 个样本。首先检查合法率及两种合法句子的质量分配，再报告调度轮次。\n\n“3 轮”和“6 轮”仅是这个 Python 程序的依赖轮次，不是 GPU 测速。真实比较还涉及一次前向计算的长度、缓存、批量、网络结构、硬件和样本质量；本册没有测出扩散语言模型比自回归更快。",
   "cell_type": "markdown"
  },
  {
   "id": "cbf7e82803664f44aad4f17bf4b40590",
   "metadata": {
    "deepnote_block_id": "cbf7e82803664f44aad4f17bf4b40590",
    "deepnote_block_type": "code",
    "cloud_source_sha256": "cdee48dd814186c4b14c8fcc0e7012b2df6a63349f72b639ec8c17185be039cb",
    "execution_provenance": {
     "provider": "Deepnote",
     "run_id": "31d43ed5-a356-481c-9e72-9a48e0a078ab",
     "completed_at": "2026-09-28T15:30:48.794Z"
    }
   },
   "source": "SAMPLE_COUNT = 4000\nprint(\"sampler | valid rate | cat mass | dog mass | mean rounds\")\nfor index, (name, sampler) in enumerate([\n    (\"parallel once\", parallel_once), (\"iterative\", iterative), (\"AR\", autoregressive)\n]):\n    rng = random.Random(20260926 + index)\n    counts = Counter()\n    round_sum = 0\n    for _ in range(SAMPLE_COUNT):\n        output, rounds, _ = sampler(rng)\n        counts[output] += 1\n        round_sum += rounds\n    valid = sum(counts[s] for s in SENTENCES) / SAMPLE_COUNT\n    cat_mass, dog_mass = [counts[s]/SAMPLE_COUNT for s in SENTENCES]\n    print(name, f\"{valid:.4f}\", f\"{cat_mass:.4f}\", f\"{dog_mass:.4f}\", f\"{round_sum/SAMPLE_COUNT:.2f}\")\n    if name == \"parallel once\":\n        assert abs(valid - valid_mass) < 0.025\n    else:\n        assert valid == 1.0 and abs(cat_mass - 0.5) < 0.04\n\nprompt = [\"狗\", None, None, None, None, None]\noutput, rounds, trace = iterative(random.Random(8), initial=prompt)\nassert output[0] == \"狗\" and output in SENTENCES\nprint(\"\\nFixed condition:\", show(prompt), \"->\", show(output), \"rounds=\", rounds)\ncontradictory = [\"猫\", None, \"汪\", None, None, None]\ntry:\n    conditionals(contradictory)\nexcept ValueError as error:\n    print(\"Contradiction detected:\", str(error))\nelse:\n    raise AssertionError(\"Contradictory context must not be silently repaired.\")\n",
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "name": "stdout",
     "text": "sampler | valid rate | cat mass | dog mass | mean rounds\nparallel once 0.1235 0.0625 0.0610 1.00\niterative 1.0000 0.4925 0.5075 3.00\nAR 1.0000 0.4943 0.5058 6.00\n\nFixed condition: 狗 [MASK] [MASK] [MASK] [MASK] [MASK] -> 狗 会 汪 ， 狗 汪 rounds= 1\nContradiction detected: Visible tokens contradict every sentence in this fixed model.\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "id": "8a799a89f284413ab10f5c20f831db28",
   "metadata": {
    "deepnote_block_id": "8a799a89f284413ab10f5c20f831db28",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "83addb9604726dfb18d1fd9899116bd50d684e1d64c8f6d658ddddc3b94883e1"
   },
   "source": "### 历史本地保存输出（2026-09-26；本轮执行记录见开篇）\n\n```text\nsampler | valid rate | cat mass | dog mass | mean rounds\nparallel once 0.1235 0.0625 0.0610 1.00\niterative 1.0000 0.4925 0.5075 3.00\nAR 1.0000 0.4943 0.5058 6.00\n\nFixed condition: 狗 [MASK] [MASK] [MASK] [MASK] [MASK] -> 狗 会 汪 ， 狗 汪 rounds= 1\nContradiction detected: Visible tokens contradict every sentence in this fixed model.\n```\n\n## 只改一个条件：提交门槛\n\n把 `iterative` 的 `threshold` 从 0.99 改成 0.5。先预测：哪些位置会在同一轮一起提交？它会不会退化成一次并行独立采样？再固定种子重复试验，报告合法率和轮次。\n\n另一个独立问题是给定“狗”作为条件；上格显示在本模型中条件足以决定所有剩余内容，不能把这种很容易的补全与完全无条件生成混在一起排名。若给定相互矛盾的可见 token，程序直接报错，不静默改写用户条件。",
   "cell_type": "markdown"
  },
  {
   "id": "59a5819aa0f941c491c80eabc11495a4",
   "metadata": {
    "deepnote_block_id": "59a5819aa0f941c491c80eabc11495a4",
    "deepnote_block_type": "code",
    "cloud_source_sha256": "b0482b70ae0c23543a89b109654b8543e1721c7976b78b97f9efb3edee8bebf8",
    "execution_provenance": {
     "provider": "Deepnote",
     "run_id": "31d43ed5-a356-481c-9e72-9a48e0a078ab",
     "completed_at": "2026-09-28T15:30:48.794Z"
    }
   },
   "source": "rng_threshold = random.Random(20260930)\ncounts_threshold = Counter()\nfor _ in range(SAMPLE_COUNT):\n    output, rounds, _ = iterative(rng_threshold, threshold=0.5)\n    counts_threshold[output] += 1\n    assert rounds == 1\nvalidity_low_threshold = sum(counts_threshold[s] for s in SENTENCES)/SAMPLE_COUNT\nprint(\"threshold=0.5: observed valid rate =\", round(validity_low_threshold, 4))\nprint(\"exact one-shot independent valid rate =\", valid_mass)\nassert abs(validity_low_threshold-valid_mass) < 0.025\nprint(\"All exact support, seeded sampling, condition and scheduler checks passed.\")\n",
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "name": "stdout",
     "text": "threshold=0.5: observed valid rate = 0.1185\nexact one-shot independent valid rate = 0.125\nAll exact support, seeded sampling, condition and scheduler checks passed.\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "id": "1e1726c5355b48f1a78003367dfffda7",
   "metadata": {
    "deepnote_block_id": "1e1726c5355b48f1a78003367dfffda7",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "95140868c7a49c5351c2c953b64d304fa19caa21dda06e46215aa88fb8587568"
   },
   "source": "### 历史本地保存输出（2026-09-26；本轮执行记录见开篇）\n\n```text\nthreshold=0.5: observed valid rate = 0.1185\nexact one-shot independent valid rate = 0.125\nAll exact support, seeded sampling, condition and scheduler checks passed.\n```\n\n## 与扩散语言模型的联系和距离\n\n[LLaDA 原论文](https://arxiv.org/abs/2502.09992)以 token 遮挡和恢复组织语言建模，使用网络学习遮挡位置的预测。本册只借用“破坏—条件预测—逐步揭示”的解释结构。\n\n我们没有训练损失优化、时间条件网络、大词表、重遮挡或论文采样器；轮次与合法率只是手工有限世界的计算结果。当前例子能说明**并行候选之间仍需相容性**，不能支持关于大语言模型能力或速度的结论。",
   "cell_type": "markdown"
  },
  {
   "id": "41e5ce4504cf44979084d022f67c1e7d",
   "metadata": {
    "deepnote_block_id": "41e5ce4504cf44979084d022f67c1e7d",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "d7970f0ef7f0f8102b2ab701d3c1063b3c163c3f9bc2694d9f862a767cc3e55b"
   },
   "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- [保持条件、计算损失，再评价迭代成本](https://deepnote.com/project/6f83a923-d155-47be-be58-680db701ff7f/notebook/3585d77fe4f740a0a28f9e9f6dc620fd?utm_source=openai&utm_medium=mcp&utm_campaign=openaimcp&utm_content=3585d77fe4f740a0a28f9e9f6dc620fd&utm_term=get_notebook#63632dc9eb894b869ba3c02353b7ec67)\n- [训练信号：只对被遮住的位置算损失](https://deepnote.com/project/6f83a923-d155-47be-be58-680db701ff7f/notebook/3585d77fe4f740a0a28f9e9f6dc620fd?utm_source=openai&utm_medium=mcp&utm_campaign=openaimcp&utm_content=3585d77fe4f740a0a28f9e9f6dc620fd&utm_term=get_notebook#d6aca8e1855f4ee2be04caaac7c698a6)\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": "63632dc9eb894b869ba3c02353b7ec67",
   "metadata": {
    "deepnote_block_id": "63632dc9eb894b869ba3c02353b7ec67",
    "deepnote_block_type": "markdown",
    "cloud_source_sha256": "bdc254a1b80e371e53f62b98bead26164e5176b743f7dd7fe7f65d486c7241ec"
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   "source": "### 保持条件、计算损失，再评价迭代成本\n\n离散状态先定义破坏规则：对 a、b、[MASK] 的单步转移，可令 a/b 各以0.8保留、0.2变为[MASK]，遮罩保持自身。连续 n 步保留率为0.8^n；token 编号的数值大小没有参与。\n\n训练问题应固定可见提示，只遮住回答；监督原句用于评分，不作为未知位置的输入。在线性遮罩概率 t 的一种目标中，只对 mask 位置累加 −(1/t)log pθ(x_i|x_t)。这里说明 LLaDA 的目标结构；本册 oracle 代码没有优化该损失，也没有训练时间条件网络。\n\n前面的代码已经精确展示一次并行独立抽样合法率1/8，而本例迭代规则在更新条件后恢复相容性。它只支持这个有限分布的结论。比较3轮与6轮时，还缺每轮网络工作、序列长度、缓存、批量、设备与同等质量的延迟测量；轮次减少不能直接报速度胜负。\n\n\n### 编辑评价：保持、改变与多样性分开检查\n\n原图差异小，是否就代表编辑做得好？\n\n一个什么也不改的系统，在像素差异指标上可能表现很好，却没有完成编辑。一个大幅重画的系统可能满足新描述，却破坏了应保留的背景。编辑评价因此至少要拆开目标完成、非目标保持与整体协调；对存在多解的任务，还要观察合理输出的覆盖。Palette 使用多种自动评价与人工评价研究图像到图像结果，提示我们不同指标关注不同性质。课堂讨论可以设计一个“完全复制原图”的简单基线，检查评价方案是否会错误奖励它。\n\n**追问：**评价项越来越多，会不会只是让我们更容易挑好看的结果？\n\n有这个风险，所以应在看结果前说明每项服务哪个主张，并保留固定样本和失败例。多个指标不是任意挑选的菜单，而是检查不同要求的工具。比如目标颜色改变和背景保持应分别报告，不能因为一项好就隐藏另一项差。一个复制原图的基线还能帮助检验指标是否真的辨认了任务完成程度。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N41.html?view=notes)\n\n相关阅读：[Palette: Image-to-Image Diffusion Models](https://arxiv.org/pdf/2111.05826v2)\n\n### 动手：只改变条件注入的位置\n\n是先验、起点还是遮罩造成了变化？\n\n设计一个小型修补观察：固定同一幅图、遮罩、模型与采样预算，对照已知区域是否在每步参与更新。记录已知区域误差、缺口边界和若干随机种子的输出，再讨论条件信息进入过程的位置为何重要。若计算资源不足，可先用低维离散网格和预存轨迹练习读图；必须标明这是机制演示，不是 RePaint 的性能复现。扩展时再加入不同遮罩大小和局部回跳，避免同时更换模型、预算与遮罩而无法解释差异。\n\n**追问：**如果这次两组看起来差不多，实验是不是没有意义？\n\n仍然有意义。它说明在当前图片、遮罩和预算下，差异可能不明显；也可能观察方式太粗。先检查操作是否真的改变、数据是否保存，再看多个固定种子和更敏感的边界指标。不能因为一次不符合预期就更换所有设置。把结论限制在已比较的范围，反而能为下一次选取更有区分力的条件提供依据。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N41.html?view=notes)\n\n相关阅读：[RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://arxiv.org/pdf/2201.09865v4)\n\n### 视频评价：流畅、遵循条件与物理一致分开问\n\n一段令人信服的视频能支持多大的结论？\n\n视频扩散论文使用分布指标和具体任务评价研究样本质量，但一个总体分数不能替代所有行为检查。课堂可以将观察分为单帧质量、跨帧身份与运动、文字条件符合，以及需要外部知识的因果或物理约束。每一项都对应不同失败：画面清晰但对象增减、运动流畅但动作错误，或表面连续却违反几何关系。本页提出教学性的检查方法，不宣称这些指标已经充分定义理解。若要提出世界建模能力的主张，需要进一步设计有区分力的任务与反例。\n\n**追问：**视频看起来符合物理规律，为什么不能说它理解了物理？\n\n可以说它在这个例子中产生了符合某些规律的表现，但更强结论需要跨场景、干预和反例检验。外观相似可能来自训练分布中的相关性，也可能包含可迁移结构；单个视频不足以区分。先明确你说的物理理解要支持什么预测或行动，再设置能够区分两种解释的测试，才知道已有证据支持到哪里。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N42.html?view=notes)\n\n相关阅读：[Video Diffusion Models](https://arxiv.org/pdf/2204.03458v2)\n\n### D3PM：用转移矩阵写出破坏规则\n\n每一步，一个类别可能转到哪里？\n\n设状态只有 a、b 和 [MASK]。一个简单教学转移让 a、b 各以 0.8 概率保持原值、以 0.2 概率进入遮罩，而遮罩以概率 1 保持遮罩；每行概率和均为 1。连续应用这些矩阵会逐渐减少可见信息。D3PM 的一般框架允许更丰富的离散转移，本例只取吸收状态这一种。理解矩阵时要先固定行列约定，再区分单步转移与累计转移：一次保留率为 0.8，不表示经过许多步仍保留 80%。\n\n**追问：**每一步只遮掉 20%，为什么最后可以几乎全被遮住？\n\n因为未被遮住的 token 下一步仍面临再次被遮住的机会，而已经进入遮罩的状态不会在前向过程返回。经过 n 步，原 token 的保留概率是 0.8 的 n 次方，会随步数下降。这里假设每步采用相同规则；实际模型可以改变日程。关键是累计破坏由多个条件转移组成，不能把单步比例直接当作最终比例。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N44.html?view=notes)\n\n相关阅读：[Structured Denoising Diffusion Models in Discrete State-Spaces](https://arxiv.org/pdf/2107.03006v3)",
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   "source": "### 训练信号：只对被遮住的位置算损失\n\n为什么不能奖励网络复制已经可见的词？\n\n训练时保留原序列 x₀，同时构造受损序列 xₜ。模型读取 xₜ，为被遮住的位置输出词表概率；交叉熵检查它给原 token 分配了多少概率。未遮住的位置是上下文，不应通过简单复制贡献主要训练奖励。LLaDA 的目标使用指示函数选择遮罩位置，再按时间进行加权。可以把一个五 token 句子的损失展开，逐项标记哪些参与梯度。这比只看“交叉熵”三个字更能说明训练问题，也能帮助学生发现实现中的答案泄漏或损失掩码错误。\n\n**追问：**模型训练时不是有原句吗，为什么说它不知道答案？\n\n原句用于提供监督标签，受损句子才是模型前向计算的输入。只要实现正确，原词不会通过输入或其他旁路泄漏给被遮住的位置。训练比较预测与标签，随后更新参数；这与考试结束后核对答案类似，不能把批改者持有答案误认为作答时已经看到。检查代码时应特别核对输入构造与损失掩码是否独立正确。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N44.html?view=notes)\n\n相关阅读：[Large Language Diffusion Models](https://arxiv.org/pdf/2502.09992v3)\n\n### 并行预测，不等于各位置真正独立\n\n两个空位都合理，放在一起为什么可能不合理？\n\n考虑一句含两个相互制约空位的句子，每个位置单独都有多个合理候选。如果同一轮在不完整上下文下独立采样，组合可能出现语法或语义不一致。遮罩扩散通过多轮恢复，让已确定部分进入后续条件；这有助于表达依赖，但不保证每次组合都正确。不能把“每轮同时计算多个位置”误讲成联合分布被精确地一次分解成独立项。教学中可以用主谓一致或数量对应的小语法展示矛盾，观察生成日程怎样改变信息流。\n\n**追问：**这不就说明并行生成一定不如自回归吗？\n\n不能这样推断。例子揭示一次独立采样可能忽略依赖，而迭代、条件预测和不同采样器正是在处理这个问题。自回归也会把早期错误传到后面，并有自己的顺序约束。比较应固定任务、模型与计算预算，观察错误类型和整体表现。这个机制分析帮助提出实验问题，并不能独自证明某个模型家族在所有场景中的优劣。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N45.html?view=notes)\n\n相关阅读：[Simple and Effective Masked Diffusion Language Models](https://arxiv.org/pdf/2406.07524v2)\n\n### 动手：用小语法观察生成顺序\n\n在可枚举的语言里，怎样检查联合关系？\n\n设计一个只有少量合法句子的玩具语法，让两个相隔位置必须满足配对关系。可以精确列出合法序列及其概率，再比较一次独立填空、逐位置生成和多轮遮罩恢复的输出分布。记录非法组合率、覆盖与调用次数，而不只展示一条流畅句子。这个实验不复现 LLaDA 的大规模能力，也不能代表真实语言难度；它把依赖关系与生成顺序隔离出来，帮助学生理解并行预测为何仍可能需要迭代。后续运行真实模型时，再保留同样的观察问题。\n\n**追问：**这么小的实验，能对大语言模型得出什么结论？\n\n它不能直接预测大模型排名，但能检验我们的机制解释是否自洽。例如，是否把边缘概率误当成联合概率，是否漏记多轮调用，是否把候选当成最终输出。这些问题在大系统中更难看清。小实验给出可核查的认识起点，真实模型还需要另行评测；两者的作用是相互补充，而不是用简单例子替代规模证据。\n\n[返回当前页说明](https://codingai-lec04.pages.dev/classroom/N45.html?view=notes)\n\n相关阅读：[Simple and Effective Masked Diffusion Language Models](https://arxiv.org/pdf/2406.07524v2)",
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